Question

the dimensions of a rectangle can be represented by the functions shown. which function represents the area of the rectangle, h(x)=f(x)g(x)? f(x) 5x - 2 g(x) 3x - 7 x h(x)=15x² - 29x + 14 h(x)=15x² - 41x - 9 h(x)=15x² - 29x - 14 h(x)=15x² - 41x + 14

Explanation:

Step1: Recall area formula for rectangle

The area $A(x)$ of a rectangle with length $f(x)$ and width $g(x)$ is $A(x)=f(x)\times g(x)$. Here $f(x) = 5x - 2$ and $g(x)=3x - 7$.

Step2: Multiply the two binomials

$(5x - 2)(3x - 7)=5x\times(3x - 7)-2\times(3x - 7)$.
First, $5x\times(3x - 7)=15x^{2}-35x$.
Second, $-2\times(3x - 7)=-6x + 14$.

Step3: Combine like - terms

$(15x^{2}-35x)+(-6x + 14)=15x^{2}+(-35x-6x)+14=15x^{2}-41x + 14$.

Answer:

$h(x)=15x^{2}-41x + 14$