0 | | f of, g of x |
1 | | f of, g of x, equals f of x, plus g of x |
2 | | sine x y |
3 | | 2 lines, Line 1: a. Line 2: blank |
4 | | 2 lines, Line 1: a. Line 2: blank |
5 | | 2 lines, Line 1: a. Line 2: blank |
6 | | 2 lines, Line 1: a; equals; b |
7 | | 2 lines, Line 1: a; equals; b. Line 2: blank |
8 | | 2 lines, Line 1: a; equals; b. Line 2: blank |
9 | | 2 lines, Line 1: a; equals; b. Line 2: 1; blank; 2 |
10 | | 45 degrees, 10 minutes, 20 seconds |
11 | | 1 degree, 10 minutes, 20 seconds |
12 | | 45 degrees, 1 minute, 20 seconds |
13 | | 45 degrees, 10 minutes, 1 second |
14 | | 1 foot, 20 inches |
15 | | 10 feet, 1 inch |
16 | | enclosed with box 12 |
17 | | crossed out 12 |
18 | | 12 crossed out with 2 |
19 | | 12 crossed out with 2 |
20 | | 12 crossed out with 2 |
21 | | 12 crossed out with 2 |
22 | | vertical bar A |
23 | | A horizontal bar |
24 | | A vertical bar |
25 | | A over horizontal bar |
26 | | the square root of, the cube root of a, plus b |
27 | | the square root of, the fourth root of a, plus b |
28 | | the square root of, the square root of a, plus b |
29 | | left sub a left super b x right sub c right super d |
30 | | left sub a b left super g h x right sub c d right super e f |
31 | | left sub a left super b x; right super d |
32 | | left sub a left super b x right sub c; r |
33 | | l; left super b x right sub c right super d |
34 | | left sub a; x right sub c right super d |
35 | | the set of all x not in A such that B |
36 | | the set B |
37 | | the empty set |
38 | | the positive rational numbers |
39 | | the positive rational numbers |
40 | | the negative rational numbers |
41 | | the negative rational numbers |
42 | | q-two |
43 | | q-two |
44 | | n-two |
45 | | n-two |
46 | | a |
47 | | 10 over 20 |
48 | | 2 kilometers over b |
49 | | the repeating decimal 1 point 4 followed by repeating digit 3 |
50 | | 3 raised to the 2 squared power |
51 | | 3 raised to the i squared power |
52 | | 3 raised to the two thirds squared power |
53 | | 3 raised to the 2 cubed power |
54 | | 3 raised to the i cubed power |
55 | | 3 raised to the two thirds cubed power |
56 | | a is less than or equal to b equals c |
57 | | 3 raised to the sine of, open paren, 2 plus x, close paren, power |
58 | | sum under I |
59 | | A under B |
0 | | 3 squared |
1 | 33 | 3 cubed |
2 | 35 | 3 to the fifth power |
3 | 31 | 3 to the first power |
4 | b1 | b to the first power |
5 | 35.0 | 3 raised to the 5.0 power |
6 | 30 | 3 to the 0 power |
7 | 411 | 4 to the 11th power |
8 | 3−2 | 3 to the negative 2 power |
9 | 3−2.0 | 3 raised to the negative 2.0 power |
10 | 4x | 4 to the x-th power |
11 | 3y+2 | 3 raised to the y plus 2 power |
12 | (2y−3)3z+8 | open paren, 2 y, minus 3, close paren, raised to the 3 z, plus 8 power |
13 | p12 | p sub 1, squared |
14 | p13 | p sub 1, cubed |
15 | p14 | p sub 1, to the fourth power |
16 | p110 | p sub 1, to the tenth power |
17 | p1x+1 | p sub 1, raised to the x plus 1 power |
18 | px12 | p sub, x sub 1, squared |
19 | px13 | p sub, x sub 1, cubed |
20 | px14 | p sub, x sub 1, to the fourth power |
21 | px110 | p sub, x sub 1, to the tenth power |
22 | px1y+1 | p sub, x sub 1, raised to the y plus 1 power |
23 | 322 | 3 raised to the 2 squared power |
24 | 32x2 | 3 raised to the 2 x squared power |
25 | 523 | 5 raised to the 2 cubed power |
26 | 52x3 | 5 raised to the 2 x cubed power |
27 | 322+1 | 3 raised to the exponent, 2 squared plus 1, end exponent |
28 | 322+1 | 3 raised to the 2 squared power, plus 1 |
29 | 2x2+3x3 | 2 raised to the exponent, x squared plus 3 x cubed, end exponent |
30 | 334 | 3 raised to the exponent, 3 to the fourth power, end exponent |
31 | 334+2 | 3 raised to the exponent, 3 to the fourth power, plus 2, end exponent |
32 | 334+2 | 3 raised to the exponent, 3 to the fourth power, end exponent, plus 2 |
33 | 2x4 | 2 raised to the exponent, x to the fourth power, end exponent |
34 | 210x+3 | 2 raised to the exponent, 10 raised to the x plus 3 power, end exponent |
35 | 3310 | 3 raised to the exponent, 3 to the tenth power, end exponent |
36 | 3310+1 | 3 raised to the exponent, 3 to the tenth power, plus 1, end exponent |
37 | 3310+1 | 3 raised to the exponent, 3 to the tenth power, end exponent, plus 1 |
38 | 3(x+1)2 | 3 raised to the exponent, open paren, x plus 1, close paren, squared, end exponent |
39 | 3(x+1)10 | 3 raised to the exponent, open paren, x plus 1, close paren, to the tenth power, end exponent |
40 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, raised to the y plus 2 power, end exponent |
41 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, to the y-th power, plus 2, end exponent |
42 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, to the y-th power, end exponent, plus 2 |
43 | e−12(x−μσ)2 | e raised to the exponent, negative one half times, open paren, the fraction with numerator x minus mu, and denominator sigma, close paren, squared, end exponent |
44 | 2n | 2 to the n-th power |
45 | 2m | 2 to the m-th power |
46 | 2i | 2 to the i-th power |
47 | 2j | 2 to the j-th power |
48 | 2a | 2 to the a-th power |
0 | 32 | 3 to the second |
1 | 33 | 3 to the third |
2 | 30 | 3 to the zero |
3 | 31 | 3 to the first |
4 | 35 | 3 to the fifth |
5 | 43.0 | 4 raised to the 3.0 power |
6 | 411 | 4 to the eleventh |
7 | 3−2 | 3 to the negative 2 |
8 | 3−2.0 | 3 raised to the negative 2.0 power |
9 | 4x | 4 to the x-th |
10 | 3y+2 | 3 raised to the y plus 2 power |
11 | (2y−3)3z+8 | open paren, 2 y, minus 3, close paren, raised to the 3 z, plus 8 power |
12 | p12 | p sub 1, to the second |
13 | p13 | p sub 1, to the third |
14 | p14 | p sub 1, to the fourth |
15 | p110 | p sub 1, to the tenth |
16 | p1x+1 | p sub 1, raised to the x plus 1 power |
17 | px12 | p sub, x sub 1, to the second |
18 | px13 | p sub, x sub 1, to the third |
19 | px14 | p sub, x sub 1, to the fourth |
20 | px110 | p sub, x sub 1, to the tenth |
21 | px1y+1 | p sub, x sub 1, raised to the y plus 1 power |
22 | 322 | 3 raised to the exponent, 2 to the second, end exponent |
23 | 32x2 | 3 raised to the exponent, 2 x to the second, end exponent |
24 | 523 | 5 raised to the exponent, 2 to the third, end exponent |
25 | 52x3 | 5 raised to the exponent, 2 x to the third, end exponent |
26 | 322+1 | 3 raised to the exponent, 2 to the second, plus 1, end exponent |
27 | 322+1 | 3 raised to the exponent, 2 to the second, end exponent, plus 1 |
28 | 2x2+3x3 | 2 raised to the exponent, x to the second, plus 3 x to the third, end exponent |
29 | 334 | 3 raised to the exponent, 3 to the fourth, end exponent |
30 | 334+2 | 3 raised to the exponent, 3 to the fourth, plus 2, end exponent |
31 | 334+2 | 3 raised to the exponent, 3 to the fourth, end exponent, plus 2 |
32 | 2x4 | 2 raised to the exponent, x to the fourth, end exponent |
33 | 210x+3 | 2 raised to the exponent, 10 raised to the x plus 3 power, end exponent |
34 | 3310 | 3 raised to the exponent, 3 to the tenth, end exponent |
35 | 3310+1 | 3 raised to the exponent, 3 to the tenth, plus 1, end exponent |
36 | 3310+1 | 3 raised to the exponent, 3 to the tenth, end exponent, plus 1 |
37 | 3(x+1)2 | 3 raised to the exponent, open paren, x plus 1, close paren, to the second, end exponent |
38 | 3(x+1)10 | 3 raised to the exponent, open paren, x plus 1, close paren, to the tenth, end exponent |
39 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, raised to the y plus 2 power, end exponent |
40 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, to the y-th, plus 2, end exponent |
41 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, to the y-th, end exponent, plus 2 |
42 | e−12x2 | e raised to the exponent, negative one half x to the second, end exponent |
43 | e−12(x−μσ)2 | e raised to the exponent, negative one half times, open paren, the fraction with numerator x minus mu, and denominator sigma, close paren, to the second, end exponent |
0 | 32 | 3 to the second power |
1 | 33 | 3 to the third power |
2 | 30 | 3 to the zero power |
3 | 31 | 3 to the first power |
4 | 35 | 3 to the fifth power |
5 | 35.0 | 3 raised to the 5.0 power |
6 | 411 | 4 to the eleventh power |
7 | 3−2 | 3 to the negative 2 power |
8 | 3−2.0 | 3 raised to the negative 2.0 power |
9 | 4x | 4 to the x-th power |
10 | 3y+2 | 3 raised to the y plus 2 power |
11 | (2y−3)3z+8 | open paren, 2 y, minus 3, close paren, raised to the 3 z, plus 8 power |
12 | p12 | p sub 1, to the second power |
13 | p13 | p sub 1, to the third power |
14 | p14 | p sub 1, to the fourth power |
15 | p110 | p sub 1, to the tenth power |
16 | p1x+1 | p sub 1, raised to the x plus 1 power |
17 | px12 | p sub, x sub 1, to the second power |
18 | px13 | p sub, x sub 1, to the third power |
19 | px14 | p sub, x sub 1, to the fourth power |
20 | px110 | p sub, x sub 1, to the tenth power |
21 | px1y+1 | p sub, x sub 1, raised to the y plus 1 power |
22 | 322 | 3 raised to the exponent, 2 to the second power, end exponent |
23 | 32x2 | 3 raised to the exponent, 2 x to the second power, end exponent |
24 | 523 | 5 raised to the exponent, 2 to the third power, end exponent |
25 | 52x3 | 5 raised to the exponent, 2 x to the third power, end exponent |
26 | 322+1 | 3 raised to the exponent, 2 to the second power, plus 1, end exponent |
27 | 322+1 | 3 raised to the exponent, 2 to the second power, end exponent, plus 1 |
28 | 2x2+3x3 | 2 raised to the exponent, x to the second power, plus 3 x to the third power, end exponent |
29 | 334 | 3 raised to the exponent, 3 to the fourth power, end exponent |
30 | 334+2 | 3 raised to the exponent, 3 to the fourth power, plus 2, end exponent |
31 | 334+2 | 3 raised to the exponent, 3 to the fourth power, end exponent, plus 2 |
32 | 2x4 | 2 raised to the exponent, x to the fourth power, end exponent |
33 | 210x+3 | 2 raised to the exponent, 10 raised to the x plus 3 power, end exponent |
34 | 3310 | 3 raised to the exponent, 3 to the tenth power, end exponent |
35 | 3310+1 | 3 raised to the exponent, 3 to the tenth power, plus 1, end exponent |
36 | 3310+1 | 3 raised to the exponent, 3 to the tenth power, end exponent, plus 1 |
37 | 3(x+1)2 | 3 raised to the exponent, open paren, x plus 1, close paren, to the second power, end exponent |
38 | 3(x+1)10 | 3 raised to the exponent, open paren, x plus 1, close paren, to the tenth power, end exponent |
39 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, raised to the y plus 2 power, end exponent |
40 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, to the y-th power, plus 2, end exponent |
41 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, to the y-th power, end exponent, plus 2 |
42 | e−12x2 | e raised to the exponent, negative one half x to the second power, end exponent |
43 | e−12(x−μσ)2 | e raised to the exponent, negative one half times, open paren, the fraction with numerator x minus mu, and denominator sigma, close paren, to the second power, end exponent |
0 | 32 | 3 raised to the power 2 |
1 | 33 | 3 raised to the power 3 |
2 | 31 | 3 raised to the power 1 |
3 | 30 | 3 raised to the power 0 |
4 | 35 | 3 raised to the power 5 |
5 | 35.0 | 3 raised to the power 5.0 |
6 | 411 | 4 raised to the power 11 |
7 | 3−2 | 3 raised to the power negative 2 |
8 | 3−2.0 | 3 raised to the power negative 2.0 |
9 | 4x | 4 raised to the power x |
10 | 3y+2 | 3 raised to the power y plus 2 |
11 | (2y−3)3z+8 | open paren, 2 y, minus 3, close paren, raised to the power 3 z plus 8 |
12 | p12 | p sub 1, raised to the power 2 |
13 | p13 | p sub 1, raised to the power 3 |
14 | p14 | p sub 1, raised to the power 4 |
15 | p110 | p sub 1, raised to the power 10 |
16 | p1x+1 | p sub 1, raised to the power x plus 1 |
17 | px12 | p sub, x sub 1, raised to the power 2 |
18 | px13 | p sub, x sub 1, raised to the power 3 |
19 | px14 | p sub, x sub 1, raised to the power 4 |
20 | px110 | p sub, x sub 1, raised to the power 10 |
21 | px1y+1 | p sub, x sub 1, raised to the power y plus 1 |
22 | 322 | 3 raised to the exponent, 2 raised to the power 2, end exponent |
23 | 32x2 | 3 raised to the exponent, 2 x raised to the power 2, end exponent |
24 | 322 | 3 raised to the exponent, 2 raised to the power 2, end exponent |
25 | 32x2 | 3 raised to the exponent, 2 x raised to the power 2, end exponent |
26 | 523 | 5 raised to the exponent, 2 raised to the power 3, end exponent |
27 | 52x3 | 5 raised to the exponent, 2 x raised to the power 3, end exponent |
28 | 322+1 | 3 raised to the exponent, 2 raised to the power 2, plus 1, end exponent |
29 | 322+1 | 3 raised to the exponent, 2 raised to the power 2, end exponent, plus 1 |
30 | 2x2+3x3 | 2 raised to the exponent, x raised to the power 2, plus 3 x raised to the power 3, end exponent |
31 | 334 | 3 raised to the exponent, 3 raised to the power 4, end exponent |
32 | 334+2 | 3 raised to the exponent, 3 raised to the power 4, plus 2, end exponent |
33 | 334+2 | 3 raised to the exponent, 3 raised to the power 4, end exponent, plus 2 |
34 | 2x4 | 2 raised to the exponent, x raised to the power 4, end exponent |
35 | 210x+3 | 2 raised to the exponent, 10 raised to the power x plus 3, end exponent |
36 | 3310 | 3 raised to the exponent, 3 raised to the power 10, end exponent |
37 | 3310+1 | 3 raised to the exponent, 3 raised to the power 10, plus 1, end exponent |
38 | 3310+1 | 3 raised to the exponent, 3 raised to the power 10, end exponent, plus 1 |
39 | 3(x+1)2 | 3 raised to the exponent, open paren, x plus 1, close paren, raised to the power 2, end exponent |
40 | 3(x+1)10 | 3 raised to the exponent, open paren, x plus 1, close paren, raised to the power 10, end exponent |
41 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, raised to the power y plus 2, end exponent |
42 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, raised to the power y, plus 2, end exponent |
43 | 3(x+1)y+2 | 3 raised to the exponent, open paren, x plus 1, close paren, raised to the power y, end exponent, plus 2 |
44 | e−12x2 | e raised to the exponent, negative one half x raised to the power 2, end exponent |
45 | e−12(x−μσ)2 | e raised to the exponent, negative one half times, open paren, the fraction with numerator x minus mu, and denominator sigma, close paren, raised to the power 2, end exponent |
0 | 12 | one half |
1 | 1232 | 12 over 32 |
2 | xy | x over y |
3 | 2x3y | 2 x over 3 y |
4 | xycd | x y over c d |
5 | 1213 | one half over one third |
6 | −xy | negative x over y |
7 | −2x3y | negative 2 x over 3 y |
8 | xy−cd | x y over negative c d |
9 | 12−13 | one half over negative one third |
10 | 2+313 | the fraction with numerator 2 plus 3, and denominator 13 |
11 | x+y2 | the fraction with numerator x plus y, and denominator 2 |
12 | x+yx−y | the fraction with numerator x plus y, and denominator x minus y |
13 | x+yx−y+23 | the fraction with numerator x plus y, and denominator x minus y, plus two thirds |
14 | milesgallon | miles over gallon |
15 | 2miles3gallons | 2 miles over 3 gallons |
16 | 2miles3gallons | 2 miles over 3 gallons |
17 | riserun | rise over run |
18 | successful outcomestotal outcomes | successful outcomes over total outcomes |
19 | 6ways of rolling a 736ways of rolling the pair of dice | 6 ways of rolling a 7 over 36 ways of rolling the pair of dice |
20 | 1213 | one half over one third |
21 | 1213 | the fraction with numerator 1, and denominator, 2 over one third |
22 | 123 | one half over 3 |
23 | 123 | 1 over two thirds |
24 | 11321651 | the fraction with numerator, 11 over 32, and denominator, 16 over 51 |
25 | 11321651 | the fraction with numerator 11, and denominator, the fraction with numerator 32, and denominator, 16 over 51 |
26 | 1+4x2 | the fraction with numerator 1 plus, 4 over x, and denominator 2 |
27 | 32+4x | the fraction with numerator 3, and denominator 2 plus, 4 over x |
28 | 102212 | the fraction with numerator, 10 over 22, and denominator one half |
29 | 1+231−23 | the fraction with numerator 1 plus two thirds, and denominator 1 minus two thirds |
30 | 1+x21−x2 | the fraction with numerator 1 plus, x over 2, and denominator 1 minus, x over 2 |
31 | x+1x−1+1x+1 | the fraction with numerator, the fraction with numerator x plus 1, and denominator x minus 1, plus 1, and denominator x plus 1 |
32 | x+1x−4+12x+116 | the fraction with numerator, the fraction with numerator x plus 1, and denominator x minus 4, plus one half, and denominator x plus, 1 over 16 |
33 | 1+x1+2x | 1 plus, the fraction with numerator x, and denominator 1 plus, 2 over x |
34 | 1+x+31+2x+3 | 1 plus, the fraction with numerator x plus 3, and denominator 1 plus, the fraction with numerator 2, and denominator x plus 3 |
35 | 1+11+11+11+1 | 1 plus, the fraction with numerator 1, and denominator 1 plus, the fraction with numerator 1, and denominator 1 plus, the fraction with numerator 1, and denominator 1 plus 1 |
36 | 1+11+11+11+⋯ | 1 plus, the fraction with numerator 1, and denominator 1 plus, the fraction with numerator 1, and denominator 1 plus, the fraction with numerator 1, and denominator 1 plus dot dot dot |
