Select all expressions that are equivalent to 5x - 15 - 20x + 10. A. 5x – ( 15 + 20x ) + 10
B. 5x + -15 + -20x + 10
C. 5 ( x-3 - 4x + 2 )
D. -5 ( -x + 3 + 4x + -2 )
E. -15x - 5
F. -5 ( 3x + 1 )

[MA]:

-5 (3 x + 1)

The explanation:

Simplify:

(5 x - 20) + (10 - 15)

Grouping like terms, 5 x - 20 x - 15 + 10 = (5 x - 20 x) + (10 - 15):

(5 x - 20 x) + (10 - 15)

5 x - 20 x = -15 x:

- 15 x + (10 - 15)

10 - 15  = -5:

-5 - 15 x

Factor: -5 out of -15 x - 5:

-5 (3 x + 1)

[Artsy}

step-by-step explanation:

(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