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
(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.
To find the area of a rectangle, we multiply its length (L) by its width (W). In this case, the length is represented by the function L(x) = 5x and the width is represented by the function W(x) = 2x^2 - 4x + 13.
So, the area of the rectangle in terms of x is given by the product of L(x) and W(x), which can be written as (L ⋅ W)(x).
(L ⋅ W)(x) = (5x) * (2x^2 - 4x + 13)
= 10x^3 - 20x^2 + 65x
Therefore, the correct answer is: (L ⋅ W)(x) = 10x^3 - 20x^2 + 65x.