37 | a0+1a1+1a2+1a3+⋯ | a sub 0, plus, the fraction with numerator 1, and denominator, a sub 1, plus, the fraction with numerator 1, and denominator, a sub 2, plus, the fraction with numerator 1, and denominator, a sub 3, plus dot dot dot |
38 | f(x)g(x) | f of x, over g of x |
39 | f(x)+g(x)g(x) | the fraction with numerator f of x, plus g of x, and denominator g of x |
40 | f(x+1)g(x) | the fraction with numerator f of, open paren, x plus 1, close paren, and denominator g of x |
41 | f(x)2 | f of x, over 2 |
42 | 2f(x) | 2 over f of x |
43 | 2g(x)+g(x+1) | the fraction with numerator 2, and denominator g of x, plus g of, open paren, x plus 1, close paren |
44 | sinxcosx | sine x over cosine x |
45 | sinx+cosxcosx | the fraction with numerator sine x plus cosine x, and denominator cosine x |
46 | sin2xcos3x | sine 2 x over cosine 3 x |
47 | sin(x+y)cos(x+y) | the fraction with numerator, the sine of, open paren, x plus y, close paren, and denominator, the cosine of, open paren, x plus y, close paren |
48 | f(2x)g(3x) | f of 2 x, over g of 3 x |
49 | logxlogy | log x over log y |
50 | log2xlog3y | log 2 x over log 3 y |
51 | log10xlog5y | the log base 10 of, x, over, the log base 5 of, y |
52 | log102xlog53y | the log base 10 of, 2 x, over, the log base 5 of, 3 y |
53 | log(x+1)logy | the fraction with numerator, the log of, open paren, x plus 1, close paren, and denominator log y |
54 | f1(x)g1(x) | f sub 1, of x, over, g sub 1, of x |
0 | 12 | one half |
1 | 1232 | 12 over 32, end fraction |
2 | 2+313 | the fraction with numerator 2 plus 3, and denominator 13, end fraction |
3 | x+y2 | the fraction with numerator x plus y, and denominator 2, end fraction |
4 | x+yx−y | the fraction with numerator x plus y, and denominator x minus y, end fraction |
5 | x+yx−y+23 | the fraction with numerator x plus y, and denominator x minus y, end fraction, plus two thirds |
6 | milesgallons | miles over gallons |
7 | 2miles3gallons | 2 miles over 3 gallons |
8 | 1213 | one half over one third |
9 | 1213 | the fraction with numerator 1, and denominator, 2 over one third, end fraction |
10 | 123 | one half over 3, end fraction |
11 | 123 | 1 over two thirds, end fraction |
12 | 11321651 | the fraction with numerator, 11 over 32, and denominator, 16 over 51, end fraction |
13 | 11321651 | the fraction with numerator 11, and denominator, the fraction with numerator 32, and denominator, 16 over 51, end fraction |
14 | 1+4x2 | the fraction with numerator 1 plus, 4 over x, and denominator 2, end fraction |
15 | 32+4x | the fraction with numerator 3, and denominator 2 plus, 4 over x, end fraction |
16 | 102212 | the fraction with numerator, 10 over 22, and denominator one half, end fraction |
17 | 1+231−23 | the fraction with numerator 1 plus two thirds, and denominator 1 minus two thirds, end fraction |
18 | 1+x21−x2 | the fraction with numerator 1 plus, x over 2, and denominator 1 minus, x over 2, end fraction |
19 | x+1x−1+1x+1 | the fraction with numerator, the fraction with numerator x plus 1, and denominator x minus 1, plus 1, and denominator x plus 1, end fraction |
20 | x+1x−4+12x+116 | the fraction with numerator, the fraction with numerator x plus 1, and denominator x minus 4, plus one half, and denominator x plus, 1 over 16, end fraction |
21 | 1+x1+2x | 1 plus, the fraction with numerator x, and denominator 1 plus, 2 over x, end fraction |
22 | 1+x+31+2x+3 | 1 plus, the fraction with numerator x plus 3, and denominator 1 plus, the fraction with numerator 2, and denominator x plus 3, end fraction |
23 | 1+11+11+11+1 | 1 plus, the fraction with numerator 1, and denominator 1 plus, the fraction with numerator 1, and denominator 1 plus, the fraction with numerator 1, and denominator 1 plus 1, end fraction |
24 | 1+11+11+11+⋯ | 1 plus, the fraction with numerator 1, and denominator 1 plus, the fraction with numerator 1, and denominator 1 plus, the fraction with numerator 1, and denominator 1 plus dot dot dot, end fraction |
25 | a0+1a1+1a2+1a3+⋯ | a sub 0, plus, the fraction with numerator 1, and denominator, a sub 1, plus, the fraction with numerator 1, and denominator, a sub 2, plus, the fraction with numerator 1, and denominator, a sub 3, plus dot dot dot, end fraction |
0 | f(x) | f of x |
1 | g(x) | g of x |
2 | h(x) | h of x |
3 | f(2x) | f of 2 x |
4 | g(−2x) | g of negative 2 x |
5 | h(12) | h of one half |
6 | f(x+1)=f(x)+1 | f of, open paren, x plus 1, close paren, equals f of x, plus 1 |
7 | g(2x+1) | g of, open paren, 2 x, plus 1, close paren |
8 | g(x2) | g of, open paren, x squared, close paren |
9 | f−1(x) | f inverse of x |
10 | g−1(x) | g inverse of x |
11 | h−1(x) | h inverse of x |
12 | f−1(2x) | f inverse of 2 x |
13 | g−1(−2x) | g inverse of negative 2 x |
14 | f−1(3x−1) | f inverse of, open paren, 3 x, minus 1, close paren |
15 | g−1(x2) | g inverse of, open paren, x squared, close paren |
16 | h−1(12) | h inverse of one half |
17 | f−1(f(x)) | f inverse of, f of x |
18 | g−1(g(x)) | g inverse of, g of x |
19 | h−1(h(x)) | h inverse of, h of x |
20 | f−1(f(2x)) | f inverse of, f of 2 x |
21 | g−1(g(−2x)) | g inverse of, g of negative 2 x |
22 | h−1(h(12)) | h inverse of, h of one half |
23 | f−1(f(x+1))=x+1 | f inverse of, open paren, f of, open paren, x plus 1, close paren, close paren, equals x plus 1 |
24 | g−1(g(2x+1)) | g inverse of, open paren, g of, open paren, 2 x, plus 1, close paren, close paren |
25 | g−1(g(x2)) | g inverse of, open paren, g of, open paren, x squared, close paren, close paren |
26 | f(f−1(x)) | f of, f inverse of x |
27 | g(g−1(x)) | g of, g inverse of x |
28 | h(h−1(x)) | h of, h inverse of x |
29 | f(f−1(2x)) | f of, f inverse of 2 x |
30 | g(g−1(−2x)) | g of, g inverse of negative 2 x |
31 | f(f−1(3x−1)) | f of, open paren, f inverse of, open paren, 3 x, minus 1, close paren, close paren |
32 | g(g−1(x2)) | g of, g inverse of, open paren, x squared, close paren |
33 | h(h−1(12)) | h of, h inverse of one half |
34 | f(g(x)) | f of, g of x |
35 | f(g(x+1)) | f of, open paren, g of, open paren, x plus 1, close paren, close paren |
36 | h(g(x)) | h of, g of x |
37 | h(g(xx+1)) | h of, open paren, g of, open paren, the fraction with numerator x, and denominator x plus 1, close paren, close paren |
38 | (f+g)(x)=f(x)+g(x) | open paren, f plus g, close paren, of x, equals f of x, plus g of x |
39 | (f+g)(x+1)=f(x+1)+g(x+1) | open paren, f plus g, close paren, of, open paren, x plus 1, close paren, equals f of, open paren, x plus 1, close paren, plus g of, open paren, x plus 1, close paren |
40 | (f⋅g)(x) | open paren, f times g, close paren, of x |
41 | (f⋅g)(2x+5) | open paren, f times g, close paren, of, open paren, 2 x, plus 5, close paren |
42 | (fg)(x)=f(x)g(x) | open paren, f over g, close paren, of x, equals, f of x, over g of x |
43 | (fg)(2x+5)=f(2x+5)g(2x+5) | open paren, f over g, close paren, of, open paren, 2 x, plus 5, close paren, equals, the fraction with numerator f of, open paren, 2 x, plus 5, close paren, and denominator g of, open paren, 2 x, plus 5, close paren |
44 | (f∘g)(x)=f(g(x)) | open paren, f composed with g, close paren, of x, equals f of, g of x |
45 | 2f(x) | 2 f of x |
46 | cf(x) | c f of x |
47 | f2(x) | f squared of x |
48 | f2(2x+1) | f squared of, open paren, 2 x, plus 1, close paren |
49 | f3(x) | f cubed of x |
50 | f3(2x+1) | f cubed of, open paren, 2 x, plus 1, close paren |
51 | f4(x) | the fourth power of, f of x |
52 | f4(2x+1) | the fourth power of, f of, open paren, 2 x, plus 1, close paren |
53 | f5(x) | the fifth power of, f of x |
54 | f5(2x+1) | the fifth power of, f of, open paren, 2 x, plus 1, close paren |
55 | fn(x) | the n-th power of, f of x |
56 | fn(2x+1) | the n-th power of, f of, open paren, 2 x, plus 1, close paren |
57 | g2(x) | g squared of x |
58 | g2(2x+1) | g squared of, open paren, 2 x, plus 1, close paren |
59 | h3(x) | h cubed of x |
60 | h3(2x+1) | h cubed of, open paren, 2 x, plus 1, close paren |
61 | g4(x) | the fourth power of, g of x |
62 | g4(2x+1) | the fourth power of, g of, open paren, 2 x, plus 1, close paren |
63 | h5(x) | the fifth power of, h of x |
64 | h5(2x+1) | the fifth power of, h of, open paren, 2 x, plus 1, close paren |
65 | gn(x) | the n-th power of, g of x |
66 | gn(2x+1) | the n-th power of, g of, open paren, 2 x, plus 1, close paren |
67 | f1(x) | f sub 1, of x |
68 | g2(x3) | g sub 2, of, open paren, x cubed, close paren |
69 | hn(3x−2) | h sub n, of, open paren, 3 x, minus 2, close paren |
70 | f1−1(x) | f sub 1, inverse of x |
71 | g2−1(2x+1) | g sub 2, inverse of, open paren, 2 x, plus 1, close paren |
72 | hn−1(x) | h sub n, inverse of x |
73 | g1−1(g2(x)) | g sub 1, inverse of, g sub 2, of x |
74 | f1(g2−1(x)) | f sub 1, of, g sub 2, inverse of x |
75 | f(x,y) | f of, open paren, x comma y, close paren |
76 | f(x,y,z) | f of, open paren, x comma y comma z, close paren |
77 | f(x+1,2y) | f of, open paren, x plus 1, comma, 2 y, close paren |
78 | f(2x,x+1,x2) | f of, open paren, 2 x, comma, x plus 1, comma, x squared, close paren |
0 | f(x) | f times x |
1 | g(x) | g times x |
2 | h(x) | h times x |
3 | f(2x) | f times 2 x |
4 | g(−2x) | g times negative 2 x |
5 | h(12) | h times one half |
6 | f(x+1)=f(x)+1 | f times, open paren, x plus 1, close paren, equals, f times x, plus 1 |
7 | g(2x+1) | g times, open paren, 2 x, plus 1, close paren |
8 | g(x2) | g times, open paren, x squared, close paren |
9 | f−1(x) | f to the negative 1 power, times x |
10 | g−1(x) | g to the negative 1 power, times x |
11 | h−1(x) | h to the negative 1 power, times x |
12 | f−1(2x) | f to the negative 1 power, times 2 x |
13 | g−1(−2x) | g to the negative 1 power, times negative 2 x |
14 | f−1(3x−1) | f to the negative 1 power, times, open paren, 3 x, minus 1, close paren |
15 | g−1(x2) | g to the negative 1 power, times, open paren, x squared, close paren |
16 | h−1(12) | h to the negative 1 power, times one half |
17 | f−1(f(x)) | f to the negative 1 power, times, f times x |
18 | g−1(g(x)) | g to the negative 1 power, times, g times x |
19 | h−1(h(x)) | h to the negative 1 power, times, h times x |
20 | f−1(f(2x)) | f to the negative 1 power, times, f times 2 x |
21 | g−1(g(−2x)) | g to the negative 1 power, times, g times negative 2 x |
22 | h−1(h(12)) | h to the negative 1 power, times, h times one half |
23 | f−1(f(x+1))=x+1 | f to the negative 1 power, times, open paren, f times, open paren, x plus 1, close paren, close paren, equals x plus 1 |
24 | g−1(g(2x+1)) | g to the negative 1 power, times, open paren, g times, open paren, 2 x, plus 1, close paren, close paren |
25 | g−1(g(x2)) | g to the negative 1 power, times, open paren, g times, open paren, x squared, close paren, close paren |
26 | f(f−1(x)) | f times, open paren, f to the negative 1 power, times x, close paren |
27 | g(g−1(x)) | g times, open paren, g to the negative 1 power, times x, close paren |
28 | h(h−1(x)) | h times, open paren, h to the negative 1 power, times x, close paren |
29 | f(f−1(2x)) | f times, open paren, f to the negative 1 power, times 2 x, close paren |
30 | g(g−1(−2x)) | g times, open paren, g to the negative 1 power, times negative 2 x, close paren |
31 | f(f−1(3x−1)) | f times, open paren, f to the negative 1 power, times, open paren, 3 x, minus 1, close paren, close paren |
32 | g(g−1(x2)) | g times, open paren, g to the negative 1 power, times, open paren, x squared, close paren, close paren |
33 | h(h−1(12)) | h times, open paren, h to the negative 1 power, times one half, close paren |
34 | f(g(x)) | f times, g times x |
35 | f(g(x+1)) | f times, open paren, g times, open paren, x plus 1, close paren, close paren |
36 | h(g(x)) | h times, g times x |
37 | h(g(xx+1)) | h times, open paren, g times, open paren, the fraction with numerator x, and denominator x plus 1, close paren, close paren |
38 | (f+g)(x)=f(x)+g(x) | open paren, f plus g, close paren, times x, equals, f times x, plus, g times x |
39 | (f+g)(x+1)=f(x+1)+g(x+1) | open paren, f plus g, close paren, times, open paren, x plus 1, close paren, equals, f times, open paren, x plus 1, close paren, plus, g times, open paren, x plus 1, close paren |
40 | (f⋅g)(x) | open paren, f times g, close paren, times x |
41 | (f⋅g)(2x+5) | open paren, f times g, close paren, times, open paren, 2 x, plus 5, close paren |
42 | (fg)(x)=f(x)g(x) | open paren, f over g, close paren, times x, equals, the fraction with numerator, f times x, and denominator, g times x |
43 | (fg)(2x+5)=f(2x+5)g(2x+5) | open paren, f over g, close paren, times, open paren, 2 x, plus 5, close paren, equals, the fraction with numerator, f times, open paren, 2 x, plus 5, close paren, and denominator, g times, open paren, 2 x, plus 5, close paren |
44 | 2f(x) | 2, f times x |
45 | cf(x) | c, f times x |
46 | f2(x) | f squared times x |
47 | f2(2x+1) | f squared times, open paren, 2 x, plus 1, close paren |
48 | f3(x) | f cubed times x |
49 | f3(2x+1) | f cubed times, open paren, 2 x, plus 1, close paren |
50 | f4(x) | f to the fourth power, times x |
51 | f4(2x+1) | f to the fourth power, times, open paren, 2 x, plus 1, close paren |
52 | f5(x) | f to the fifth power, times x |
53 | f5(2x+1) | f to the fifth power, times, open paren, 2 x, plus 1, close paren |
54 | fn(x) | f to the n-th power, times x |
55 | fn(2x+1) | f to the n-th power, times, open paren, 2 x, plus 1, close paren |
56 | g2(x) | g squared times x |
57 | g2(2x+1) | g squared times, open paren, 2 x, plus 1, close paren |
58 | h3(x) | h cubed times x |
59 | h3(2x+1) | h cubed times, open paren, 2 x, plus 1, close paren |
60 | g4(x) | g to the fourth power, times x |
61 | g4(2x+1) | g to the fourth power, times, open paren, 2 x, plus 1, close paren |
62 | h5(x) | h to the fifth power, times x |
63 | h5(2x+1) | h to the fifth power, times, open paren, 2 x, plus 1, close paren |
64 | gn(x) | g to the n-th power, times x |
65 | gn(2x+1) | g to the n-th power, times, open paren, 2 x, plus 1, close paren |
66 | f1(x) | f sub 1, times x |
67 | g2(x3) | g sub 2, times, open paren, x cubed, close paren |
68 | hn(3x−2) | h sub n, times, open paren, 3 x, minus 2, close paren |
69 | f1−1(x) | f sub 1, to the negative 1 power, times x |
70 | g2−1(2x+1) | g sub 2, to the negative 1 power, times, open paren, 2 x, plus 1, close paren |
71 | hn−1(x) | h sub n, to the negative 1 power, times x |
72 | g1−1(g2(x)) | g sub 1, to the negative 1 power, times, open paren, g sub 2, times x, close paren |
73 | f1(g2−1(x)) | f sub 1, times, open paren, g sub 2, to the negative 1 power, times x, close paren |
74 | f(x,y) | f times, open paren, x comma y, close paren |
75 | f(x,y,z) | f times, open paren, x comma y comma z, close paren |
76 | f(x+1,2y) | f times, open paren, x plus 1, comma, 2 y, close paren |
77 | f(2x,x+1,x2) | f times, open paren, 2 x, comma, x plus 1, comma, x squared, close paren |
0 | 2(3) | 2 times 3 |
1 | 2[3] | 2 times 3 |
2 | 24(3) | 2 to the fourth power, times 3 |
3 | 2(3+4) | 2 times, open paren, 3 plus 4, close paren |
4 | 2[3+4] | 2 times, open bracket, 3 plus 4, close bracket |
5 | (3)(2) | 3 times 2 |
6 | 2(3+4)2 | 2 times, open paren, 3 plus 4, close paren, squared |
7 | (2+7)(3−6) | open paren, 2 plus 7, close paren, times, open paren, 3 minus 6, close paren |
8 | [2+7][3−6] | open bracket, 2 plus 7, close bracket, times, open bracket, 3 minus 6, close bracket |
9 | x(y+z) | x times, open paren, y plus z, close paren |
10 | 2(y+1) | 2 times, open paren, y plus 1, close paren |
11 | (2−1)x | open paren, 2 minus 1, close paren, times x |
12 | p1(3+7) | p sub 1, times, open paren, 3 plus 7, close paren |
13 | p1a1p2a2 | p sub 1, raised to the, a sub 1, power, p sub 2, raised to the, a sub 2, power |
14 | (x+y)−4(x−y)−4 | open paren, x plus y, close paren, to the negative 4 power, times, open paren, x minus y, close paren, to the negative 4 power |
15 | 24(x+y) | 2 raised to the 4 times, open paren, x plus y, close paren, power |
16 | xy | x y |
17 | x2y3 | x squared, y cubed |
18 | xy+1xy+2 | x raised to the y plus 1 power, x raised to the y plus 2 power |
19 | ab=ab | the square root of a, the square root of b, equals the square root of a b |
20 | 310=30 | the square root of 3, the square root of 10, equals the square root of 30 |
21 | 23 | 2 the square root of 3 |
22 | 1+23 | 1 plus 2 the square root of 3 |
23 | f(x)=x2(x+1) | f of x, equals x squared times, open paren, x plus 1, close paren |
24 | sinxcosy+cosxsiny | sine x cosine y, plus, cosine x sine y |
25 | sin(x+y)cos(x+y) | the sine of, open paren, x plus y, close paren, the cosine of, open paren, x plus y, close paren |
26 | log10xy | the log base 10 of, x y |
27 | log(x+y)=logxlogy | the log of, open paren, x plus y, close paren, equals, log x log y |
28 | (1352)(7401) | the 2 by 2 matrix. Row 1: 1, 3 Row 2: 5, 2. times the 2 by 2 matrix. Row 1: 7, 4 Row 2: 0, 1 |
29 | 2(3((4+5)+6)) | 2 times, open paren, 3 times, open paren, open paren, 4 plus 5, close paren, plus 6, close paren, close paren |
30 | 2[3((4+5)+6)] | 2 times, open bracket, 3 times, open paren, open paren, 4 plus 5, close paren, plus 6, close paren, close bracket |
31 | 2|x| | 2 times, the absolute value of x |
