Question

the dimensions of a rectangle are represented by the functions shown. f(x) = 3x - 2, g(x) = 4x + 5. which function represents the area of the rectangle? options: 12x² + 15x -10, 12x² +7x +10, 12x² -8x -10, 12x² +7x -10

Explanation:

Step1: Recall area of rectangle formula

The area \( A \) of a rectangle is the product of its length and width. Here, the length and width are given by the functions \( f(x) = 3x - 2 \) and \( g(x)=4x + 5 \), so \( A(x)=f(x)\times g(x)=(3x - 2)(4x + 5) \).

Step2: Expand the product using FOIL method

First, multiply the First terms: \( 3x\times4x = 12x^{2} \).
Then, the Outer terms: \( 3x\times5=15x \).
Next, the Inner terms: \( - 2\times4x=-8x \).
Finally, the Last terms: \( -2\times5 = - 10 \).

Now, combine like terms: \( 12x^{2}+15x-8x - 10=12x^{2}+7x - 10 \).

Answer:

\( 12x^{2}+7x - 10 \) (corresponding to the option \( 12x^{2}+7x - 10 \))