Question

the dimensions of a rectangle are represented by the functions shown. which function represents the area of the rectangle? f(x)=2x - 9 g(x)=3x - 4 6x^{2}-35x + 36 6x^{2}-8x + 36 6x^{2}-27x + 36 6x^{2}+35x + 36

Explanation:

Step1: Recall area formula

The area $A$ of a rectangle is $A = \text{length}\times\text{width}$. Here, if length is $f(x)$ and width is $g(x)$, then $A(x)=f(x)\times g(x)$.

Step2: Multiply the functions

$(2x - 9)(3x - 4)=2x\times(3x - 4)-9\times(3x - 4)$.
First, $2x\times(3x - 4)=6x^{2}-8x$.
Second, $-9\times(3x - 4)=-27x + 36$.
Then combine: $6x^{2}-8x-27x + 36=6x^{2}-35x + 36$.

Answer:

$6x^{2}-35x + 36$