32 | |x||y| | the absolute value of x, times, the absolute value of y |
33 | |x+1||y−1| | the absolute value of x plus 1, times, the absolute value of y minus 1 |
34 | |x+1||y|−1 | the absolute value of x plus 1, times, the absolute value of y, minus 1 |
35 | A=h(b1+b22) | A equals h of, open paren, the fraction with numerator, b sub 1, plus, b sub 2, and denominator 2, close paren |
36 | a(0)=0(a)=0 | a of 0, equals 0 times a equals 0 |
37 | a(−1)=−a | a of negative 1, equals negative a |
38 | B(2,6) | B of, open paren, 2 comma 6, close paren |
39 | p(w) | p of w |
40 | x(t)=2t+4 | x of t, equals 2 t, plus 4 |
41 | k(x)=(x+3)(x−5) | k of x, equals, open paren, x plus 3, close paren, times, open paren, x minus 5, close paren |
42 | T(t)=Ts+(T0−Ts)e−kt | T of t, equals, T sub s, plus, open paren, T sub 0, minus, T sub s, close paren, times e raised to the negative k t, power |
43 | V=lw(8) | V equals script l, w of 8 |
0 | 2(3) | 2 times 3 |
1 | 2[3] | 2 times 3 |
2 | 24(3) | 2 to the fourth power, times 3 |
3 | 2(3+4) | 2 times, open paren, 3 plus 4, close paren |
4 | 2[3+4] | 2 times, open bracket, 3 plus 4, close bracket |
5 | (3)(2) | 3 times 2 |
6 | 2(3+4)2 | 2 times, open paren, 3 plus 4, close paren, squared |
7 | (2+7)(3−6) | open paren, 2 plus 7, close paren, times, open paren, 3 minus 6, close paren |
8 | [2+7][3−6] | open bracket, 2 plus 7, close bracket, times, open bracket, 3 minus 6, close bracket |
9 | x(y+z) | x times, open paren, y plus z, close paren |
10 | 2(y+1) | 2 times, open paren, y plus 1, close paren |
11 | (2−1)x | open paren, 2 minus 1, close paren, times x |
12 | p1(3+7) | p sub 1, times, open paren, 3 plus 7, close paren |
13 | p1a1p2a2 | p sub 1, raised to the, a sub 1, power, times, p sub 2, raised to the, a sub 2, power |
14 | (x+y)−4(x−y)−4 | open paren, x plus y, close paren, to the negative 4 power, times, open paren, x minus y, close paren, to the negative 4 power |
15 | 24(x+y) | 2 raised to the 4 times, open paren, x plus y, close paren, power |
16 | xy | x times y |
17 | x2y3 | x squared times y cubed |
18 | xy+1xy+2 | x raised to the y plus 1 power, times x raised to the y plus 2 power |
19 | ab=ab | the square root of a, times the square root of b, equals the square root of a times b |
20 | 310=30 | the square root of 3, times the square root of 10, equals the square root of 30 |
21 | 23 | 2 times the square root of 3 |
22 | 1+23 | 1 plus 2 times the square root of 3 |
23 | f(x)=x2(x+1) | f of x, equals x squared times, open paren, x plus 1, close paren |
24 | sinxcosy+cosxsiny | sine x, times cosine y plus cosine x, times sine y |
25 | sin(x+y)cos(x+y) | the sine of, open paren, x plus y, close paren, times, the cosine of, open paren, x plus y, close paren |
26 | log10xy | the log base 10 of, x times y |
27 | log(x+y)=logxlogy | the log of, open paren, x plus y, close paren, equals log x, times log y |
28 | (1352)(7401) | the 2 by 2 matrix. Row 1: 1, 3 Row 2: 5, 2. times the 2 by 2 matrix. Row 1: 7, 4 Row 2: 0, 1 |
29 | 2(3((4+5)+6)) | 2 times, open paren, 3 times, open paren, open paren, 4 plus 5, close paren, plus 6, close paren, close paren |
30 | 2[3((4+5)+6)] | 2 times, open bracket, 3 times, open paren, open paren, 4 plus 5, close paren, plus 6, close paren, close bracket |
31 | 2|x| | 2 times, the absolute value of x |
32 | |x||y| | the absolute value of x, times, the absolute value of y |
33 | |x+1||y−1| | the absolute value of x plus 1, times, the absolute value of y minus 1 |
34 | |x+1||y|−1 | the absolute value of x plus 1, times, the absolute value of y, minus 1 |
0 | 2(3) | 2, open paren, 3, close paren |
1 | 2[3] | 2, open bracket, 3, close bracket |
2 | 24(3) | 2 to the fourth power, open paren, 3, close paren |
3 | 2(3+4) | 2, open paren, 3 plus 4, close paren |
4 | 2[3+4] | 2, open bracket, 3 plus 4, close bracket |
5 | (3)(2) | open paren, 3, close paren, open paren, 2, close paren |
6 | 2(3+4)2 | 2, open paren, 3 plus 4, close paren, squared |
7 | (2+7)(3−6) | open paren, 2 plus 7, close paren, open paren, 3 minus 6, close paren |
8 | [2+7][3−6] | open bracket, 2 plus 7, close bracket, open bracket, 3 minus 6, close bracket |
9 | x(y+z) | x, open paren, y plus z, close paren |
10 | 2(y+1) | 2, open paren, y plus 1, close paren |
11 | (2−1)x | open paren, 2 minus 1, close paren, x |
12 | p1(3+7) | p sub 1, open paren, 3 plus 7, close paren |
13 | p1a1p2a2 | p sub 1, raised to the, a sub 1, power, p sub 2, raised to the, a sub 2, power |
14 | (x+y)−4(x−y)−4 | open paren, x plus y, close paren, to the negative 4 power, open paren, x minus y, close paren, to the negative 4 power |
15 | 24(x+y) | 2 raised to the 4, open paren, x plus y, close paren, power |
16 | xy | x y |
17 | x2y3 | x squared y cubed |
18 | xy+1xy+2 | x raised to the y plus 1 power, x raised to the y plus 2 power |
19 | ab=ab | the square root of a, the square root of b, equals the square root of a b |
20 | 310=30 | the square root of 3, the square root of 10, equals the square root of 30 |
21 | 23 | 2 the square root of 3 |
22 | 1+23 | 1 plus 2 the square root of 3 |
23 | sinxcosy+cosxsiny | sine x cosine y, plus, cosine x sine y |
24 | log10xy | the log base 10 of, x y |
25 | log(x+y)=logxlogy | the log of, open paren, x plus y, close paren, equals, log x log y |
26 | (1352)(7401) | the 2 by 2 matrix. Row 1: 1, 3 Row 2: 5, 2. the 2 by 2 matrix. Row 1: 7, 4 Row 2: 0, 1 |
27 | 2(3((4+5)+6)) | 2, open paren, 3, open paren, open paren, 4 plus 5, close paren, plus 6, close paren, close paren |
28 | 2[3((4+5)+6)] | 2, open bracket, 3, open paren, open paren, 4 plus 5, close paren, plus 6, close paren, close bracket |
29 | 2|x| | 2, the absolute value of x |
30 | |x||y| | the absolute value of x, the absolute value of y |
31 | |x+1||y−1| | the absolute value of x plus 1, the absolute value of y minus 1 |
32 | |x+1||y|−1 | the absolute value of x plus 1, the absolute value of y, minus 1 |
33 | f(x)=x2(x+1) | f of x, equals x squared, open paren, x plus 1, close paren |
34 | log(x+y)=logxlogy | the log of, open paren, x plus y, close paren, equals, log x log y |
0 | 2(3) | 2, open paren, 3, close paren |
1 | 2[3] | 2, open bracket, 3, close bracket |
2 | 24(3) | 2 to the fourth power, open paren, 3, close paren |
3 | 2(3+4) | 2, open paren, 3 plus 4, close paren |
4 | 2[3+4] | 2, open bracket, 3 plus 4, close bracket |
5 | (3)(2) | open paren, 3, close paren, open paren, 2, close paren |
6 | 2(3+4)2 | 2, open paren, 3 plus 4, close paren, squared |
7 | (2+7)(3−6) | open paren, 2 plus 7, close paren, open paren, 3 minus 6, close paren |
8 | [2+7][3−6] | open bracket, 2 plus 7, close bracket, open bracket, 3 minus 6, close bracket |
9 | x(y+z) | x, open paren, y plus z, close paren |
10 | 2(y+1) | 2, open paren, y plus 1, close paren |
11 | (2−1)x | open paren, 2 minus 1, close paren, x |
12 | p1(3+7) | p sub 1, open paren, 3 plus 7, close paren |
13 | (x+y)−4(x−y)−4 | open paren, x plus y, close paren, to the negative 4 power, open paren, x minus y, close paren, to the negative 4 power |
14 | 24(x+y) | 2 raised to the 4, open paren, x plus y, close paren, power |
15 | (1352)(7401) | the 2 by 2 matrix. Row 1: 1, 3 Row 2: 5, 2. the 2 by 2 matrix. Row 1: 7, 4 Row 2: 0, 1 |
16 | 2(3((4+5)+6)) | 2, open paren, 3, open paren, open paren, 4 plus 5, close paren, plus 6, close paren, close paren |
17 | 2[3((4+5)+6)] | 2, open bracket, 3, open paren, open paren, 4 plus 5, close paren, plus 6, close paren, close bracket |
0 | logx | log x |
1 | log10x | the log base 10 of, x |
2 | logbax=logba+logbx | the log base b of, a x, equals, the log base b of, a, plus, the log base b of, x |
3 | logbST=logbS−logbT | the log base b of, S over T, equals, the log base b of, S, minus, the log base b of, T |
4 | logb(xk)=klogbx | the log base b of, open paren, x to the k-th power, close paren, equals k, the log base b of, x |
5 | 10log10x=x | 10 raised to the log base 10 of, x, power, equals x |
6 | log1010x=x | the log base 10 of, 10 to the x-th power, equals x |
7 | 10log105=5 | 10 raised to the log base 10 of, 5, power, equals 5 |
8 | log10103=3 | the log base 10 of, 10 cubed, equals 3 |
9 | logax=logbxlogba | the log base a of, x, equals, the log base b of, x, over, the log base b of, a |
10 | log1018log103=log318 | the log base 10 of, 18, over, the log base 10 of, 3, equals, the log base 3 of, 18 |
11 | logxloga | log x over log a |
12 | log(x+1) | the log of, open paren, x plus 1, close paren |
13 | log(x+1)2 | the log of, open paren, x plus 1, close paren, squared |
14 | log(xy) | log x y |
15 | log(x+1)log(x+2) | the fraction with numerator, the log of, open paren, x plus 1, close paren, and denominator, the log of, open paren, x plus 2, close paren |
16 | log6(x+1)log6(x+2) | the fraction with numerator, the log base 6 of, open paren, x plus 1, close paren, and denominator, the log base 6 of, open paren, x plus 2, close paren |
17 | log40+log60log5 | the fraction with numerator log 40 plus log 60, and denominator log 5 |
18 | log340+log360log35 | the fraction with numerator, the log base 3 of, 40, plus, the log base 3 of, 60, and denominator, the log base 3 of, 5 |
19 | log(34129)=4log3+9log12 | the log of, open paren, 3 to the fourth power, 12 to the ninth power, close paren, equals 4 log 3, plus 9 log 12 |
20 | log(xy) | the log of, open paren, x over y, close paren |
21 | log(34810)=4log3−10log8 | the log of, open paren, the fraction with numerator 3 to the fourth power, and denominator 8 to the tenth power, close paren, equals 4 log 3, minus 10 log 8 |
22 | 10logx | 10 raised to the log x power |
23 | lnx | l n x |
24 | lnx−ln(x−1)=ln(xx−1) | l n x, minus l n of, open paren, x minus 1, close paren, equals l n of, open paren, the fraction with numerator x, and denominator x minus 1, close paren |
25 | ln(ex)=x | l n of, open paren, e to the x-th power, close paren, equals x |
26 | elnx=x | e raised to the l n x power, equals x |
27 | ln(ex)=x | l n of, open paren, e to the x-th power, close paren, equals x |
28 | eln4=4 | e raised to the l n 4 power, equals 4 |
29 | ln40ln5=log540 | l n 40, over l n 5, equals, the log base 5 of, 40 |
30 | ln40+ln60ln5 | the fraction with numerator l n 40, plus l n 60, and denominator l n 5 |
0 | (2175) | the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 |
1 | [2175] | the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 |
2 | (314026) | the 2 by 3 matrix. Row 1: 3, 1, 4 Row 2: 0, 2, 6 |
3 | [314026] | the 2 by 3 matrix. Row 1: 3, 1, 4 Row 2: 0, 2, 6 |
4 | (123) | the 3 by 1 column matrix. 1, 2, 3 |
5 | [123] | the 3 by 1 column matrix. 1, 2, 3 |
6 | (35) | the 1 by 2 row matrix. 3, 5 |
7 | [35] | the 1 by 2 row matrix. 3, 5 |
8 | (3) | the 1 by 1 matrix with entry 3 |
9 | (3) | the 1 by 1 matrix with entry 3 |
10 | (x+1x−1) | the 2 by 1 column matrix. Row 1: x plus 1 Row 2: x minus 1 |
11 | (3612) | the 4 by 1 column matrix. Row 1: 3 Row 2: 6 Row 3: 1 Row 4: 2 |
12 | (x+12x) | the 1 by 2 row matrix. Column 1: x plus 1 Column 2: 2 x |
13 | (3612) | the 1 by 4 row matrix. Column 1: 3 Column 2: 6 Column 3: 1 Column 4: 2 |
14 | (241352147) | the 3 by 3 matrix. Row 1: 2, 4, 1 Row 2: 3, 5, 2 Row 3: 1, 4, 7 |
15 | (0343210930216290) | the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0 |
16 | (2105334270) | the 2 by 5 matrix. Row 1: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 5; Column 5, 3. Row 2: Column 1, 3; Column 2, 4; Column 3, 2; Column 4, 7; Column 5, 0 |
17 | (13422105) | the 4 by 2 matrix. Row 1: Column 1, 1; Column 2, 3. Row 2: Column 1, 4; Column 2, 2. Row 3: Column 1, 2; Column 2, 1. Row 4: Column 1, 0; Column 2, 5 |
18 | (2175+x) | the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 plus x |
19 | (31−x4026) | the 2 by 3 matrix. Row 1: Column 1, 3; Column 2, 1 minus x; Column 3, 4. Row 2: Column 1, 0; Column 2, 2; Column 3, 6 |
20 | (2x175) | the 2 by 2 matrix. Row 1: 2 x, 1 Row 2: 7, 5 |
21 | (2xy1223) | the 2 by 2 matrix. Row 1: 2 x, y Row 2: one half, two thirds |
22 | (12233415) | the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth |
23 | (b11b12b21b22) | the 2 by 2 matrix. Row 1: b sub 1 1, b sub 1 2 Row 2: b sub 2 1, b sub 2 2 |
24 | 3(2175)(314026) | 3 times the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5. times the 2 by 3 matrix. Row 1: 3, 1, 4 Row 2: 0, 2, 6 |
25 | (12233415)(31−x4026) | the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth. times the 2 by 3 matrix. Row 1: Column 1, 3; Column 2, 1 minus x; Column 3, 4. Row 2: Column 1, 0; Column 2, 2; Column 3, 6 |
26 | (0343210930216290)(13422105) | the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0. times the 4 by 2 matrix. Row 1: Column 1, 1; Column 2, 3. Row 2: Column 1, 4; Column 2, 2. Row 3: Column 1, 2; Column 2, 1. Row 4: Column 1, 0; Column 2, 5 |
27 | |2175| | the determinant of the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 |
28 | det(2175) | the determinant of the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 |
29 | |241352147| | the determinant of the 3 by 3 matrix. Row 1: 2, 4, 1 Row 2: 3, 5, 2 Row 3: 1, 4, 7 |
30 | det(241352147) | the determinant of the 3 by 3 matrix. Row 1: 2, 4, 1 Row 2: 3, 5, 2 Row 3: 1, 4, 7 |
31 | |0343210930216290| | the determinant of the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0 |
32 | det(0343210930216290) | the determinant of the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0 |
33 | |2175+x| | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 plus x |
34 | det(2175+x) | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 plus x |
35 | |2x175| | the determinant of the 2 by 2 matrix. Row 1: 2 x, 1 Row 2: 7, 5 |
36 | det(2x175) | the determinant of the 2 by 2 matrix. Row 1: 2 x, 1 Row 2: 7, 5 |
37 | |2xy1223| | the determinant of the 2 by 2 matrix. Row 1: 2 x, y Row 2: one half, two thirds |
38 | det(2xy1223) | the determinant of the 2 by 2 matrix. Row 1: 2 x, y Row 2: one half, two thirds |
39 | |12233415| | the determinant of the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth |
40 | det(12233415) | the determinant of the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth |
0 | (2175) | the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 |
1 | [2175] | the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 |
2 | (314026) | the 2 by 3 matrix. Row 1: Column 1, 3; Column 2, 1; Column 3, 4. Row 2: Column 1, 0; Column 2, 2; Column 3, 6 |
3 | [314026] | the 2 by 3 matrix. Row 1: Column 1, 3; Column 2, 1; Column 3, 4. Row 2: Column 1, 0; Column 2, 2; Column 3, 6 |
4 | (123) | the 3 by 1 column matrix. Row 1: 1 Row 2: 2 Row 3: 3 |
5 | [123] | the 3 by 1 column matrix. Row 1: 1 Row 2: 2 Row 3: 3 |
6 | (35) | the 1 by 2 row matrix. Column 1: 3 Column 2: 5 |
7 | [35] | the 1 by 2 row matrix. Column 1: 3 Column 2: 5 |
8 | (1234) | the 1 by 4 row matrix. Column 1: 1 Column 2: 2 Column 3: 3 Column 4: 4 |
9 | [1234] | the 1 by 4 row matrix. Column 1: 1 Column 2: 2 Column 3: 3 Column 4: 4 |
10 | (1234) | the 4 by 1 column matrix. Row 1: 1 Row 2: 2 Row 3: 3 Row 4: 4 |
11 | [1234] | the 4 by 1 column matrix. Row 1: 1 Row 2: 2 Row 3: 3 Row 4: 4 |
12 | (x+1x−1) | the 2 by 1 column matrix. Row 1: x plus 1 Row 2: x minus 1 |
13 | (3612) | the 4 by 1 column matrix. Row 1: 3 Row 2: 6 Row 3: 1 Row 4: 2 |
14 | (x+12x) | the 1 by 2 row matrix. Column 1: x plus 1 Column 2: 2 x |
15 | (3612) | the 1 by 4 row matrix. Column 1: 3 Column 2: 6 Column 3: 1 Column 4: 2 |
16 | (241352147) | the 3 by 3 matrix. Row 1: Column 1, 2; Column 2, 4; Column 3, 1. Row 2: Column 1, 3; Column 2, 5; Column 3, 2. Row 3: Column 1, 1; Column 2, 4; Column 3, 7 |
17 | (0343210930216290) | the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0 |
18 | (2105334270) | the 2 by 5 matrix. Row 1: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 5; Column 5, 3. Row 2: Column 1, 3; Column 2, 4; Column 3, 2; Column 4, 7; Column 5, 0 |
19 | (13422105) | the 4 by 2 matrix. Row 1: Column 1, 1; Column 2, 3. Row 2: Column 1, 4; Column 2, 2. Row 3: Column 1, 2; Column 2, 1. Row 4: Column 1, 0; Column 2, 5 |
20 | (2175+x) | the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 plus x |
21 | (31−x4026) | the 2 by 3 matrix. Row 1: Column 1, 3; Column 2, 1 minus x; Column 3, 4. Row 2: Column 1, 0; Column 2, 2; Column 3, 6 |
22 | (2x175) | the 2 by 2 matrix. Row 1: Column 1, 2 x; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 |
23 | (2xy1223) | the 2 by 2 matrix. Row 1: Column 1, 2 x; Column 2, y. Row 2: Column 1, one half; Column 2, two thirds |
24 | (12233415) | the 2 by 2 matrix. Row 1: Column 1, one half; Column 2, two thirds. Row 2: Column 1, three fourths; Column 2, one fifth |
25 | (b11b12b21b22) | the 2 by 2 matrix. Row 1: Column 1, b sub 1 1; Column 2, b sub 1 2. Row 2: Column 1, b sub 2 1; Column 2, b sub 2 2 |
26 | 3(2175)(314026) | 3 times the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5. times the 2 by 3 matrix. Row 1: Column 1, 3; Column 2, 1; Column 3, 4. Row 2: Column 1, 0; Column 2, 2; Column 3, 6 |
