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The height of a rectangle is 20 cm. The diagonal is 8 cm more than the length. Determine the length of the rectangle.
a. 20
b. 23
c. 22
d. 21
d. To determine the length of the rectangle, we will use the Pythagorean theorem. The width, a, is 20. The diagonal, c, is x + 8. The length, b, is x; a2 + b2 = c2; 202 + x2 = (x + 8)2. After multiplying the two binomials (using FOIL), 400 + x2 = x2 + 16x + 64. Subtract x2 from both sides; 400 = 16x + 64. Subtract 64 from both sides; 336 = 16x. Divide both sides by 16; 21 = x. If you select a, you incorrectly calculated the diagonal to be 28.
-x^3+6x-7
If 3x2 is multiplied by the quantity 2x3y raised to the fourth power, what would this expression simplify to? The statement in the question would translate to 3x 2 (2x 3 y) 4 .
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