The length of a rectangle is represented by the function L(x) = 5x. The width of that same rectangle is represented by the function W(x) = 2x2 − 4x + 13. Which of the following shows the area of the rectangle in terms of x?

(L ⋅ W)(x) = 10x3 − 4x + 13
(L ⋅ W)(x) = 10x3 − 20x2 + 65x
(L + W)(x) = 2x2 + 1x + 13
(L + W)(x) = 2x2 − 9x + 13

1 answer

(L ⋅ W)(x) = 10x3 − 20x2 + 65x.

To find the area of a rectangle, we multiply its length by its width. Therefore, (L ⋅ W)(x) represents the area of the rectangle in terms of x.

Substituting L(x) = 5x and W(x) = 2x2 − 4x + 13, we get:

(L ⋅ W)(x) = 5x(2x2 − 4x + 13)

Simplifying this expression, we get:

(L ⋅ W)(x) = 10x3 − 20x2 + 65x

Therefore, the correct answer is (L ⋅ W)(x) = 10x3 − 20x2 + 65x.