27 | (12233415)(31−x4026) | the 2 by 2 matrix. Row 1: Column 1, one half; Column 2, two thirds. Row 2: Column 1, three fourths; Column 2, one fifth. times the 2 by 3 matrix. Row 1: Column 1, 3; Column 2, 1 minus x; Column 3, 4. Row 2: Column 1, 0; Column 2, 2; Column 3, 6 |
28 | (0343210930216290)(13422105) | the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0. times the 4 by 2 matrix. Row 1: Column 1, 1; Column 2, 3. Row 2: Column 1, 4; Column 2, 2. Row 3: Column 1, 2; Column 2, 1. Row 4: Column 1, 0; Column 2, 5 |
29 | |2175| | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 |
30 | det(2175) | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 |
31 | |241352147| | the determinant of the 3 by 3 matrix. Row 1: Column 1, 2; Column 2, 4; Column 3, 1. Row 2: Column 1, 3; Column 2, 5; Column 3, 2. Row 3: Column 1, 1; Column 2, 4; Column 3, 7 |
32 | det(241352147) | the determinant of the 3 by 3 matrix. Row 1: Column 1, 2; Column 2, 4; Column 3, 1. Row 2: Column 1, 3; Column 2, 5; Column 3, 2. Row 3: Column 1, 1; Column 2, 4; Column 3, 7 |
33 | |0343210930216290| | the determinant of the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0 |
34 | det(0343210930216290) | the determinant of the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0 |
35 | |2175+x| | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 plus x |
36 | det(2175+x) | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 plus x |
37 | |2x175| | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2 x; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 |
38 | det(2x175) | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2 x; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 |
39 | |2xy1223| | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2 x; Column 2, y. Row 2: Column 1, one half; Column 2, two thirds |
40 | det(2xy1223) | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2 x; Column 2, y. Row 2: Column 1, one half; Column 2, two thirds |
41 | |12233415| | the determinant of the 2 by 2 matrix. Row 1: Column 1, one half; Column 2, two thirds. Row 2: Column 1, three fourths; Column 2, one fifth |
42 | det(12233415) | the determinant of the 2 by 2 matrix. Row 1: Column 1, one half; Column 2, two thirds. Row 2: Column 1, three fourths; Column 2, one fifth |
0 | (2175) | the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 |
1 | [2175] | the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 |
2 | (314026) | the 2 by 3 matrix. Row 1: 3, 1, 4 Row 2: 0, 2, 6 |
3 | [314026] | the 2 by 3 matrix. Row 1: 3, 1, 4 Row 2: 0, 2, 6 |
4 | (123) | the 3 by 1 column matrix. 1, 2, 3 |
5 | [123] | the 3 by 1 column matrix. 1, 2, 3 |
6 | (35) | the 1 by 2 row matrix. 3, 5 |
7 | [35] | the 1 by 2 row matrix. 3, 5 |
8 | (x+1x−1) | the 2 by 1 column matrix. x plus 1, x minus 1 |
9 | (3612) | the 4 by 1 column matrix. 3, 6, 1, 2 |
10 | (x+12x) | the 1 by 2 row matrix. x plus 1, 2 x |
11 | (3612) | the 1 by 4 row matrix. 3, 6, 1, 2 |
12 | (241352147) | the 3 by 3 matrix. Row 1: 2, 4, 1 Row 2: 3, 5, 2 Row 3: 1, 4, 7 |
13 | (0343210930216290) | the 4 by 4 matrix. Row 1: 0, 3, 4, 3 Row 2: 2, 1, 0, 9 Row 3: 3, 0, 2, 1 Row 4: 6, 2, 9, 0 |
14 | (2105334270) | the 2 by 5 matrix. Row 1: 2, 1, 0, 5, 3 Row 2: 3, 4, 2, 7, 0 |
15 | (13422105) | the 4 by 2 matrix. Row 1: 1, 3 Row 2: 4, 2 Row 3: 2, 1 Row 4: 0, 5 |
16 | (2175+x) | the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 plus x |
17 | (31−x4026) | the 2 by 3 matrix. Row 1: 3, 1 minus x, 4 Row 2: 0, 2, 6 |
18 | (2x175) | the 2 by 2 matrix. Row 1: 2 x, 1 Row 2: 7, 5 |
19 | (2xy1223) | the 2 by 2 matrix. Row 1: 2 x, y Row 2: one half, two thirds |
20 | (12233415) | the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth |
21 | (b11b12b21b22) | the 2 by 2 matrix. Row 1: b sub 1 1, b sub 1 2 Row 2: b sub 2 1, b sub 2 2 |
22 | 3(2175)(314026) | 3 times the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5. times the 2 by 3 matrix. Row 1: 3, 1, 4 Row 2: 0, 2, 6 |
23 | (12233415)(31−x4026) | the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth. times the 2 by 3 matrix. Row 1: 3, 1 minus x, 4 Row 2: 0, 2, 6 |
24 | (0343210930216290)(13422105) | the 4 by 4 matrix. Row 1: 0, 3, 4, 3 Row 2: 2, 1, 0, 9 Row 3: 3, 0, 2, 1 Row 4: 6, 2, 9, 0. times the 4 by 2 matrix. Row 1: 1, 3 Row 2: 4, 2 Row 3: 2, 1 Row 4: 0, 5 |
25 | |2175| | the determinant of the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 |
26 | det(2175) | the determinant of the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 |
27 | |241352147| | the determinant of the 3 by 3 matrix. Row 1: 2, 4, 1 Row 2: 3, 5, 2 Row 3: 1, 4, 7 |
28 | det(241352147) | the determinant of the 3 by 3 matrix. Row 1: 2, 4, 1 Row 2: 3, 5, 2 Row 3: 1, 4, 7 |
29 | |0343210930216290| | the determinant of the 4 by 4 matrix. Row 1: 0, 3, 4, 3 Row 2: 2, 1, 0, 9 Row 3: 3, 0, 2, 1 Row 4: 6, 2, 9, 0 |
30 | det(0343210930216290) | the determinant of the 4 by 4 matrix. Row 1: 0, 3, 4, 3 Row 2: 2, 1, 0, 9 Row 3: 3, 0, 2, 1 Row 4: 6, 2, 9, 0 |
31 | |2175+x| | the determinant of the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 plus x |
32 | det(2175+x) | the determinant of the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5 plus x |
33 | |2x175| | the determinant of the 2 by 2 matrix. Row 1: 2 x, 1 Row 2: 7, 5 |
34 | det(2x175) | the determinant of the 2 by 2 matrix. Row 1: 2 x, 1 Row 2: 7, 5 |
35 | |2xy1223| | the determinant of the 2 by 2 matrix. Row 1: 2 x, y Row 2: one half, two thirds |
36 | det(2xy1223) | the determinant of the 2 by 2 matrix. Row 1: 2 x, y Row 2: one half, two thirds |
37 | |12233415| | the determinant of the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth |
38 | det(12233415) | the determinant of the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth |
0 | (2175) | the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5. end matrix |
1 | [2175] | the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5. end matrix |
2 | (314026) | the 2 by 3 matrix. Row 1: 3, 1, 4 Row 2: 0, 2, 6. end matrix |
3 | [314026] | the 2 by 3 matrix. Row 1: 3, 1, 4 Row 2: 0, 2, 6. end matrix |
4 | (123) | the 3 by 1 column matrix. 1, 2, 3. end matrix |
5 | [123] | the 3 by 1 column matrix. 1, 2, 3. end matrix |
6 | (35) | the 1 by 2 row matrix. 3, 5. end matrix |
7 | [35] | the 1 by 2 row matrix. 3, 5. end matrix |
8 | (x+1x−1) | the 2 by 1 column matrix. Row 1: x plus 1 Row 2: x minus 1. end matrix |
9 | (3612) | the 4 by 1 column matrix. Row 1: 3 Row 2: 6 Row 3: 1 Row 4: 2. end matrix |
10 | (x+12x) | the 1 by 2 row matrix. Column 1: x plus 1 Column 2: 2 x. end matrix |
11 | (3612) | the 1 by 4 row matrix. Column 1: 3 Column 2: 6 Column 3: 1 Column 4: 2. end matrix |
12 | (241352147) | the 3 by 3 matrix. Row 1: 2, 4, 1 Row 2: 3, 5, 2 Row 3: 1, 4, 7. end matrix |
13 | (0343210930216290) | the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0. end matrix |
14 | (2105334270) | the 2 by 5 matrix. Row 1: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 5; Column 5, 3. Row 2: Column 1, 3; Column 2, 4; Column 3, 2; Column 4, 7; Column 5, 0. end matrix |
15 | (13422105) | the 4 by 2 matrix. Row 1: Column 1, 1; Column 2, 3. Row 2: Column 1, 4; Column 2, 2. Row 3: Column 1, 2; Column 2, 1. Row 4: Column 1, 0; Column 2, 5. end matrix |
16 | (2175+x) | the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 plus x. end matrix |
17 | (31−x4026) | the 2 by 3 matrix. Row 1: Column 1, 3; Column 2, 1 minus x; Column 3, 4. Row 2: Column 1, 0; Column 2, 2; Column 3, 6. end matrix |
18 | (2x175) | the 2 by 2 matrix. Row 1: 2 x, 1 Row 2: 7, 5. end matrix |
19 | (2xy1223) | the 2 by 2 matrix. Row 1: 2 x, y Row 2: one half, two thirds. end matrix |
20 | (12233415) | the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth. end matrix |
21 | (b11b12b21b22) | the 2 by 2 matrix. Row 1: b sub 1 1, b sub 1 2 Row 2: b sub 2 1, b sub 2 2. end matrix |
22 | 3(2175)(314026) | 3 times the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5. end matrix times the 2 by 3 matrix. Row 1: 3, 1, 4 Row 2: 0, 2, 6. end matrix |
23 | (12233415)(31−x4026) | the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth. end matrix times the 2 by 3 matrix. Row 1: Column 1, 3; Column 2, 1 minus x; Column 3, 4. Row 2: Column 1, 0; Column 2, 2; Column 3, 6. end matrix |
24 | (0343210930216290)(13422105) | the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0. end matrix times the 4 by 2 matrix. Row 1: Column 1, 1; Column 2, 3. Row 2: Column 1, 4; Column 2, 2. Row 3: Column 1, 2; Column 2, 1. Row 4: Column 1, 0; Column 2, 5. end matrix |
25 | |2175| | the determinant of the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5. end determinant |
26 | det(2175) | the determinant of the 2 by 2 matrix. Row 1: 2, 1 Row 2: 7, 5. end matrix |
27 | |241352147| | the determinant of the 3 by 3 matrix. Row 1: 2, 4, 1 Row 2: 3, 5, 2 Row 3: 1, 4, 7. end determinant |
28 | det(241352147) | the determinant of the 3 by 3 matrix. Row 1: 2, 4, 1 Row 2: 3, 5, 2 Row 3: 1, 4, 7. end matrix |
29 | |0343210930216290| | the determinant of the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0. end determinant |
30 | det(0343210930216290) | the determinant of the 4 by 4 matrix. Row 1: Column 1, 0; Column 2, 3; Column 3, 4; Column 4, 3. Row 2: Column 1, 2; Column 2, 1; Column 3, 0; Column 4, 9. Row 3: Column 1, 3; Column 2, 0; Column 3, 2; Column 4, 1. Row 4: Column 1, 6; Column 2, 2; Column 3, 9; Column 4, 0. end matrix |
31 | |2175+x| | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 plus x. end determinant |
32 | det(2175+x) | the determinant of the 2 by 2 matrix. Row 1: Column 1, 2; Column 2, 1. Row 2: Column 1, 7; Column 2, 5 plus x. end matrix |
33 | |2x175| | the determinant of the 2 by 2 matrix. Row 1: 2 x, 1 Row 2: 7, 5. end determinant |
34 | det(2x175) | the determinant of the 2 by 2 matrix. Row 1: 2 x, 1 Row 2: 7, 5. end matrix |
35 | |2xy1223| | the determinant of the 2 by 2 matrix. Row 1: 2 x, y Row 2: one half, two thirds. end determinant |
36 | det(2xy1223) | the determinant of the 2 by 2 matrix. Row 1: 2 x, y Row 2: one half, two thirds. end matrix |
37 | |12233415| | the determinant of the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth. end determinant |
38 | det(12233415) | the determinant of the 2 by 2 matrix. Row 1: one half, two thirds Row 2: three fourths, one fifth. end matrix |
0 | x+y=72x+3y=17 | 2 lines, Line 1: x plus y equals 7. Line 2: 2 x, plus 3 y, equals 17 |
1 | x+y=72x+3y=17 | 2 lines, Line 1: x plus y; equals; 7. Line 2: 2 x, plus 3 y; equals; 17 |
2 | x+y=72x+3y=17 | 2 lines, Line 1: x; plus; y; equals; 7. Line 2: 2 x; plus; 3 y; equals; 17 |
3 | Equation 1: x+y=7Equation 2: 2x+3y=17 | 2 lines, Line 1: Equation 1 colon x plus y equals 7. Line 2: Equation 2 colon 2 x, plus 3 y, equals 17 |
4 | Equation 1:x+y=7Equation 2:2x+3y=17 | 2 lines, Line 1: Equation 1 colon; x plus y equals 7. Line 2: Equation 2 colon; 2 x, plus 3 y, equals 17 |
5 | Equation 1:x+y=7Equation 2:2x+3y=17 | 2 lines, Line 1: Equation 1 colon; x plus y; equals; 7. Line 2: Equation 2 colon; 2 x, plus 3 y; equals; 17 |
6 | 4x+3y+2z=172x+4y+6z=63x+2y+5z=1 | 3 lines, Line 1: 4 x, plus 3 y, plus 2 z, equals 17. Line 2: 2 x, plus 4 y, plus 6 z, equals 6. Line 3: 3 x, plus 2 y, plus 5 z, equals 1 |
7 | 4x+3y+2z=12x+4y+6z=63x+2y+5z=1 | 3 lines, Line 1: 4 x; plus; 3 y; plus; 2 z; equals; 1. Line 2: 2 x; plus; 4 y; plus; 6 z; equals; 6. Line 3: 3 x; plus; 2 y; plus; 5 z; equals; 1 |
8 | Equation 1: 4x+3y+2z=17Equation 2: 2x+4y+6z=6Equation 3: 3x+2y+5z=1 | 3 lines, Line 1: Equation 1 colon 4 x, plus 3 y, plus 2 z, equals 17. Line 2: Equation 2 colon 2 x, plus 4 y, plus 6 z, equals 6. Line 3: Equation 3 colon 3 x, plus 2 y, plus 5 z, equals 1 |
9 | x≥0y≥03x−5y≤30 | 3 lines, Line 1: x is greater than or equal to 0. Line 2: y is greater than or equal to 0. Line 3: 3 x, minus 5 y, is less than or equal to 30 |
10 | 3x+8=5x8=5x−3x8=2x4=x | 4 lines, Line 1: 3 x, plus 8 equals 5 x. Line 2: 8 equals 5 x, minus 3 x. Line 3: 8 equals 2 x. Line 4: 4 equals x |
11 | 3x+8=5x8=5x−3x8=2x4=x | 4 lines, Line 1: 3 x; plus; 8; equals; 5 x; blank; blank. Line 2: blank; blank; 8; equals; 5 x; minus; 3 x. Line 3: blank; blank; 8; equals; 2 x; blank; blank. Line 4: blank; blank; 4; equals; x; blank; blank |
12 | Step 1: 3x+8=5xStep 2: 8=5x−3xStep 3: 8=2xStep 4: 4=x | 4 lines, Line 1: Step 1 colon 3 x, plus 8 equals 5 x. Line 2: Step 2 colon 8 equals 5 x, minus 3 x. Line 3: Step 3 colon 8 equals 2 x. Line 4: Step 4 colon 4 equals x |
13 | f(x)={−x if x<0x if x≥0 | f of x, equals, 2 cases, Case 1: negative x if x is less than 0. Case 2: x if x is greater than or equal to 0 |
14 | f(x)={−xif x<0xif x≥0 | f of x, equals, 2 cases, Case 1: negative x; if x is less than 0. Case 2: x; if x is greater than or equal to 0 |
0 | x+y=72x+3y=17 | 2 lines, Line 1: x plus y, equals, 7. Line 2: 2 x, plus 3 y, equals, 17 |
1 | x+y=72x+3y=17 | 2 lines, Line 1: x, plus, y, equals, 7. Line 2: 2 x, plus, 3 y, equals, 17 |
2 | Equation 1:x+y=7Equation 2:2x+3y=17 | 2 lines, Line 1: Equation 1 colon, x plus y equals 7. Line 2: Equation 2 colon, 2 x, plus 3 y, equals 17 |
3 | Equation 1:x+y=7Equation 2:2x+3y=17 | 2 lines, Line 1: Equation 1 colon, x plus y, equals, 7. Line 2: Equation 2 colon, 2 x, plus 3 y, equals, 17 |
4 | 4x+3y+2z=12x+4y+6z=63x+2y+5z=1 | 3 lines, Line 1: 4 x, plus, 3 y, plus, 2 z, equals, 1. Line 2: 2 x, plus, 4 y, plus, 6 z, equals, 6. Line 3: 3 x, plus, 2 y, plus, 5 z, equals, 1 |
5 | 3x+8=5x8=5x−3x8=2x4=x | 4 lines, Line 1: 3 x, plus, 8, equals, 5 x, blank, blank. Line 2: blank, blank, 8, equals, 5 x, minus, 3 x. Line 3: blank, blank, 8, equals, 2 x, blank, blank. Line 4: blank, blank, 4, equals, x, blank, blank |
6 | f(x)={−xif x<0xif x≥0 | f of x, equals, 2 cases, Case 1: negative x, if x is less than 0. Case 2: x, if x is greater than or equal to 0 |
0 | f(g(x)) | f of, g of x |
1 | f(g(x+1)) | f of, open paren, g of, open paren, x plus 1, close paren, close paren |
2 | 6−[2−(3+5)] | 6 minus, open bracket, 2 minus, open paren, 3 plus 5, close paren, close bracket |
3 | 6−(2−(3+5)) | 6 minus, open paren, 2 minus, open second paren, 3 plus 5, close second paren, close paren |
4 | 4[x+3(2x+1)] | 4 times, open bracket, x plus 3 times, open paren, 2 x, plus 1, close paren, close bracket |
5 | 4(x+3(2x+1)) | 4 times, open paren, x plus 3 times, open second paren, 2 x, plus 1, close second paren, close paren |
6 | 1+(2+(3+7)−(2+8)) | 1 plus, open paren, 2 plus, open second paren, 3 plus 7, close second paren, minus, open second paren, 2 plus 8, close second paren, close paren |
7 | 1+(2+(3−(4−5))) | 1 plus, open paren, 2 plus, open second paren, 3 minus, open third paren, 4 minus 5, close third paren, close second paren, close paren |
8 | ((2+(3+4)+5)+6+((7+(8+1))+2)) | open paren, open second paren, 2 plus, open third paren, 3 plus 4, close third paren, plus 5, close second paren, plus 6 plus, open second paren, open third paren, 7 plus, open fourth paren, 8 plus 1, close fourth paren, close third paren, plus 2, close second paren, close paren |
0 | 2 | the square root of 2 |
1 | 3+2 | 3 plus the square root of 2 |
2 | 3±2 | 3 plus or minus the square root of 2 |
3 | 3∓2 | 3 minus or plus the square root of 2 |
4 | −2 | the negative square root of 2 |
5 | 3−2 | 3 minus the square root of 2 |
6 | 3+−2 | 3 plus the negative square root of 2 |
7 | 3−−2 | 3 minus the negative square root of 2 |
8 | 3+(−2) | 3 plus, open paren, the negative square root of 2, close paren |
9 | 3−(−2) | 3 minus, open paren, the negative square root of 2, close paren |
10 | x+1 | the square root of x plus 1 |
11 | x+1 | the square root of x, plus 1 |
12 | −x | the negative square root of x |
13 | (x)2 | open paren, the square root of x, close paren, squared |
14 | −(x)2 | negative, open paren, the square root of x, close paren, squared |
15 | x2 | the square root of x, squared |
16 | x2 | the square root of x squared |
17 | x2+y2 | the square root of x squared plus y squared |
18 | x12+x22 | the square root of, x sub 1, squared plus, x sub 2, squared |
19 | (x2−x1)2+(y2−y1)2 | the square root of, open paren, x sub 2, minus, x sub 1, close paren, squared plus, open paren, y sub 2, minus, y sub 1, close paren, squared |
20 | 12 | the square root of one half |
21 | 2366 | the square root of, 23 over 66 |
22 | x+12x+5 | the square root of, the fraction with numerator x plus 1, and denominator 2 x, plus 5 |
23 | −b±b2−4ac2a | the fraction with numerator negative b plus or minus the square root of b squared minus 4 a c, and denominator 2 a |
24 | y3 | the cube root of y |
25 | n4 | the fourth root of n |
26 | 355 | the fifth root of 35 |
27 | 1469 | the ninth root of 146 |
28 | dn | the n-th root of d |
29 | 243m | the m-th root of 243 |
30 | 2ii | the i-th root of 2 to the i-th power |
31 | 125j | the j-th root of 125 |
32 | −y3 | negative the cube root of y |
33 | −n4 | negative the fourth root of n |
0 | 2 | the positive square root of 2 |
1 | 3+2 | 3 plus the positive square root of 2 |
2 | 3±2 | 3 plus or minus the square root of 2 |
3 | 3∓2 | 3 minus or plus the square root of 2 |
4 | −2 | the negative square root of 2 |
5 | 3−2 | 3 minus the positive square root of 2 |
6 | 3+−2 | 3 plus the negative square root of 2 |
