While walking to the gym, Marie decides to play a game using a her lucky fair six-sided die (which she carries with her all the time). Tossing an even number would
indicate walking forward that many steps and, likewise, tossing an odd number would
mean walking backwards that many steps (i. e. if she tosses a 3, she walks backward 3
steps). If the probability that after 2 rolls of the die, she is further away from the gym
that she was at the beginning of the game, can be represented as m/n
for m and n being relatively prime positive integers, find m^2 + n^2 ?

i would say b) is your answer

sorry if im wrong

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

a

step-by-step explanation: