Question

1. (06.04 mc) the length of a rectangle is represented by the function l(x)=4x. the width of that same rectangle is represented by the function w(x)=7x^2 - 4x + 2. which of the following shows the area of the rectangle in terms of x? (1 point) (l + w)(x)=7x^2 + 2 (l + w)(x)=7x^2 - 8x + 2 (l • w)(x)=28x^3 - 16x^2 + 8x (l • w)(x)=28x^3 - 4x + 2 21. (06.04 mc) the length of a rectangular table is represented by the function l(x)=3x. the width of the table is represented by the function w(x)=4x^2 - 6x + 5. what is the area of the table in terms of x? (1 point) (l • w)(x)=12x^3 - 18x^2 + 15x

Explanation:

Step1: Recall area formula

The area of a rectangle is $A=(L\cdot W)(x)=L(x)\cdot W(x)$. Given $L(x) = 3x$ and $W(x)=4x^{2}-6x + 5$.

Step2: Multiply the functions

$(L\cdot W)(x)=3x(4x^{2}-6x + 5)$.
Using the distributive - property $a(b + c + d)=ab+ac + ad$, we have:
\[

$$\begin{align*} 3x(4x^{2}-6x + 5)&=3x\cdot4x^{2}-3x\cdot6x+3x\cdot5\\ &=12x^{3}-18x^{2}+15x \end{align*}$$

\]

Answer:

$(L\cdot W)(x)=12x^{3}-18x^{2}+15x$