Question

1. (06.02 mc)

the following table shows the length and width of a rectangle:
length width
rectangle a 3x + 5 2x - 3
which expression is the result of the perimeter of rectangle a and demonstrates the closure property? (1 point)
10x + 4; the answer is a polynomial
2x + 4; the answer is a polynomial
10x + 4; the answer may or may not be a polynomial
2x + 4; the answer may or may not be a polynomial

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is length and $w$ is width. Here, $l=3x + 5$ and $w = 2x-3$.

Step2: Substitute values into formula

$P=2((3x + 5)+(2x - 3))$.

Step3: Simplify the expression inside parentheses

$(3x + 5)+(2x - 3)=3x+2x + 5-3=5x + 2$.

Step4: Multiply by 2

$P = 2(5x + 2)=10x+4$.

Step5: Analyze closure property

Since the sum, difference, and product of polynomials result in polynomials, and $10x + 4$ is a polynomial, the perimeter $10x + 4$ demonstrates the closure property of polynomials under addition and multiplication.

Answer:

10x + 4; the answer is a polynomial