Zachary is standing in a stadium and has the option of running up a staircase or down a staircase for exercise. The function f(x) = 1/25 ( |4x|+ 2x) will determine how many calories Zachary will burn if he runs up x steps. Use a negative value for x if he runs down the stairs. Find and interpret the given function values and determine an appropriate domain for the function.

false

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.