In a proportional relationship, the constant of proportionality is the number you can multiply each value of x by to get the related value of y. You can use this idea to figure out whether a set of values is in a proportional relationship. Divide each value of y by the related value of x. Do you get the same number every time? In our ice cream example, $2 divided by 1 scoop equals 2. $4 divided by 2 scoops also equals 2. And $6 divided by 3 scoops…you get the picture! The relationship’s proportional, and the constant is 2.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

true

step-by-step explanation:

it is more then likely a review to you prepare for an upcomign test or quiz