7 | 3−−2 | 3 minus the negative square root of 2 |
8 | 3+(−2) | 3 plus, open paren, the negative square root of 2, close paren |
9 | 3−(−2) | 3 minus, open paren, the negative square root of 2, close paren |
10 | x+1 | the positive square root of x plus 1 |
11 | x+1 | the positive square root of x, plus 1 |
12 | −x | the negative square root of x |
13 | (x)2 | open paren, the positive square root of x, close paren, squared |
14 | (−x)2 | open paren, the negative square root of x, close paren, squared |
15 | −(x)2 | negative, open paren, the positive square root of x, close paren, squared |
16 | x2 | the positive square root of x, squared |
17 | x2 | the positive square root of x squared |
18 | x2+y2 | the positive square root of x squared plus y squared |
19 | x12+x22 | the positive square root of, x sub 1, squared plus, x sub 2, squared |
20 | (x2−x1)2+(y2−y1)2 | the positive square root of, open paren, x sub 2, minus, x sub 1, close paren, squared plus, open paren, y sub 2, minus, y sub 1, close paren, squared |
21 | 12 | the positive square root of one half |
22 | 2366 | the positive square root of, 23 over 66 |
23 | x+12x+5 | the positive square root of, the fraction with numerator x plus 1, and denominator 2 x, plus 5 |
24 | −b±b2−4ac2a | the fraction with numerator negative b plus or minus the square root of b squared minus 4 a c, and denominator 2 a |
25 | y3 | the cube root of y |
26 | n4 | the fourth root of n |
27 | 355 | the fifth root of 35 |
28 | 1469 | the ninth root of 146 |
29 | dn | the n-th root of d |
30 | 243m | the m-th root of 243 |
31 | 2ii | the i-th root of 2 to the i-th power |
32 | 125j | the j-th root of 125 |
33 | −y3 | negative the cube root of y |
34 | −n4 | negative the fourth root of n |
0 | 2 | the square root of 2, end root |
1 | 3+2 | 3 plus the square root of 2, end root |
2 | 3±2 | 3 plus or minus the square root of 2, end root |
3 | 3∓2 | 3 minus or plus the square root of 2, end root |
4 | −2 | the negative square root of 2, end root |
5 | 3−2 | 3 minus the square root of 2, end root |
6 | 3+−2 | 3 plus the negative square root of 2, end root |
7 | 3−−2 | 3 minus the negative square root of 2, end root |
8 | 3+(−2) | 3 plus, open paren, the negative square root of 2, end root, close paren |
9 | 3−(−2) | 3 minus, open paren, the negative square root of 2, end root, close paren |
10 | x+1 | the square root of x plus 1, end root |
11 | x+1 | the square root of x, end root, plus 1 |
12 | −x | the negative square root of x, end root |
13 | (x)2 | open paren, the square root of x, end root, close paren, squared |
14 | −(x)2 | negative, open paren, the square root of x, end root, close paren, squared |
15 | x2 | the square root of x, end root, squared |
16 | x2 | the square root of x squared, end root |
17 | x2+y2 | the square root of x squared plus y squared, end root |
18 | x12+x22 | the square root of, x sub 1, squared plus, x sub 2, squared, end root |
19 | (x2−x1)2+(y2−y1)2 | the square root of, open paren, x sub 2, minus, x sub 1, close paren, squared plus, open paren, y sub 2, minus, y sub 1, close paren, squared, end root |
20 | 12 | the square root of one half, end root |
21 | 2366 | the square root of, 23 over 66, end root |
22 | x+12x+5 | the square root of, the fraction with numerator x plus 1, and denominator 2 x, plus 5, end root |
23 | −b±b2−4ac2a | the fraction with numerator negative b plus or minus the square root of b squared minus 4 a c, end root, and denominator 2 a |
24 | y3 | the cube root of y, end root |
25 | n4 | the fourth root of n, end root |
26 | 355 | the fifth root of 35, end root |
27 | 1469 | the ninth root of 146, end root |
28 | dn | the n-th root of d, end root |
29 | 243m | the m-th root of 243, end root |
30 | 2ii | the i-th root of 2 to the i-th power, end root |
31 | 125j | the j-th root of 125, end root |
32 | −y3 | negative the cube root of y, end root |
33 | −n4 | negative the fourth root of n, end root |
0 | 2 | the positive square root of 2, end root |
1 | 3+2 | 3 plus the positive square root of 2, end root |
2 | 3±2 | 3 plus or minus the square root of 2, end root |
3 | 3∓2 | 3 minus or plus the square root of 2, end root |
4 | −2 | the negative square root of 2, end root |
5 | 3−2 | 3 minus the positive square root of 2, end root |
6 | 3+−2 | 3 plus the negative square root of 2, end root |
7 | 3−−2 | 3 minus the negative square root of 2, end root |
8 | 3+(−2) | 3 plus, open paren, the negative square root of 2, end root, close paren |
9 | 3−(−2) | 3 minus, open paren, the negative square root of 2, end root, close paren |
10 | x+1 | the positive square root of x plus 1, end root |
11 | x+1 | the positive square root of x, end root, plus 1 |
12 | −x | the negative square root of x, end root |
13 | (x)2 | open paren, the positive square root of x, end root, close paren, squared |
14 | (−x)2 | open paren, the negative square root of x, end root, close paren, squared |
15 | x2 | the positive square root of x, end root, squared |
16 | x2 | the positive square root of x squared, end root |
17 | x2+y2 | the positive square root of x squared plus y squared, end root |
18 | x12+x22 | the positive square root of, x sub 1, squared plus, x sub 2, squared, end root |
19 | (x2−x1)2+(y2−y1)2 | the positive square root of, open paren, x sub 2, minus, x sub 1, close paren, squared plus, open paren, y sub 2, minus, y sub 1, close paren, squared, end root |
20 | 12 | the positive square root of one half, end root |
21 | 2366 | the positive square root of, 23 over 66, end root |
22 | x+12x+5 | the positive square root of, the fraction with numerator x plus 1, and denominator 2 x, plus 5, end root |
23 | −b±b2−4ac2a | the fraction with numerator negative b plus or minus the square root of b squared minus 4 a c, end root, and denominator 2 a |
24 | y3 | the cube root of y, end root |
25 | n4 | the fourth root of n, end root |
26 | 355 | the fifth root of 35, end root |
27 | 1469 | the ninth root of 146, end root |
28 | dn | the n-th root of d, end root |
29 | 243m | the m-th root of 243, end root |
30 | 2ii | the i-th root of 2 to the i-th power, end root |
31 | 125j | the j-th root of 125, end root |
32 | −y3 | negative the cube root of y, end root |
33 | −n4 | negative the fourth root of n, end root |
0 | sinx | sine x |
1 | cosx | cosine x |
2 | tanθ | tangent theta |
3 | secθ | secant theta |
4 | cscx | cosecant x |
5 | cotx | cotangent x |
6 | sin2x | sine squared x |
7 | cos3x | cosine cubed x |
8 | tan2x | tangent squared x |
9 | sec3x | secant cubed x |
10 | csc2x | cosecant squared x |
11 | cot2x | cotangent squared x |
12 | sin2π | sine 2 pi |
13 | sin(πk+π2) | the sine of, open paren, pi k, plus, pi over 2, close paren |
14 | cosπ2 | the cosine of, pi over 2 |
15 | sinπ2 | the sine of, pi over 2 |
16 | sinπ2 | sine pi over 2 |
17 | 2sinπ | 2 over sine pi |
18 | sinπ23 | the fraction with numerator, the sine of, pi over 2, and denominator 3 |
19 | tan(−π) | tangent negative pi |
20 | sin(x+π) | the sine of, open paren, x plus pi, close paren |
21 | cos(x+π2) | the cosine of, open paren, x plus, pi over 2, close paren |
22 | cos(π2+x) | the cosine of, open paren, pi over 2, plus x, close paren |
23 | sin2x+cos2x=1 | sine squared x, plus, cosine squared x, equals 1 |
24 | sin4x | the fourth power of sine x |
25 | cos5x | the fifth power of cosine x |
26 | tannx | the n-th power of tangent x |
27 | sinxcosx | sine x over cosine x |
28 | tan35° | tangent 35 degrees |
29 | tan(∠DEF) | the tangent of, open paren, angle D E F, close paren |
30 | tan(∠D) | the tangent of, open paren, angle D, close paren |
31 | sin(x+y)=sinxcosy+cosxsiny | the sine of, open paren, x plus y, close paren, equals, sine x cosine y, plus, cosine x sine y |
32 | cos(x+y)=cosxcosy−sinxsiny | the cosine of, open paren, x plus y, close paren, equals, cosine x cosine y, minus, sine x sine y |
33 | tan(x+y)=tanx−tany1−tanxtany | the tangent of, open paren, x plus y, close paren, equals, the fraction with numerator tangent x minus tangent y, and denominator 1 minus, tangent x tangent y |
34 | tan(π6+2π3)=tanπ6−tan2π31−tanπ6tan2π3 | the tangent of, open paren, pi over 6, plus, 2 pi over 3, close paren, equals, the fraction with numerator, the tangent of, pi over 6, minus, the tangent of, 2 pi over 3, and denominator 1 minus, the tangent of, pi over 6, the tangent of, 2 pi over 3 |
35 | tan2x=2tanx1−tan2x | tangent 2 x, equals, the fraction with numerator 2 tangent x, and denominator 1 minus, tangent squared x |
36 | cos2x=2cos2x−1 | cosine 2 x, equals 2, cosine squared x, minus 1 |
37 | sinx2=±1−cosx2 | the sine of, x over 2, equals plus or minus the square root of, the fraction with numerator 1 minus cosine x, and denominator 2 |
38 | tanx2=±1−cosx1+cosx | the tangent of, x over 2, equals plus or minus the square root of, the fraction with numerator 1 minus cosine x, and denominator 1 plus cosine x |
39 | cosxcosy=2cosx+y2cosx−y2 | cosine x cosine y, equals 2, the cosine of, the fraction with numerator x plus y, and denominator 2, the cosine of, the fraction with numerator x minus y, and denominator 2 |
40 | sin−1x | the inverse sine of x |
41 | cos−1x | the inverse cosine of x |
42 | tan−1x | the inverse tangent of x |
43 | cot−1x | the inverse cotangent of x |
44 | sec−1x | the inverse secant of x |
45 | csc−1x | the inverse cosecant of x |
46 | sin−122 | the inverse sine of, the fraction with numerator the square root of 2, and denominator 2 |
47 | cos−112 | the inverse cosine of one half |
48 | tan−117 | the inverse tangent of 17 |
49 | cot−132 | the inverse cotangent of 32 |
50 | sec−1100 | the inverse secant of 100 |
51 | csc−185 | the inverse cosecant of 85 |
52 | sin−1(−x) | the inverse sine of negative x |
53 | cos−1(−x) | the inverse cosine of negative x |
54 | tan−1(−x+12) | the inverse tangent of, open paren, negative x plus 12, close paren |
55 | cot−1(−x−1) | the inverse cotangent of, open paren, negative x minus 1, close paren |
56 | sin−1(sin0) | the inverse sine of sine 0 |
57 | csc−1(cscx) | the inverse cosecant of cosecant x |
58 | cos(cos−1(−22)) | the cosine of, open paren, the inverse cosine of, open paren, negative, the fraction with numerator the square root of 2, and denominator 2, close paren, close paren |
59 | cos(−cos−1(22)) | the cosine of, open paren, negative, the inverse cosine of, open paren, the fraction with numerator the square root of 2, and denominator 2, close paren, close paren |
60 | sin−1(cosπ4) | the inverse sine of, open paren, the cosine of, pi over 4, close paren |
61 | sin(cos−112) | sine, the inverse cosine of one half |
62 | sin(tan−11) | sine, the inverse tangent of 1 |
63 | sin(−tan−11) | the sine of, open paren, negative, the inverse tangent of 1, close paren |
64 | sin(−tan−1(−1)) | the sine of, open paren, negative, the inverse tangent of negative 1, close paren |
65 | sec−1(secx) | the inverse secant of secant x |
66 | arcsinx | arc sine x |
67 | arccosx | arc cosine x |
68 | arctanx | arc tangent x |
69 | sinhx | hyperbolic sine of x |
70 | coshx | hyperbolic cosine of x |
71 | tanhx | hyperbolic tangent of x |
72 | cothx | hyperbolic cotangent of x |
73 | sechx | hyperbolic secant of x |
74 | cschx | hyperbolic cosecant of x |
75 | sinh−1x | the inverse hyperbolic sine of x |
76 | cosh−1x | the inverse hyperbolic cosine of x |
77 | tanh−1x | the inverse hyperbolic tangent of x |
78 | coth−1x | the inverse hyperbolic cotangent of x |
79 | sech−1x | the inverse hyperbolic secant of x |
80 | csch−1x | the inverse hyperbolic cosecant of x |
81 | sinh(sinh−1x) | hyperbolic sine of, the inverse hyperbolic sine of x |
82 | cosh(cosh−1x) | hyperbolic cosine of, the inverse hyperbolic cosine of x |
83 | tanh(tanh−1x) | hyperbolic tangent of, the inverse hyperbolic tangent of x |
84 | coth(coth−1x) | hyperbolic cotangent of, the inverse hyperbolic cotangent of x |
85 | sinh−1(sinhx) | the inverse hyperbolic sine of, hyperbolic sine of x |
86 | cosh−1(coshx) | the inverse hyperbolic cosine of, hyperbolic cosine of x |
87 | tanh−1(tanhx) | the inverse hyperbolic tangent of, hyperbolic tangent of x |
88 | coth−1(cothx) | the inverse hyperbolic cotangent of, hyperbolic cotangent of x |
0 | in2 | square inches |
1 | s2 | seconds to the second power |
2 | m2 | square meters |
3 | in3 | cubic inches |
4 | s3 | seconds to the third power |
5 | m3 | cubic meters |
6 | in-1 | reciprocal inches |
7 | in-1mm-1 | reciprocal inches per millimeter |
8 | inmm | inches per millimeter |
9 | km | kilometers |
10 | A | amperes |
11 | Ω | ohms |
12 | kΩ | kilohms |
13 | °C | Celsius |
14 | minmin | min of minutes |
15 | 3km | 3 kilometers |
16 | km+s | kilometers plus seconds |
17 | km2 | square kilometers |
18 | m3 | cubic meters |
19 | km4 | kilometers to the fourth power |
20 | m-1 | reciprocal meters |
21 | sm-1 | seconds per meter |
22 | sm-1 | seconds per meter to the negative 1 power |
23 | sm-1 | seconds per meter to the negative 1 power |
24 | 3m-1 | 3 reciprocal meters |
25 | kmh | kilometers per hour |
26 | Nkmh | Newtons kilometers per hour |
27 | mkm | m over kilometers |
28 | 3kmh | 3 kilometers hours |
29 | s3mkmh | seconds 3 m kilometers hours |
30 | kms23mkmh | kilometers seconds to the second power 3 m kilometers hours |
31 | 3mkmhNs2 | 3 m kilometers hours the fraction with numerator N and denominator seconds to the second power |
32 | 3mkmhNs2 | 3 m kilometers hours Newtons per second to the second power |
33 | 4⁢mm | 4 millimeters |
34 | 1⁢mm | 1 millimeter |
35 | 4mm | 4 millimeters |
36 | 1mm | 1 millimeter |
37 | m⁢s | meters seconds |
38 | m⁢s | m seconds |
39 | m⁢s | meters s |
40 | ms | meters seconds |
41 | ms | m seconds |
42 | ms | meters s |
43 | m⁢sl | meters seconds liters |
44 | 63360in=63360in.=63360″=63360inches=5280ft=5280ft.=5280′=5280feet=1760yd=1760yd.=1760yards=1mi=1mi.=1mile | 63360 inches equals 63360 inches equals 63360 inches equals 63360 inches equals 5280 feet equals 5280 feet equals 5280 feet equals 5280 feet equals 1760 yards equals 1760 yards equals 1760 yards equals 1 mile equals 1 mile equals 1 mile |
45 | 8000li=8000li.=8000links=320rd=320rd.=320rods=80ch=80ch.=80chains=8fur=8fur.=8furlongs=1mi=1mi.=1mile | 8000 links equals 8000 links equals 8000 links equals 320 rods equals 320 rods equals 320 rods equals 80 chains equals 80 chains equals 80 chains equals 8 furlongs equals 8 furlongs equals 8 furlongs equals 1 mile equals 1 mile equals 1 mile |
46 | 43560sq ft=43560sq. ft.=43560ft2=43560′2=43560square feet=4840sq yd=4840sq. yd.=4840yd2=4840square yards=160sq rd=160sq. rd.=160rd2=160square rods=1ac=1ac.=1acre=1640sq mi=1640sq. mi.=1640mi2=1640square miles | 43560 square feet equals 43560 square feet equals 43560 square feet equals 43560 feet squared equals 43560 square feet equals 4840 square yards equals 4840 square yards equals 4840 square yards equals 4840 square yards equals 160 square rods equals 160 square rods equals 160 square rods equals 160 square rods equals 1 acre equals 1 acre equals 1 acre equals 1 over 640 square miles equals 1 over 640 square miles equals 1 over 640 square miles equals 1 over 640 square miles |
47 | 46656cu in=46656cu. in.=46656in3=46656″3=46656cubic inches=27cu ft=27cu. ft.=27ft3=27′3=27cubic feet=1cu yd=1cu. yd.=1yd3=1cubic yard | 46656 cubic inches equals 46656 cubic inches equals 46656 cubic inches equals 46656 inches cubed equals 46656 cubic inches equals 27 cubic feet equals 27 cubic feet equals 27 cubic feet equals 27 feet cubed equals 27 cubic feet equals 1 cubic yard equals 1 cubic yard equals 1 cubic yard equals 1 cubic yard |
48 | 1024fl dr=1024fl. dr.=1024fluid drams=768tsp=768tsp.=768teaspoons=256Tbsp=256Tbsp.=256tablespoons=128fl oz=128fl. oz.=128fluid ounces=16cp=16cp.=16cups=8pt=8pt.=8pints=4qt=4qt.=4quarts=1gal=1gal.=1gallon | 1024 fluid drams equals 1024 fluid drams equals 1024 fluid drams equals 768 teaspoons equals 768 teaspoons equals 768 teaspoons equals 256 tablespoons equals 256 tablespoons equals 256 tablespoons equals 128 fluid ounces equals 128 fluid ounces equals 128 fluid ounces equals 16 cups equals 16 cups equals 16 cups equals 8 pints equals 8 pints equals 8 pints equals 4 quarts equals 4 quarts equals 4 quarts equals 1 gallon equals 1 gallon equals 1 gallon |
49 | 256dr=256dr.=256drams=16oz=16oz.=16ounces=1#=1lb=1lb.=1pounds=100cwt=100cwt.=100hundredweights=2000tons | 256 drams equals 256 drams equals 256 drams equals 16 ounces equals 16 ounces equals 16 ounces equals 1 # equals 1 pound equals 1 pound equals 1 pounds equals 100 hundredweights equals 100 hundredweights equals 100 hundredweights equals 2000 tons |
50 | 63360in=63360in.=63360″=63360inches=5280ft=5280ft.=5280′=5280feet=1760yd=1760yd.=1760yards=1mi=1mi.=1mile | 63360 inches equals 63360 inches equals 63360 inches equals 63360 inches equals 5280 feet equals 5280 feet equals 5280 feet equals 5280 feet equals 1760 yards equals 1760 yards equals 1760 yards equals 1 mile equals 1 mile equals 1 mile |
51 | 1J=1kg·m2·s-2 | 1 joule equals 1 kilogram times square meters times seconds to the negative 2 power |
