What the distributive properyti rewrite 5(3a+5)

Step-by-step explanation:

Distributive property upon addition: a*(c+d) = a*c + a*d

5(3a+5) = 5*3a + 5 * 5  = 15a + 25

15a+25

Step-by-step explanation:

The distributive property: example of this is your question. I'll use it as an example. You take 5 on the left of the parentheses, and you multiply it by 1 number at a time, such as 5(3a+5). You would take 5 and 3a and multiply them first. That's it's own number now, 15a. Now take 5 and 5. You'll get 25. Take these two variables and put them in an equation. 15a+25.

(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