Question

which expression is equivalent to the area of metal sheet required to make this square - shaped traffic sign? question 2(multiple choice worth 4 points) (06.04 mc) the function f(x)=4x + 30 represents the length of a rectangle. the function g(x)=x - 1 represents the width of the rectangle. use (f·g)(5) to determine the area of the rectangle.

Explanation:

Step1: Recall area formula for square

The area of a square is $A = s^2$, where $s$ is the side - length. Here, $s=x + 1$.

Step2: Expand $(x + 1)^2$

Using the formula $(a + b)^2=a^2+2ab + b^2$, with $a=x$ and $b = 1$, we have $(x + 1)^2=x^2+2x\times1+1^2=x^2+2x + 1$.

for second question:

Step1: Recall the formula for the product of functions

$(f\cdot g)(x)=f(x)\cdot g(x)$. Given $f(x)=4x + 30$ and $g(x)=x - 1$, then $(f\cdot g)(x)=(4x + 30)(x - 1)$.

Step2: Expand the product

Using the FOIL method: $(4x + 30)(x - 1)=4x\times x-4x\times1+30\times x-30\times1=4x^2-4x + 30x-30=4x^2+26x-30$.

Step3: Evaluate at $x = 5$

Substitute $x = 5$ into $4x^2+26x-30$.
$4\times5^2+26\times5-30=4\times25+130 - 30=100+130 - 30=200$.

Answer:

$x^2+2x + 1$