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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

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kudzordzifrancis

ANSWER

[tex](L \bullet \: W)(x)= 10 {x}^{3} - 20 {x}^{2} + 65x[/tex]

EXPLANATION

The length of a rectangle is represented by the function:

[tex]L(x) = 5x[/tex]

and the width is represented by

[tex]W(x)= 2 {x}^{2} - 4x + 13[/tex]

The area of a rectangle is calculated using the formula:

[tex]Area = LW[/tex]

In terms x, we have

[tex]Area = (L \bullet \: W)(x)= L(x) \times W(x)[/tex]

We plug in the functions representing the length and width to obtain;

[tex](L \bullet \: W)(x)= 5x(2 {x}^{2} - 4x + 13)[/tex]

We expand the parenthesis to obtain;

[tex](L \bullet \: W)(x)= 10 {x}^{3} - 20 {x}^{2} + 65x[/tex]

caarmstrong87

Answer:

B/Second Answer: (L • W)(x) = 10x^3 − 20x^2 + 65x