52 | 1J=1kgm2s-2 | 1 joule equals 1 kilogram square meters seconds to the negative 2 power |
53 | 1J=1·kg·m2·s-2 | 1 joule equals 1 kilogram square meters seconds to the negative 2 power |
54 | in3 | cubic inches |
55 | kmkgs2J | kilometers kilograms seconds to the second power per joule |
56 | 3km1kgs2J | 3 kilometers 1 kilogram seconds to the second power over joules |
57 | 1kmkgs2J | 1 kilometer kilograms seconds to the second power over joules |
58 | 1kmkgs25J | 1 kilometer kilograms seconds to the second power over 5 joules |
59 | km | kilometers |
60 | 3kmkgs2J | 3 kilometers kilograms seconds to the second power joules |
61 | 3kmkgs2J | 3 kilometers kilograms seconds to the second power joules |
62 | 3km4kgs2J | 3 kilometers 4 kilograms seconds to the second power joules |
63 | 3km1kgs2J | 3 kilometers 1 kilogram seconds to the second power joules |
64 | 1kms+2kms+0kms+akms+ | 1 kilometer seconds plus 2 kilometers seconds plus 0 kilometers seconds plus a kilometers seconds plus |
65 | 1km+2km+0km+akm | 1 kilometer plus 2 kilometers plus 0 kilometers plus a kilometers |
66 | 123kg | 1 and two thirds kilograms |
67 | 123kgkm | 1 and two thirds kilograms kilometers |
68 | 1km2kgkm | 1 kilometer 2 kilograms kilometers |
69 | 1kmkgs+2kmkgs+0kmkgs+akmkgs+ | 1 kilometer kilograms seconds plus 2 kilometers kilograms seconds plus 0 kilometers kilograms seconds plus a kilometers kilograms seconds plus |
70 | 1$ | 1 dollar |
71 | $1 | 1 dollars |
72 | $ | dollars |
73 | $ | dollars |
74 | 2$ | 2 dollars |
75 | $2 | 2 dollars |
76 | 1$+2$+0$+a$ | 1 dollar plus 2 dollars plus 0 dollars plus a dollars |
77 | 1$+$2+0$+$a | 1 dollar plus 2 dollars plus 0 dollars plus a dollars |
78 | 1€+2€+0€+a€ | 1 euro plus 2 euros plus 0 euros plus a euros |
79 | 1£+2£+0£+a£ | 1 pound plus 2 pounds plus 0 pounds plus a pounds |
0 | 32 | 3 to the second power |
1 | 33 | 3 to the third power |
2 | 30 | 3 to the zero power |
3 | 31 | 3 to the first power |
4 | 35 | 3 to the fifth power |
5 | 35.0 | 3 raised to the 5.0 power |
6 | 411 | 4 to the eleventh power |
7 | 3−2 | 3 to the negative 2 power |
8 | 3−2.0 | 3 raised to the negative 2.0 power |
9 | 4x | 4 to the x-th power |
10 | 3y+2 | 3 raised to the y plus 2 power |
11 | (2y−3)3z+8 | open paren 2 y minus 3 close paren raised to the 3 z plus 8 power |
12 | p12 | p sub 1 to the second power |
13 | p13 | p sub 1 to the third power |
14 | p14 | p sub 1 to the fourth power |
15 | p110 | p sub 1 to the tenth power |
16 | p1x+1 | p sub 1 raised to the x plus 1 power |
17 | px12 | p sub x sub 1 to the second power |
18 | px13 | p sub x sub 1 to the third power |
19 | px14 | p sub x sub 1 to the fourth power |
20 | px110 | p sub x sub 1 to the tenth power |
21 | px1y+1 | p sub x sub 1 raised to the y plus 1 power |
22 | 322 | 3 raised to the exponent 2 to the second power end exponent |
23 | 32x2 | 3 raised to the exponent 2 x to the second power end exponent |
24 | 523 | 5 raised to the exponent 2 to the third power end exponent |
25 | 52x3 | 5 raised to the exponent 2 x to the third power end exponent |
26 | 322+1 | 3 raised to the exponent 2 to the second power plus 1 end exponent |
27 | 322+1 | 3 raised to the exponent 2 to the second power end exponent plus 1 |
28 | 2x2+3x3 | 2 raised to the exponent x to the second power plus 3 x to the third power end exponent |
29 | 334 | 3 raised to the exponent 3 to the fourth power end exponent |
30 | 334+2 | 3 raised to the exponent 3 to the fourth power plus 2 end exponent |
31 | 334+2 | 3 raised to the exponent 3 to the fourth power end exponent plus 2 |
32 | 2x4 | 2 raised to the exponent x to the fourth power end exponent |
33 | 210x+3 | 2 raised to the exponent 10 raised to the x plus 3 power end exponent |
34 | 3310 | 3 raised to the exponent 3 to the tenth power end exponent |
35 | 3310+1 | 3 raised to the exponent 3 to the tenth power plus 1 end exponent |
36 | 3310+1 | 3 raised to the exponent 3 to the tenth power end exponent plus 1 |
37 | 3(x+1)2 | 3 raised to the exponent open paren x plus 1 close paren to the second power end exponent |
38 | 3(x+1)10 | 3 raised to the exponent open paren x plus 1 close paren to the tenth power end exponent |
39 | 3(x+1)y+2 | 3 raised to the exponent open paren x plus 1 close paren raised to the y plus 2 power end exponent |
40 | 3(x+1)y+2 | 3 raised to the exponent open paren x plus 1 close paren to the y-th power plus 2 end exponent |
41 | 3(x+1)y+2 | 3 raised to the exponent open paren x plus 1 close paren to the y-th power end exponent plus 2 |
42 | e−12x2 | e raised to the exponent negative one half x to the second power end exponent |
43 | e−12(x−μσ)2 | e raised to the exponent negative one half times open paren the fraction with numerator x minus mu and denominator sigma close paren to the second power end exponent |
0 | 32 | 3 raised to the power 2 |
1 | 33 | 3 raised to the power 3 |
2 | 31 | 3 raised to the power 1 |
3 | 30 | 3 raised to the power 0 |
4 | 35 | 3 raised to the power 5 |
5 | 35.0 | 3 raised to the power 5.0 |
6 | 411 | 4 raised to the power 11 |
7 | 3−2 | 3 raised to the power negative 2 |
8 | 3−2.0 | 3 raised to the power negative 2.0 |
9 | 4x | 4 raised to the power x |
10 | 3y+2 | 3 raised to the power y plus 2 |
11 | (2y−3)3z+8 | open paren 2 y minus 3 close paren raised to the power 3 z plus 8 |
12 | p12 | p sub 1 raised to the power 2 |
13 | p13 | p sub 1 raised to the power 3 |
14 | p14 | p sub 1 raised to the power 4 |
15 | p110 | p sub 1 raised to the power 10 |
16 | p1x+1 | p sub 1 raised to the power x plus 1 |
17 | px12 | p sub x sub 1 raised to the power 2 |
18 | px13 | p sub x sub 1 raised to the power 3 |
19 | px14 | p sub x sub 1 raised to the power 4 |
20 | px110 | p sub x sub 1 raised to the power 10 |
21 | px1y+1 | p sub x sub 1 raised to the power y plus 1 |
22 | 322 | 3 raised to the exponent 2 raised to the power 2 end exponent |
23 | 32x2 | 3 raised to the exponent 2 x raised to the power 2 end exponent |
24 | 322 | 3 raised to the exponent 2 raised to the power 2 end exponent |
25 | 32x2 | 3 raised to the exponent 2 x raised to the power 2 end exponent |
26 | 523 | 5 raised to the exponent 2 raised to the power 3 end exponent |
27 | 52x3 | 5 raised to the exponent 2 x raised to the power 3 end exponent |
28 | 322+1 | 3 raised to the exponent 2 raised to the power 2 plus 1 end exponent |
29 | 322+1 | 3 raised to the exponent 2 raised to the power 2 end exponent plus 1 |
30 | 2x2+3x3 | 2 raised to the exponent x raised to the power 2 plus 3 x raised to the power 3 end exponent |
31 | 334 | 3 raised to the exponent 3 raised to the power 4 end exponent |
32 | 334+2 | 3 raised to the exponent 3 raised to the power 4 plus 2 end exponent |
33 | 334+2 | 3 raised to the exponent 3 raised to the power 4 end exponent plus 2 |
34 | 2x4 | 2 raised to the exponent x raised to the power 4 end exponent |
35 | 210x+3 | 2 raised to the exponent 10 raised to the power x plus 3 end exponent |
36 | 3310 | 3 raised to the exponent 3 raised to the power 10 end exponent |
37 | 3310+1 | 3 raised to the exponent 3 raised to the power 10 plus 1 end exponent |
38 | 3310+1 | 3 raised to the exponent 3 raised to the power 10 end exponent plus 1 |
39 | 3(x+1)2 | 3 raised to the exponent open paren x plus 1 close paren raised to the power 2 end exponent |
40 | 3(x+1)10 | 3 raised to the exponent open paren x plus 1 close paren raised to the power 10 end exponent |
41 | 3(x+1)y+2 | 3 raised to the exponent open paren x plus 1 close paren raised to the power y plus 2 end exponent |
42 | 3(x+1)y+2 | 3 raised to the exponent open paren x plus 1 close paren raised to the power y plus 2 end exponent |
43 | 3(x+1)y+2 | 3 raised to the exponent open paren x plus 1 close paren raised to the power y end exponent plus 2 |
44 | e−12x2 | e raised to the exponent negative one half x raised to the power 2 end exponent |
45 | e−12(x−μσ)2 | e raised to the exponent negative one half times open paren the fraction with numerator x minus mu and denominator sigma close paren raised to the power 2 end exponent |
0 | 12 | one half |
1 | 1232 | 12 over 32 |
2 | xy | x over y |
3 | 2x3y | 2 x over 3 y |
4 | xycd | x y over c d |
5 | 1213 | one half over one third |
6 | −xy | negative x over y |
7 | −2x3y | negative 2 x over 3 y |
8 | xy−cd | x y over negative c d |
9 | 12−13 | one half over negative one third |
10 | 2+313 | the fraction with numerator 2 plus 3 and denominator 13 |
11 | x+y2 | the fraction with numerator x plus y and denominator 2 |
12 | x+yx−y | the fraction with numerator x plus y and denominator x minus y |
13 | x+yx−y+23 | the fraction with numerator x plus y and denominator x minus y plus two thirds |
14 | milesgallon | miles over gallon |
15 | 2miles3gallons | 2 miles over 3 gallons |
16 | 2miles3gallons | 2 miles over 3 gallons |
17 | riserun | rise over run |
18 | successful outcomestotal outcomes | successful outcomes over total outcomes |
19 | 6ways of rolling a 736ways of rolling the pair of dice | 6 ways of rolling a 7 over 36 ways of rolling the pair of dice |
20 | 1213 | one half over one third |
21 | 1213 | the fraction with numerator 1 and denominator 2 over one third |
22 | 123 | one half over 3 |
23 | 123 | 1 over two thirds |
24 | 11321651 | the fraction with numerator 11 over 32 and denominator 16 over 51 |
25 | 11321651 | the fraction with numerator 11 and denominator the fraction with numerator 32 and denominator 16 over 51 |
26 | 1+4x2 | the fraction with numerator 1 plus 4 over x and denominator 2 |
27 | 32+4x | the fraction with numerator 3 and denominator 2 plus 4 over x |
28 | 102212 | the fraction with numerator 10 over 22 and denominator one half |
29 | 1+231−23 | the fraction with numerator 1 plus two thirds and denominator 1 minus two thirds |
30 | 1+x21−x2 | the fraction with numerator 1 plus x over 2 and denominator 1 minus x over 2 |
31 | x+1x−1+1x+1 | the fraction with numerator the fraction with numerator x plus 1 and denominator x minus 1 plus 1 and denominator x plus 1 |
32 | x+1x−4+12x+116 | the fraction with numerator the fraction with numerator x plus 1 and denominator x minus 4 plus one half and denominator x plus 1 over 16 |
33 | 1+x1+2x | 1 plus the fraction with numerator x and denominator 1 plus 2 over x |
34 | 1+x+31+2x+3 | 1 plus the fraction with numerator x plus 3 and denominator 1 plus the fraction with numerator 2 and denominator x plus 3 |
35 | 1+11+11+11+1 | 1 plus the fraction with numerator 1 and denominator 1 plus the fraction with numerator 1 and denominator 1 plus the fraction with numerator 1 and denominator 1 plus 1 |
36 | 1+11+11+11+⋯ | 1 plus the fraction with numerator 1 and denominator 1 plus the fraction with numerator 1 and denominator 1 plus the fraction with numerator 1 and denominator 1 plus dot dot dot |
37 | a0+1a1+1a2+1a3+⋯ | a sub 0 plus the fraction with numerator 1 and denominator a sub 1 plus the fraction with numerator 1 and denominator a sub 2 plus the fraction with numerator 1 and denominator a sub 3 plus dot dot dot |
38 | f(x)g(x) | f of x over g of x |
39 | f(x)+g(x)g(x) | the fraction with numerator f of x plus g of x and denominator g of x |
40 | f(x+1)g(x) | the fraction with numerator f of open paren x plus 1 close paren and denominator g of x |
41 | f(x)2 | f of x over 2 |
42 | 2f(x) | 2 over f of x |
43 | 2g(x)+g(x+1) | the fraction with numerator 2 and denominator g of x plus g of open paren x plus 1 close paren |
44 | sinxcosx | sine x over cosine x |
45 | sinx+cosxcosx | the fraction with numerator sine x plus cosine x and denominator cosine x |
46 | sin2xcos3x | sine 2 x over cosine 3 x |
47 | sin(x+y)cos(x+y) | the fraction with numerator the sine of open paren x plus y close paren and denominator the cosine of open paren x plus y close paren |
48 | f(2x)g(3x) | f of 2 x over g of 3 x |
49 | logxlogy | log x over log y |
50 | log2xlog3y | log 2 x over log 3 y |
51 | log10xlog5y | the log base 10 of x over the log base 5 of y |
52 | log102xlog53y | the log base 10 of 2 x over the log base 5 of 3 y |
53 | log(x+1)logy | the fraction with numerator the log of open paren x plus 1 close paren and denominator log y |
54 | f1(x)g1(x) | f sub 1 of x over g sub 1 of x |
0 | f(x) | f of x |
1 | g(x) | g of x |
2 | h(x) | h of x |
3 | f(2x) | f of 2 x |
4 | g(−2x) | g of negative 2 x |
5 | h(12) | h of one half |
6 | f(x+1)=f(x)+1 | f of open paren x plus 1 close paren equals f of x plus 1 |
7 | g(2x+1) | g of open paren 2 x plus 1 close paren |
8 | g(x2) | g of open paren x squared close paren |
9 | f−1(x) | f inverse of x |
10 | g−1(x) | g inverse of x |
11 | h−1(x) | h inverse of x |
12 | f−1(2x) | f inverse of 2 x |
13 | g−1(−2x) | g inverse of negative 2 x |
14 | f−1(3x−1) | f inverse of open paren 3 x minus 1 close paren |
15 | g−1(x2) | g inverse of open paren x squared close paren |
16 | h−1(12) | h inverse of one half |
17 | f−1(f(x)) | f inverse of f of x |
18 | g−1(g(x)) | g inverse of g of x |
19 | h−1(h(x)) | h inverse of h of x |
20 | f−1(f(2x)) | f inverse of f of 2 x |
21 | g−1(g(−2x)) | g inverse of g of negative 2 x |
22 | h−1(h(12)) | h inverse of h of one half |
23 | f−1(f(x+1))=x+1 | f inverse of open paren f of open paren x plus 1 close paren close paren equals x plus 1 |
24 | g−1(g(2x+1)) | g inverse of open paren g of open paren 2 x plus 1 close paren close paren |
25 | g−1(g(x2)) | g inverse of open paren g of open paren x squared close paren close paren |
26 | f(f−1(x)) | f of f inverse of x |
27 | g(g−1(x)) | g of g inverse of x |
28 | h(h−1(x)) | h of h inverse of x |
29 | f(f−1(2x)) | f of f inverse of 2 x |
30 | g(g−1(−2x)) | g of g inverse of negative 2 x |
31 | f(f−1(3x−1)) | f of open paren f inverse of open paren 3 x minus 1 close paren close paren |
32 | g(g−1(x2)) | g of g inverse of open paren x squared close paren |
33 | h(h−1(12)) | h of h inverse of one half |
34 | f(g(x)) | f of g of x |
35 | f(g(x+1)) | f of open paren g of open paren x plus 1 close paren close paren |
36 | h(g(x)) | h of g of x |
37 | h(g(xx+1)) | h of open paren g of open paren the fraction with numerator x and denominator x plus 1 close paren close paren |
38 | (f+g)(x)=f(x)+g(x) | open paren f plus g close paren of x equals f of x plus g of x |
39 | (f+g)(x+1)=f(x+1)+g(x+1) | open paren f plus g close paren of open paren x plus 1 close paren equals f of open paren x plus 1 close paren plus g of open paren x plus 1 close paren |
40 | (f⋅g)(x) | open paren f times g close paren of x |
41 | (f⋅g)(2x+5) | open paren f times g close paren of open paren 2 x plus 5 close paren |
42 | (fg)(x)=f(x)g(x) | open paren f over g close paren of x equals f of x over g of x |
43 | (fg)(2x+5)=f(2x+5)g(2x+5) | open paren f over g close paren of open paren 2 x plus 5 close paren equals the fraction with numerator f of open paren 2 x plus 5 close paren and denominator g of open paren 2 x plus 5 close paren |
44 | (f∘g)(x)=f(g(x)) | open paren f composed with g close paren of x equals f of g of x |
45 | 2f(x) | 2 f of x |
46 | cf(x) | c f of x |
47 | f2(x) | f squared of x |
48 | f2(2x+1) | f squared of open paren 2 x plus 1 close paren |
49 | f3(x) | f cubed of x |
50 | f3(2x+1) | f cubed of open paren 2 x plus 1 close paren |
51 | f4(x) | the fourth power of f of x |
52 | f4(2x+1) | the fourth power of f of open paren 2 x plus 1 close paren |
53 | f5(x) | the fifth power of f of x |
54 | f5(2x+1) | the fifth power of f of open paren 2 x plus 1 close paren |
55 | fn(x) | the n-th power of f of x |
56 | fn(2x+1) | the n-th power of f of open paren 2 x plus 1 close paren |
57 | g2(x) | g squared of x |
58 | g2(2x+1) | g squared of open paren 2 x plus 1 close paren |
59 | h3(x) | h cubed of x |
60 | h3(2x+1) | h cubed of open paren 2 x plus 1 close paren |
61 | g4(x) | the fourth power of g of x |
62 | g4(2x+1) | the fourth power of g of open paren 2 x plus 1 close paren |
63 | h5(x) | the fifth power of h of x |
64 | h5(2x+1) | the fifth power of h of open paren 2 x plus 1 close paren |
65 | gn(x) | the n-th power of g of x |
66 | gn(2x+1) | the n-th power of g of open paren 2 x plus 1 close paren |
67 | f1(x) | f sub 1 of x |
68 | g2(x3) | g sub 2 of open paren x cubed close paren |
69 | hn(3x−2) | h sub n of open paren 3 x minus 2 close paren |
70 | f1−1(x) | f sub 1 inverse of x |
71 | g2−1(2x+1) | g sub 2 inverse of open paren 2 x plus 1 close paren |
72 | hn−1(x) | h sub n inverse of x |
73 | g1−1(g2(x)) | g sub 1 inverse of g sub 2 of x |
74 | f1(g2−1(x)) | f sub 1 of g sub 2 inverse of x |
75 | f(x,y) | f of open paren x comma y close paren |
76 | f(x,y,z) | f of open paren x comma y comma z close paren |
77 | f(x+1,2y) | f of open paren x plus 1 comma 2 y close paren |
78 | f(2x,x+1,x2) | f of open paren 2 x comma x plus 1 comma x squared close paren |
0 | f(x) | f times x |
1 | g(x) | g times x |
2 | h(x) | h times x |
3 | f(2x) | f times 2 x |
4 | g(−2x) | g times negative 2 x |
5 | h(12) | h times one half |
6 | f(x+1)=f(x)+1 | f times open paren x plus 1 close paren equals f times x plus 1 |
7 | g(2x+1) | g times open paren 2 x plus 1 close paren |
