Question

The length of a rectangular table is represented by the function L(x) = 4x. The width of the table is represented by the function W(x) = 3x2 − 5x + 6. What is the area of the table in terms of x? (1 point)

(L • W)(x) = 7x3 − x2 + 10x
(L • W)(x) = 12x2 − 20x + 24
(L • W)(x) = 12x3 + 20x2 + 24x
(L • W)(x) = 12x3 − 20x2 + 24x

Answer 1

(L • W)(x) = 12x^3 − 20x^2 + 24x (the last option)

Explanation:

It's very simple actually. To find an area of a rectangle, all we have to do is multiply its two sides. We are given the length and the width of the rectangle - its sides. All we have to do is simply multiply them:
Area = L(x) * W(x)
L(x) = 4x
W(x) = 3x^2 - 5x + 6
Therefore the area is equal to:
(4x) * (3x^2 - 5x + 6) =
= 4x * 3x^2 - 4x * 5x + 6 * 4x =
= 12x^3 - 20x^2 + 24x
And there's your answer, option D, or 4 or whatever you call the last one.