Question

PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!!!
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?
a. 10x + 4; the answer is a polynomial
b. 2x + 4; the answer is a polynomial
c. 10x + 4; the answer may or may not be a polynomial
d. 2x + 4; the answer may or may not be a polynomial

Answer 1

Answer:

a. 10x + 4; the answer is a polynomial

Step-by-step explanation:

The perimeter of a rectangle is the sum of the lengths of the 4 sides.

The closure property is that if you add polynomials, the sum is a polynomial.

A rectangle has two congruent lengths and two congruent widths.

Since the length of the rectangle is 3x + 5, there is another length of 3x + 5. The width is 2x - 3, so there is a second width of also 2x - 3.

Let's add the 4 sides together:

3x + 5 + 3x + 5 + 2x - 3 + 2x - 3 =

= 3x + 3x + 2x + 2x + 5 + 5 - 3 - 3

= 10x + 4

The perimeter is 10x + 4. Each side length is a polynomial, and the sum of the all the side length is also a polynomial. This shows there is closure for the addition of polynomials.

Answer: a. 10x + 4; the answer is a polynomial

Answer 2

Answer:

a. 10x + 4; the answer is a polynomial