8 | g(x2) | g times open paren x squared close paren |
9 | f−1(x) | f to the negative 1 power times x |
10 | g−1(x) | g to the negative 1 power times x |
11 | h−1(x) | h to the negative 1 power times x |
12 | f−1(2x) | f to the negative 1 power times 2 x |
13 | g−1(−2x) | g to the negative 1 power times negative 2 x |
14 | f−1(3x−1) | f to the negative 1 power times open paren 3 x minus 1 close paren |
15 | g−1(x2) | g to the negative 1 power times open paren x squared close paren |
16 | h−1(12) | h to the negative 1 power times one half |
17 | f−1(f(x)) | f to the negative 1 power times f times x |
18 | g−1(g(x)) | g to the negative 1 power times g times x |
19 | h−1(h(x)) | h to the negative 1 power times h times x |
20 | f−1(f(2x)) | f to the negative 1 power times f times 2 x |
21 | g−1(g(−2x)) | g to the negative 1 power times g times negative 2 x |
22 | h−1(h(12)) | h to the negative 1 power times h times one half |
23 | f−1(f(x+1))=x+1 | f to the negative 1 power times open paren f times open paren x plus 1 close paren close paren equals x plus 1 |
24 | g−1(g(2x+1)) | g to the negative 1 power times open paren g times open paren 2 x plus 1 close paren close paren |
25 | g−1(g(x2)) | g to the negative 1 power times open paren g times open paren x squared close paren close paren |
26 | f(f−1(x)) | f times open paren f to the negative 1 power times x close paren |
27 | g(g−1(x)) | g times open paren g to the negative 1 power times x close paren |
28 | h(h−1(x)) | h times open paren h to the negative 1 power times x close paren |
29 | f(f−1(2x)) | f times open paren f to the negative 1 power times 2 x close paren |
30 | g(g−1(−2x)) | g times open paren g to the negative 1 power times negative 2 x close paren |
31 | f(f−1(3x−1)) | f times open paren f to the negative 1 power times open paren 3 x minus 1 close paren close paren |
32 | g(g−1(x2)) | g times open paren g to the negative 1 power times open paren x squared close paren close paren |
33 | h(h−1(12)) | h times open paren h to the negative 1 power times one half close paren |
34 | f(g(x)) | f times g times x |
35 | f(g(x+1)) | f times open paren g times open paren x plus 1 close paren close paren |
36 | h(g(x)) | h times g times x |
37 | h(g(xx+1)) | h times open paren g times open paren the fraction with numerator x and denominator x plus 1 close paren close paren |
38 | (f+g)(x)=f(x)+g(x) | open paren f plus g close paren times x equals f times x plus g times x |
39 | (f+g)(x+1)=f(x+1)+g(x+1) | open paren f plus g close paren times open paren x plus 1 close paren equals f times open paren x plus 1 close paren plus g times open paren x plus 1 close paren |
40 | (f⋅g)(x) | open paren f times g close paren times x |
41 | (f⋅g)(2x+5) | open paren f times g close paren times open paren 2 x plus 5 close paren |
42 | (fg)(x)=f(x)g(x) | open paren f over g close paren times x equals the fraction with numerator f times x and denominator g times x |
43 | (fg)(2x+5)=f(2x+5)g(2x+5) | open paren f over g close paren times open paren 2 x plus 5 close paren equals the fraction with numerator f times open paren 2 x plus 5 close paren and denominator g times open paren 2 x plus 5 close paren |
44 | 2f(x) | 2 f times x |
45 | cf(x) | c f times x |
46 | f2(x) | f squared times x |
47 | f2(2x+1) | f squared times open paren 2 x plus 1 close paren |
48 | f3(x) | f cubed times x |
49 | f3(2x+1) | f cubed times open paren 2 x plus 1 close paren |
50 | f4(x) | f to the fourth power times x |
51 | f4(2x+1) | f to the fourth power times open paren 2 x plus 1 close paren |
52 | f5(x) | f to the fifth power times x |
53 | f5(2x+1) | f to the fifth power times open paren 2 x plus 1 close paren |
54 | fn(x) | f to the n-th power times x |
55 | fn(2x+1) | f to the n-th power times open paren 2 x plus 1 close paren |
56 | g2(x) | g squared times x |
57 | g2(2x+1) | g squared times open paren 2 x plus 1 close paren |
58 | h3(x) | h cubed times x |
59 | h3(2x+1) | h cubed times open paren 2 x plus 1 close paren |
60 | g4(x) | g to the fourth power times x |
61 | g4(2x+1) | g to the fourth power times open paren 2 x plus 1 close paren |
62 | h5(x) | h to the fifth power times x |
63 | h5(2x+1) | h to the fifth power times open paren 2 x plus 1 close paren |
64 | gn(x) | g to the n-th power times x |
65 | gn(2x+1) | g to the n-th power times open paren 2 x plus 1 close paren |
66 | f1(x) | f sub 1 times x |
67 | g2(x3) | g sub 2 times open paren x cubed close paren |
68 | hn(3x−2) | h sub n times open paren 3 x minus 2 close paren |
69 | f1−1(x) | f sub 1 to the negative 1 power times x |
70 | g2−1(2x+1) | g sub 2 to the negative 1 power times open paren 2 x plus 1 close paren |
71 | hn−1(x) | h sub n to the negative 1 power times x |
72 | g1−1(g2(x)) | g sub 1 to the negative 1 power times open paren g sub 2 times x close paren |
73 | f1(g2−1(x)) | f sub 1 times open paren g sub 2 to the negative 1 power times x close paren |
74 | f(x,y) | f times open paren x comma y close paren |
75 | f(x,y,z) | f times open paren x comma y comma z close paren |
76 | f(x+1,2y) | f times open paren x plus 1 comma 2 y close paren |
77 | f(2x,x+1,x2) | f times open paren 2 x comma x plus 1 comma x squared close paren |
0 | (2175) | the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 |
1 | [2175] | the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 |
2 | (314026) | the 2 by 3 matrix Row 1: 3 1 4 Row 2: 0 2 6 |
3 | [314026] | the 2 by 3 matrix Row 1: 3 1 4 Row 2: 0 2 6 |
4 | (123) | the 3 by 1 column matrix 1 2 3 |
5 | [123] | the 3 by 1 column matrix 1 2 3 |
6 | (35) | the 1 by 2 row matrix 3 5 |
7 | [35] | the 1 by 2 row matrix 3 5 |
8 | (3) | the 1 by 1 matrix with entry 3 |
9 | (3) | the 1 by 1 matrix with entry 3 |
10 | (x+1x−1) | the 2 by 1 column matrix Row 1: x plus 1 Row 2: x minus 1 |
11 | (3612) | the 4 by 1 column matrix Row 1: 3 Row 2: 6 Row 3: 1 Row 4: 2 |
12 | (x+12x) | the 1 by 2 row matrix Column 1: x plus 1 Column 2: 2 x |
13 | (3612) | the 1 by 4 row matrix Column 1: 3 Column 2: 6 Column 3: 1 Column 4: 2 |
14 | (241352147) | the 3 by 3 matrix Row 1: 2 4 1 Row 2: 3 5 2 Row 3: 1 4 7 |
15 | (0343210930216290) | the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 |
16 | (2105334270) | the 2 by 5 matrix Row 1: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 5 Column 5, 3 Row 2: Column 1, 3 Column 2, 4 Column 3, 2 Column 4, 7 Column 5, 0 |
17 | (13422105) | the 4 by 2 matrix Row 1: Column 1, 1 Column 2, 3 Row 2: Column 1, 4 Column 2, 2 Row 3: Column 1, 2 Column 2, 1 Row 4: Column 1, 0 Column 2, 5 |
18 | (2175+x) | the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 plus x |
19 | (31−x4026) | the 2 by 3 matrix Row 1: Column 1, 3 Column 2, 1 minus x Column 3, 4 Row 2: Column 1, 0 Column 2, 2 Column 3, 6 |
20 | (2x175) | the 2 by 2 matrix Row 1: 2 x 1 Row 2: 7 5 |
21 | (2xy1223) | the 2 by 2 matrix Row 1: 2 x y Row 2: one half two thirds |
22 | (12233415) | the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth |
23 | (b11b12b21b22) | the 2 by 2 matrix Row 1: b sub 1 1 b sub 1 2 Row 2: b sub 2 1 b sub 2 2 |
24 | 3(2175)(314026) | 3 times the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 times the 2 by 3 matrix Row 1: 3 1 4 Row 2: 0 2 6 |
25 | (12233415)(31−x4026) | the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth times the 2 by 3 matrix Row 1: Column 1, 3 Column 2, 1 minus x Column 3, 4 Row 2: Column 1, 0 Column 2, 2 Column 3, 6 |
26 | (0343210930216290)(13422105) | the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 times the 4 by 2 matrix Row 1: Column 1, 1 Column 2, 3 Row 2: Column 1, 4 Column 2, 2 Row 3: Column 1, 2 Column 2, 1 Row 4: Column 1, 0 Column 2, 5 |
27 | |2175| | the determinant of the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 |
28 | det(2175) | the determinant of the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 |
29 | |241352147| | the determinant of the 3 by 3 matrix Row 1: 2 4 1 Row 2: 3 5 2 Row 3: 1 4 7 |
30 | det(241352147) | the determinant of the 3 by 3 matrix Row 1: 2 4 1 Row 2: 3 5 2 Row 3: 1 4 7 |
31 | |0343210930216290| | the determinant of the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 |
32 | det(0343210930216290) | the determinant of the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 |
33 | |2175+x| | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 plus x |
34 | det(2175+x) | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 plus x |
35 | |2x175| | the determinant of the 2 by 2 matrix Row 1: 2 x 1 Row 2: 7 5 |
36 | det(2x175) | the determinant of the 2 by 2 matrix Row 1: 2 x 1 Row 2: 7 5 |
37 | |2xy1223| | the determinant of the 2 by 2 matrix Row 1: 2 x y Row 2: one half two thirds |
38 | det(2xy1223) | the determinant of the 2 by 2 matrix Row 1: 2 x y Row 2: one half two thirds |
39 | |12233415| | the determinant of the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth |
40 | det(12233415) | the determinant of the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth |
0 | (2175) | the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 |
1 | [2175] | the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 |
2 | (314026) | the 2 by 3 matrix Row 1: Column 1, 3 Column 2, 1 Column 3, 4 Row 2: Column 1, 0 Column 2, 2 Column 3, 6 |
3 | [314026] | the 2 by 3 matrix Row 1: Column 1, 3 Column 2, 1 Column 3, 4 Row 2: Column 1, 0 Column 2, 2 Column 3, 6 |
4 | (123) | the 3 by 1 column matrix Row 1: 1 Row 2: 2 Row 3: 3 |
5 | [123] | the 3 by 1 column matrix Row 1: 1 Row 2: 2 Row 3: 3 |
6 | (35) | the 1 by 2 row matrix Column 1: 3 Column 2: 5 |
7 | [35] | the 1 by 2 row matrix Column 1: 3 Column 2: 5 |
8 | (1234) | the 1 by 4 row matrix Column 1: 1 Column 2: 2 Column 3: 3 Column 4: 4 |
9 | [1234] | the 1 by 4 row matrix Column 1: 1 Column 2: 2 Column 3: 3 Column 4: 4 |
10 | (1234) | the 4 by 1 column matrix Row 1: 1 Row 2: 2 Row 3: 3 Row 4: 4 |
11 | [1234] | the 4 by 1 column matrix Row 1: 1 Row 2: 2 Row 3: 3 Row 4: 4 |
12 | (x+1x−1) | the 2 by 1 column matrix Row 1: x plus 1 Row 2: x minus 1 |
13 | (3612) | the 4 by 1 column matrix Row 1: 3 Row 2: 6 Row 3: 1 Row 4: 2 |
14 | (x+12x) | the 1 by 2 row matrix Column 1: x plus 1 Column 2: 2 x |
15 | (3612) | the 1 by 4 row matrix Column 1: 3 Column 2: 6 Column 3: 1 Column 4: 2 |
16 | (241352147) | the 3 by 3 matrix Row 1: Column 1, 2 Column 2, 4 Column 3, 1 Row 2: Column 1, 3 Column 2, 5 Column 3, 2 Row 3: Column 1, 1 Column 2, 4 Column 3, 7 |
17 | (0343210930216290) | the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 |
18 | (2105334270) | the 2 by 5 matrix Row 1: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 5 Column 5, 3 Row 2: Column 1, 3 Column 2, 4 Column 3, 2 Column 4, 7 Column 5, 0 |
19 | (13422105) | the 4 by 2 matrix Row 1: Column 1, 1 Column 2, 3 Row 2: Column 1, 4 Column 2, 2 Row 3: Column 1, 2 Column 2, 1 Row 4: Column 1, 0 Column 2, 5 |
20 | (2175+x) | the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 plus x |
21 | (31−x4026) | the 2 by 3 matrix Row 1: Column 1, 3 Column 2, 1 minus x Column 3, 4 Row 2: Column 1, 0 Column 2, 2 Column 3, 6 |
22 | (2x175) | the 2 by 2 matrix Row 1: Column 1, 2 x Column 2, 1 Row 2: Column 1, 7 Column 2, 5 |
23 | (2xy1223) | the 2 by 2 matrix Row 1: Column 1, 2 x Column 2, y Row 2: Column 1, one half Column 2, two thirds |
24 | (12233415) | the 2 by 2 matrix Row 1: Column 1, one half Column 2, two thirds Row 2: Column 1, three fourths Column 2, one fifth |
25 | (b11b12b21b22) | the 2 by 2 matrix Row 1: Column 1, b sub 1 1 Column 2, b sub 1 2 Row 2: Column 1, b sub 2 1 Column 2, b sub 2 2 |
26 | 3(2175)(314026) | 3 times the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 times the 2 by 3 matrix Row 1: Column 1, 3 Column 2, 1 Column 3, 4 Row 2: Column 1, 0 Column 2, 2 Column 3, 6 |
27 | (12233415)(31−x4026) | the 2 by 2 matrix Row 1: Column 1, one half Column 2, two thirds Row 2: Column 1, three fourths Column 2, one fifth times the 2 by 3 matrix Row 1: Column 1, 3 Column 2, 1 minus x Column 3, 4 Row 2: Column 1, 0 Column 2, 2 Column 3, 6 |
28 | (0343210930216290)(13422105) | the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 times the 4 by 2 matrix Row 1: Column 1, 1 Column 2, 3 Row 2: Column 1, 4 Column 2, 2 Row 3: Column 1, 2 Column 2, 1 Row 4: Column 1, 0 Column 2, 5 |
29 | |2175| | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 |
30 | det(2175) | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 |
31 | |241352147| | the determinant of the 3 by 3 matrix Row 1: Column 1, 2 Column 2, 4 Column 3, 1 Row 2: Column 1, 3 Column 2, 5 Column 3, 2 Row 3: Column 1, 1 Column 2, 4 Column 3, 7 |
32 | det(241352147) | the determinant of the 3 by 3 matrix Row 1: Column 1, 2 Column 2, 4 Column 3, 1 Row 2: Column 1, 3 Column 2, 5 Column 3, 2 Row 3: Column 1, 1 Column 2, 4 Column 3, 7 |
33 | |0343210930216290| | the determinant of the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 |
34 | det(0343210930216290) | the determinant of the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 |
35 | |2175+x| | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 plus x |
36 | det(2175+x) | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 plus x |
37 | |2x175| | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 x Column 2, 1 Row 2: Column 1, 7 Column 2, 5 |
38 | det(2x175) | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 x Column 2, 1 Row 2: Column 1, 7 Column 2, 5 |
39 | |2xy1223| | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 x Column 2, y Row 2: Column 1, one half Column 2, two thirds |
40 | det(2xy1223) | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 x Column 2, y Row 2: Column 1, one half Column 2, two thirds |
41 | |12233415| | the determinant of the 2 by 2 matrix Row 1: Column 1, one half Column 2, two thirds Row 2: Column 1, three fourths Column 2, one fifth |
42 | det(12233415) | the determinant of the 2 by 2 matrix Row 1: Column 1, one half Column 2, two thirds Row 2: Column 1, three fourths Column 2, one fifth |
0 | (2175) | the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 |
1 | [2175] | the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 |
2 | (314026) | the 2 by 3 matrix Row 1: 3 1 4 Row 2: 0 2 6 |
3 | [314026] | the 2 by 3 matrix Row 1: 3 1 4 Row 2: 0 2 6 |
4 | (123) | the 3 by 1 column matrix 1 2 3 |
5 | [123] | the 3 by 1 column matrix 1 2 3 |
6 | (35) | the 1 by 2 row matrix 3 5 |
7 | [35] | the 1 by 2 row matrix 3 5 |
8 | (x+1x−1) | the 2 by 1 column matrix x plus 1 x minus 1 |
9 | (3612) | the 4 by 1 column matrix 3 6 1 2 |
10 | (x+12x) | the 1 by 2 row matrix x plus 1 2 x |
11 | (3612) | the 1 by 4 row matrix 3 6 1 2 |
12 | (241352147) | the 3 by 3 matrix Row 1: 2 4 1 Row 2: 3 5 2 Row 3: 1 4 7 |
13 | (0343210930216290) | the 4 by 4 matrix Row 1: 0 3 4 3 Row 2: 2 1 0 9 Row 3: 3 0 2 1 Row 4: 6 2 9 0 |
14 | (2105334270) | the 2 by 5 matrix Row 1: 2 1 0 5 3 Row 2: 3 4 2 7 0 |
15 | (13422105) | the 4 by 2 matrix Row 1: 1 3 Row 2: 4 2 Row 3: 2 1 Row 4: 0 5 |
16 | (2175+x) | the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 plus x |
17 | (31−x4026) | the 2 by 3 matrix Row 1: 3 1 minus x 4 Row 2: 0 2 6 |
18 | (2x175) | the 2 by 2 matrix Row 1: 2 x 1 Row 2: 7 5 |
19 | (2xy1223) | the 2 by 2 matrix Row 1: 2 x y Row 2: one half two thirds |
20 | (12233415) | the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth |
21 | (b11b12b21b22) | the 2 by 2 matrix Row 1: b sub 1 1 b sub 1 2 Row 2: b sub 2 1 b sub 2 2 |
22 | 3(2175)(314026) | 3 times the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 times the 2 by 3 matrix Row 1: 3 1 4 Row 2: 0 2 6 |
23 | (12233415)(31−x4026) | the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth times the 2 by 3 matrix Row 1: 3 1 minus x 4 Row 2: 0 2 6 |
24 | (0343210930216290)(13422105) | the 4 by 4 matrix Row 1: 0 3 4 3 Row 2: 2 1 0 9 Row 3: 3 0 2 1 Row 4: 6 2 9 0 times the 4 by 2 matrix Row 1: 1 3 Row 2: 4 2 Row 3: 2 1 Row 4: 0 5 |
25 | |2175| | the determinant of the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 |
26 | det(2175) | the determinant of the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 |
27 | |241352147| | the determinant of the 3 by 3 matrix Row 1: 2 4 1 Row 2: 3 5 2 Row 3: 1 4 7 |
28 | det(241352147) | the determinant of the 3 by 3 matrix Row 1: 2 4 1 Row 2: 3 5 2 Row 3: 1 4 7 |
29 | |0343210930216290| | the determinant of the 4 by 4 matrix Row 1: 0 3 4 3 Row 2: 2 1 0 9 Row 3: 3 0 2 1 Row 4: 6 2 9 0 |
30 | det(0343210930216290) | the determinant of the 4 by 4 matrix Row 1: 0 3 4 3 Row 2: 2 1 0 9 Row 3: 3 0 2 1 Row 4: 6 2 9 0 |
31 | |2175+x| | the determinant of the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 plus x |
32 | det(2175+x) | the determinant of the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 plus x |
33 | |2x175| | the determinant of the 2 by 2 matrix Row 1: 2 x 1 Row 2: 7 5 |
34 | det(2x175) | the determinant of the 2 by 2 matrix Row 1: 2 x 1 Row 2: 7 5 |
35 | |2xy1223| | the determinant of the 2 by 2 matrix Row 1: 2 x y Row 2: one half two thirds |
36 | det(2xy1223) | the determinant of the 2 by 2 matrix Row 1: 2 x y Row 2: one half two thirds |
