20 = r + 11
Solve the equation.

r = 9

Step-by-step explanation:

Simplifying

20 = r + 11

Reorder the terms:

20 = 11 + r

Solving

20 = 11 + r

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-1r' to each side of the equation.

20 + -1r = 11 + r + -1r

Combine like terms: r + -1r = 0

20 + -1r = 11 + 0

20 + -1r = 11

Add '-20' to each side of the equation.

20 + -20 + -1r = 11 + -20

Combine like terms: 20 + -20 = 0

0 + -1r = 11 + -20

-1r = 11 + -20

Combine like terms: 11 + -20 = -9

-1r = -9

Divide each side by '-1'.

r = 9

Simplifying

r = 9

r=9

Step-by-step explanation:

Step 1: Flip the equation

r + 11 = 20

Step 2: Subtract 11 from both sides

r + 11 - 11 = 20 - 11

y + 11 = (1/4)(x + 16)

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