Question

question 10(multiple choice worth 1 points)
(06.05 mc)
the length of a rectangle is represented by the function ( l(x)=6x ). the width of that same rectangle is represented by the function ( w(x)=4x^{2}-3x + 8 ). which of the following shows the area
of the rectangle in terms of ( x )?
( \bigcirc (lcdot w)(x)=24x^{3}-18x^{2}+48x )
( \bigcirc (lcdot w)(x)=24x^{3}-3x + 8 )
( \bigcirc (l + w)(x)=4x^{2}+3x + 8 )
( \bigcirc (l + w)(x)=4x^{2}-9x + 8 )

Explanation:

Step1: Recall the formula for the area of a rectangle

The area \(A\) of a rectangle is given by \(A = L\times W\), where \(L\) is the length and \(W\) is the width.

Step2: Substitute the given functions for \(L(x)\) and \(W(x)\)

Given \(L(x)=6x\) and \(W(x) = 4x^{2}-3x + 8\). Then \((L\cdot W)(x)=L(x)\times W(x)=6x\times(4x^{2}-3x + 8)\)

Step3: Use the distributive property \(a(b + c+d)=ab+ac + ad\)

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Answer:

\((L\cdot W)(x)=24x^{3}-18x^{2}+48x\) (the option corresponding to this expression in the multiple - choice list)