37 | |12233415| | the determinant of the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth |
38 | det(12233415) | the determinant of the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth |
0 | (2175) | the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 end matrix |
1 | [2175] | the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 end matrix |
2 | (314026) | the 2 by 3 matrix Row 1: 3 1 4 Row 2: 0 2 6 end matrix |
3 | [314026] | the 2 by 3 matrix Row 1: 3 1 4 Row 2: 0 2 6 end matrix |
4 | (123) | the 3 by 1 column matrix 1 2 3 end matrix |
5 | [123] | the 3 by 1 column matrix 1 2 3 end matrix |
6 | (35) | the 1 by 2 row matrix 3 5 end matrix |
7 | [35] | the 1 by 2 row matrix 3 5 end matrix |
8 | (x+1x−1) | the 2 by 1 column matrix Row 1: x plus 1 Row 2: x minus 1 end matrix |
9 | (3612) | the 4 by 1 column matrix Row 1: 3 Row 2: 6 Row 3: 1 Row 4: 2 end matrix |
10 | (x+12x) | the 1 by 2 row matrix Column 1: x plus 1 Column 2: 2 x end matrix |
11 | (3612) | the 1 by 4 row matrix Column 1: 3 Column 2: 6 Column 3: 1 Column 4: 2 end matrix |
12 | (241352147) | the 3 by 3 matrix Row 1: 2 4 1 Row 2: 3 5 2 Row 3: 1 4 7 end matrix |
13 | (0343210930216290) | the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 end matrix |
14 | (2105334270) | the 2 by 5 matrix Row 1: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 5 Column 5, 3 Row 2: Column 1, 3 Column 2, 4 Column 3, 2 Column 4, 7 Column 5, 0 end matrix |
15 | (13422105) | the 4 by 2 matrix Row 1: Column 1, 1 Column 2, 3 Row 2: Column 1, 4 Column 2, 2 Row 3: Column 1, 2 Column 2, 1 Row 4: Column 1, 0 Column 2, 5 end matrix |
16 | (2175+x) | the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 plus x end matrix |
17 | (31−x4026) | the 2 by 3 matrix Row 1: Column 1, 3 Column 2, 1 minus x Column 3, 4 Row 2: Column 1, 0 Column 2, 2 Column 3, 6 end matrix |
18 | (2x175) | the 2 by 2 matrix Row 1: 2 x 1 Row 2: 7 5 end matrix |
19 | (2xy1223) | the 2 by 2 matrix Row 1: 2 x y Row 2: one half two thirds end matrix |
20 | (12233415) | the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth end matrix |
21 | (b11b12b21b22) | the 2 by 2 matrix Row 1: b sub 1 1 b sub 1 2 Row 2: b sub 2 1 b sub 2 2 end matrix |
22 | 3(2175)(314026) | 3 times the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 end matrix times the 2 by 3 matrix Row 1: 3 1 4 Row 2: 0 2 6 end matrix |
23 | (12233415)(31−x4026) | the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth end matrix times the 2 by 3 matrix Row 1: Column 1, 3 Column 2, 1 minus x Column 3, 4 Row 2: Column 1, 0 Column 2, 2 Column 3, 6 end matrix |
24 | (0343210930216290)(13422105) | the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 end matrix times the 4 by 2 matrix Row 1: Column 1, 1 Column 2, 3 Row 2: Column 1, 4 Column 2, 2 Row 3: Column 1, 2 Column 2, 1 Row 4: Column 1, 0 Column 2, 5 end matrix |
25 | |2175| | the determinant of the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 end determinant |
26 | det(2175) | the determinant of the 2 by 2 matrix Row 1: 2 1 Row 2: 7 5 end matrix |
27 | |241352147| | the determinant of the 3 by 3 matrix Row 1: 2 4 1 Row 2: 3 5 2 Row 3: 1 4 7 end determinant |
28 | det(241352147) | the determinant of the 3 by 3 matrix Row 1: 2 4 1 Row 2: 3 5 2 Row 3: 1 4 7 end matrix |
29 | |0343210930216290| | the determinant of the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 end determinant |
30 | det(0343210930216290) | the determinant of the 4 by 4 matrix Row 1: Column 1, 0 Column 2, 3 Column 3, 4 Column 4, 3 Row 2: Column 1, 2 Column 2, 1 Column 3, 0 Column 4, 9 Row 3: Column 1, 3 Column 2, 0 Column 3, 2 Column 4, 1 Row 4: Column 1, 6 Column 2, 2 Column 3, 9 Column 4, 0 end matrix |
31 | |2175+x| | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 plus x end determinant |
32 | det(2175+x) | the determinant of the 2 by 2 matrix Row 1: Column 1, 2 Column 2, 1 Row 2: Column 1, 7 Column 2, 5 plus x end matrix |
33 | |2x175| | the determinant of the 2 by 2 matrix Row 1: 2 x 1 Row 2: 7 5 end determinant |
34 | det(2x175) | the determinant of the 2 by 2 matrix Row 1: 2 x 1 Row 2: 7 5 end matrix |
35 | |2xy1223| | the determinant of the 2 by 2 matrix Row 1: 2 x y Row 2: one half two thirds end determinant |
36 | det(2xy1223) | the determinant of the 2 by 2 matrix Row 1: 2 x y Row 2: one half two thirds end matrix |
37 | |12233415| | the determinant of the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth end determinant |
38 | det(12233415) | the determinant of the 2 by 2 matrix Row 1: one half two thirds Row 2: three fourths one fifth end matrix |
0 | sinx | sine x |
1 | cosx | cosine x |
2 | tanθ | tangent theta |
3 | secθ | secant theta |
4 | cscx | cosecant x |
5 | cotx | cotangent x |
6 | sin2x | sine squared x |
7 | cos3x | cosine cubed x |
8 | tan2x | tangent squared x |
9 | sec3x | secant cubed x |
10 | csc2x | cosecant squared x |
11 | cot2x | cotangent squared x |
12 | sin2π | sine 2 pi |
13 | sin(πk+π2) | the sine of open paren pi k plus pi over 2 close paren |
14 | cosπ2 | the cosine of pi over 2 |
15 | sinπ2 | the sine of pi over 2 |
16 | sinπ2 | sine pi over 2 |
17 | 2sinπ | 2 over sine pi |
18 | sinπ23 | the fraction with numerator the sine of pi over 2 and denominator 3 |
19 | tan(−π) | tangent negative pi |
20 | sin(x+π) | the sine of open paren x plus pi close paren |
21 | cos(x+π2) | the cosine of open paren x plus pi over 2 close paren |
22 | cos(π2+x) | the cosine of open paren pi over 2 plus x close paren |
23 | sin2x+cos2x=1 | sine squared x plus cosine squared x equals 1 |
24 | sin4x | the fourth power of sine x |
25 | cos5x | the fifth power of cosine x |
26 | tannx | the n-th power of tangent x |
27 | sinxcosx | sine x over cosine x |
28 | tan35° | tangent 35 degrees |
29 | tan(∠DEF) | the tangent of open paren angle D E F close paren |
30 | tan(∠D) | the tangent of open paren angle D close paren |
31 | sin(x+y)=sinxcosy+cosxsiny | the sine of open paren x plus y close paren equals sine x cosine y plus cosine x sine y |
32 | cos(x+y)=cosxcosy−sinxsiny | the cosine of open paren x plus y close paren equals cosine x cosine y minus sine x sine y |
33 | tan(x+y)=tanx−tany1−tanxtany | the tangent of open paren x plus y close paren equals the fraction with numerator tangent x minus tangent y and denominator 1 minus tangent x tangent y |
34 | tan(π6+2π3)=tanπ6−tan2π31−tanπ6tan2π3 | the tangent of open paren pi over 6 plus 2 pi over 3 close paren equals the fraction with numerator the tangent of pi over 6 minus the tangent of 2 pi over 3 and denominator 1 minus the tangent of pi over 6 the tangent of 2 pi over 3 |
35 | tan2x=2tanx1−tan2x | tangent 2 x equals the fraction with numerator 2 tangent x and denominator 1 minus tangent squared x |
36 | cos2x=2cos2x−1 | cosine 2 x equals 2 cosine squared x minus 1 |
37 | sinx2=±1−cosx2 | the sine of x over 2 equals plus or minus the square root of the fraction with numerator 1 minus cosine x and denominator 2 |
38 | tanx2=±1−cosx1+cosx | the tangent of x over 2 equals plus or minus the square root of the fraction with numerator 1 minus cosine x and denominator 1 plus cosine x |
39 | cosxcosy=2cosx+y2cosx−y2 | cosine x cosine y equals 2 the cosine of the fraction with numerator x plus y and denominator 2 the cosine of the fraction with numerator x minus y and denominator 2 |
40 | sin−1x | the inverse sine of x |
41 | cos−1x | the inverse cosine of x |
42 | tan−1x | the inverse tangent of x |
43 | cot−1x | the inverse cotangent of x |
44 | sec−1x | the inverse secant of x |
45 | csc−1x | the inverse cosecant of x |
46 | sin−122 | the inverse sine of the fraction with numerator the square root of 2 and denominator 2 |
47 | cos−112 | the inverse cosine of one half |
48 | tan−117 | the inverse tangent of 17 |
49 | cot−132 | the inverse cotangent of 32 |
50 | sec−1100 | the inverse secant of 100 |
51 | csc−185 | the inverse cosecant of 85 |
52 | sin−1(−x) | the inverse sine of negative x |
53 | cos−1(−x) | the inverse cosine of negative x |
54 | tan−1(−x+12) | the inverse tangent of open paren negative x plus 12 close paren |
55 | cot−1(−x−1) | the inverse cotangent of open paren negative x minus 1 close paren |
56 | sin−1(sin0) | the inverse sine of sine 0 |
57 | csc−1(cscx) | the inverse cosecant of cosecant x |
58 | cos(cos−1(−22)) | the cosine of open paren the inverse cosine of open paren negative the fraction with numerator the square root of 2 and denominator 2 close paren close paren |
59 | cos(−cos−1(22)) | the cosine of open paren negative the inverse cosine of open paren the fraction with numerator the square root of 2 and denominator 2 close paren close paren |
60 | sin−1(cosπ4) | the inverse sine of open paren the cosine of pi over 4 close paren |
61 | sin(cos−112) | sine the inverse cosine of one half |
62 | sin(tan−11) | sine the inverse tangent of 1 |
63 | sin(−tan−11) | the sine of open paren negative the inverse tangent of 1 close paren |
64 | sin(−tan−1(−1)) | the sine of open paren negative the inverse tangent of negative 1 close paren |
65 | sec−1(secx) | the inverse secant of secant x |
66 | arcsinx | arc sine x |
67 | arccosx | arc cosine x |
68 | arctanx | arc tangent x |
69 | sinhx | hyperbolic sine of x |
70 | coshx | hyperbolic cosine of x |
71 | tanhx | hyperbolic tangent of x |
72 | cothx | hyperbolic cotangent of x |
73 | sechx | hyperbolic secant of x |
74 | cschx | hyperbolic cosecant of x |
75 | sinh−1x | the inverse hyperbolic sine of x |
76 | cosh−1x | the inverse hyperbolic cosine of x |
77 | tanh−1x | the inverse hyperbolic tangent of x |
78 | coth−1x | the inverse hyperbolic cotangent of x |
79 | sech−1x | the inverse hyperbolic secant of x |
80 | csch−1x | the inverse hyperbolic cosecant of x |
81 | sinh(sinh−1x) | hyperbolic sine of the inverse hyperbolic sine of x |
82 | cosh(cosh−1x) | hyperbolic cosine of the inverse hyperbolic cosine of x |
83 | tanh(tanh−1x) | hyperbolic tangent of the inverse hyperbolic tangent of x |
84 | coth(coth−1x) | hyperbolic cotangent of the inverse hyperbolic cotangent of x |
85 | sinh−1(sinhx) | the inverse hyperbolic sine of hyperbolic sine of x |
86 | cosh−1(coshx) | the inverse hyperbolic cosine of hyperbolic cosine of x |
87 | tanh−1(tanhx) | the inverse hyperbolic tangent of hyperbolic tangent of x |
88 | coth−1(cothx) | the inverse hyperbolic cotangent of hyperbolic cotangent of x |
0 | in2 | square inches |
1 | s2 | seconds to the second power |
2 | m2 | square meters |
3 | in3 | cubic inches |
4 | s3 | seconds to the third power |
5 | m3 | cubic meters |
6 | in-1 | reciprocal inches |
7 | in-1mm-1 | reciprocal inches per millimeter |
8 | inmm | inches per millimeter |
9 | km | kilometers |
10 | A | amperes |
11 | Ω | ohms |
12 | kΩ | kilohms |
13 | °C | Celsius |
14 | minmin | min of minutes |
15 | 3km | 3 kilometers |
16 | km+s | kilometers plus seconds |
17 | km2 | square kilometers |
18 | m3 | cubic meters |
19 | km4 | kilometers to the fourth power |
20 | m-1 | reciprocal meters |
21 | sm-1 | seconds per meter |
22 | sm-1 | seconds per meter to the negative 1 power |
23 | sm-1 | seconds per meter to the negative 1 power |
24 | 3m-1 | 3 reciprocal meters |
25 | kmh | kilometers per hour |
26 | Nkmh | Newtons kilometers per hour |
27 | mkm | m over kilometers |
28 | 3kmh | 3 kilometers hours |
29 | s3mkmh | seconds 3 m kilometers hours |
30 | kms23mkmh | kilometers seconds to the second power 3 m kilometers hours |
31 | 3mkmhNs2 | 3 m kilometers hours the fraction with numerator N and denominator seconds to the second power |
32 | 3mkmhNs2 | 3 m kilometers hours Newtons per second to the second power |
33 | 4⁢mm | 4 millimeters |
34 | 1⁢mm | 1 millimeter |
35 | 4mm | 4 millimeters |
36 | 1mm | 1 millimeter |
37 | m⁢s | meters seconds |
38 | m⁢s | m seconds |
39 | m⁢s | meters s |
40 | ms | meters seconds |
41 | ms | m seconds |
42 | ms | meters s |
43 | m⁢sl | meters seconds liters |
44 | 63360in=63360in.=63360″=63360inches=5280ft=5280ft.=5280′=5280feet=1760yd=1760yd.=1760yards=1mi=1mi.=1mile | 63360 inches equals 63360 inches equals 63360 inches equals 63360 inches equals 5280 feet equals 5280 feet equals 5280 feet equals 5280 feet equals 1760 yards equals 1760 yards equals 1760 yards equals 1 mile equals 1 mile equals 1 mile |
45 | 8000li=8000li.=8000links=320rd=320rd.=320rods=80ch=80ch.=80chains=8fur=8fur.=8furlongs=1mi=1mi.=1mile | 8000 links equals 8000 links equals 8000 links equals 320 rods equals 320 rods equals 320 rods equals 80 chains equals 80 chains equals 80 chains equals 8 furlongs equals 8 furlongs equals 8 furlongs equals 1 mile equals 1 mile equals 1 mile |
46 | 43560sq ft=43560sq. ft.=43560ft2=43560′2=43560square feet=4840sq yd=4840sq. yd.=4840yd2=4840square yards=160sq rd=160sq. rd.=160rd2=160square rods=1ac=1ac.=1acre=1640sq mi=1640sq. mi.=1640mi2=1640square miles | 43560 square feet equals 43560 square feet equals 43560 square feet equals 43560 feet squared equals 43560 square feet equals 4840 square yards equals 4840 square yards equals 4840 square yards equals 4840 square yards equals 160 square rods equals 160 square rods equals 160 square rods equals 160 square rods equals 1 acre equals 1 acre equals 1 acre equals 1 over 640 square miles equals 1 over 640 square miles equals 1 over 640 square miles equals 1 over 640 square miles |
47 | 46656cu in=46656cu. in.=46656in3=46656″3=46656cubic inches=27cu ft=27cu. ft.=27ft3=27′3=27cubic feet=1cu yd=1cu. yd.=1yd3=1cubic yard | 46656 cubic inches equals 46656 cubic inches equals 46656 cubic inches equals 46656 inches cubed equals 46656 cubic inches equals 27 cubic feet equals 27 cubic feet equals 27 cubic feet equals 27 feet cubed equals 27 cubic feet equals 1 cubic yard equals 1 cubic yard equals 1 cubic yard equals 1 cubic yard |
48 | 1024fl dr=1024fl. dr.=1024fluid drams=768tsp=768tsp.=768teaspoons=256Tbsp=256Tbsp.=256tablespoons=128fl oz=128fl. oz.=128fluid ounces=16cp=16cp.=16cups=8pt=8pt.=8pints=4qt=4qt.=4quarts=1gal=1gal.=1gallon | 1024 fluid drams equals 1024 fluid drams equals 1024 fluid drams equals 768 teaspoons equals 768 teaspoons equals 768 teaspoons equals 256 tablespoons equals 256 tablespoons equals 256 tablespoons equals 128 fluid ounces equals 128 fluid ounces equals 128 fluid ounces equals 16 cups equals 16 cups equals 16 cups equals 8 pints equals 8 pints equals 8 pints equals 4 quarts equals 4 quarts equals 4 quarts equals 1 gallon equals 1 gallon equals 1 gallon |
49 | 256dr=256dr.=256drams=16oz=16oz.=16ounces=1#=1lb=1lb.=1pounds=100cwt=100cwt.=100hundredweights=2000tons | 256 drams equals 256 drams equals 256 drams equals 16 ounces equals 16 ounces equals 16 ounces equals 1 # equals 1 pound equals 1 pound equals 1 pounds equals 100 hundredweights equals 100 hundredweights equals 100 hundredweights equals 2000 tons |
50 | 63360in=63360in.=63360″=63360inches=5280ft=5280ft.=5280′=5280feet=1760yd=1760yd.=1760yards=1mi=1mi.=1mile | 63360 inches equals 63360 inches equals 63360 inches equals 63360 inches equals 5280 feet equals 5280 feet equals 5280 feet equals 5280 feet equals 1760 yards equals 1760 yards equals 1760 yards equals 1 mile equals 1 mile equals 1 mile |
51 | 1J=1kg·m2·s-2 | 1 joule equals 1 kilogram times square meters times seconds to the negative 2 power |
52 | 1J=1kgm2s-2 | 1 joule equals 1 kilogram square meters seconds to the negative 2 power |
53 | 1J=1·kg·m2·s-2 | 1 joule equals 1 kilogram square meters seconds to the negative 2 power |
54 | in3 | cubic inches |
55 | kmkgs2J | kilometers kilograms seconds to the second power per joule |
56 | 3km1kgs2J | 3 kilometers 1 kilogram seconds to the second power over joules |
57 | 1kmkgs2J | 1 kilometer kilograms seconds to the second power over joules |
58 | 1kmkgs25J | 1 kilometer kilograms seconds to the second power over 5 joules |
59 | km | kilometers |
60 | 3kmkgs2J | 3 kilometers kilograms seconds to the second power joules |
61 | 3kmkgs2J | 3 kilometers kilograms seconds to the second power joules |
62 | 3km4kgs2J | 3 kilometers 4 kilograms seconds to the second power joules |
63 | 3km1kgs2J | 3 kilometers 1 kilogram seconds to the second power joules |
64 | 1kms+2kms+0kms+akms+ | 1 kilometer seconds plus 2 kilometers seconds plus 0 kilometers seconds plus a kilometers seconds plus |
65 | 1km+2km+0km+akm | 1 kilometer plus 2 kilometers plus 0 kilometers plus a kilometers |
66 | 123kg | 1 and two thirds kilograms |
67 | 123kgkm | 1 and two thirds kilograms kilometers |
68 | 1km2kgkm | 1 kilometer 2 kilograms kilometers |
69 | 1kmkgs+2kmkgs+0kmkgs+akmkgs+ | 1 kilometer kilograms seconds plus 2 kilometers kilograms seconds plus 0 kilometers kilograms seconds plus a kilometers kilograms seconds plus |
70 | 1$ | 1 dollar |
71 | $1 | 1 dollars |
72 | $ | dollars |
73 | $ | dollars |
74 | 2$ | 2 dollars |
75 | $2 | 2 dollars |
76 | 1$+2$+0$+a$ | 1 dollar plus 2 dollars plus 0 dollars plus a dollars |
77 | 1$+$2+0$+$a | 1 dollar plus 2 dollars plus 0 dollars plus a dollars |
78 | 1€+2€+0€+a€ | 1 euro plus 2 euros plus 0 euros plus a euros |
79 | 1£+2£+0£+a£ | 1 pound plus 2 pounds plus 0 pounds plus a pounds |