Question

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)=7x² - 4x + 2. which of the following shows the area of the rectangle in terms of x? (1 point)
(1) (l + w)(x)=7x² + 2
(2) (l + w)(x)=7x² - 8x + 2
(3) (l·w)(x)=28x³ - 16x² + 8x
(4) (l·w)(x)=28x³ - 4x + 2

1. (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)=4x² - 6x + 5. what is the area of the table in terms of x? (1 point)
(1) (l·w)(x)=12x³ - 18x² + 15x
(2) (l·w)(x)=12x² - 18x + 15
(3) (l·w)(x)=7x³ - 3x² + 8x

Explanation:

Step1: Recall area formula for rectangle

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

Step2: Multiply the length and width functions

$(L\cdot W)(x)=3x(4x^{2}-6x + 5)$. Using the distributive - property $a(b + c + d)=ab+ac + ad$, we have $3x\times4x^{2}-3x\times6x+3x\times5$.

Step3: Simplify each term

$3x\times4x^{2}=12x^{3}$, $3x\times6x = 18x^{2}$, and $3x\times5 = 15x$. So, $(L\cdot W)(x)=12x^{3}-18x^{2}+15x$.

Answer:

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