LeonLonTimL2asc
Answered

The length of a rectangle is represented by the function L(x) = 2x. The width of that same rectangle is represented by the function W(x) = 8x2 − 4x + 1. Which of the following shows the area of the rectangle in terms of x?

(L + W)(x) = 8x2 − 2x + 1
(L + W)(x) = 8x2 − 6x + 1
(L ⋅ W)(x) = 16x3 − 4x + 1
(L ⋅ W)(x) = 16x3 − 8x2 + 2x

Answer :

nobillionaireNobley
Area of a rectangle = length * width = (2x) * [tex] 8x^{2} - 4x + 1[/tex] = [tex]16 x^{3} - 8 x^{2} + 2x[/tex]

Answer: the last option

Answer:

Option D is correct.

[tex](L \cdot W)(x) = 16x^3-8x^2+2x[/tex]

Step-by-step explanation:

Area of  rectangle(A) is given by:

[tex]A = l \cdot w[/tex]

where

l is the length of rectangle and w is the width of the rectangle respectively.

As per the statement:

Length of a rectangle L(x) = 2x and

Width of a rectangle W(x) = [tex]8x^2-4x+1[/tex]

Then by formula of area of rectangle:

[tex]A(x) = L(x) \cdot W(x) = (L \cdot W)(x)[/tex]

Substitute the given values we have;

[tex](L \cdot W)(x) = (2x) \cdot (8x^2-4x+1)[/tex]

Using the distributive property: [tex]a\ cdot (b+c) = a\cdot b+a\cdot c[/tex]

[tex](L \cdot W)(x) = 16x^3-8x^2+2x[/tex]

Therefore, the area of the rectangle in terms of x is:

[tex](L \cdot W)(x) = 16x^3-8x^2+2x[/tex]

Other Questions