Emma calculated the slope of the downhill hike to be . Her work is shown below. Determine whether her calculation was correct or incorrect, and then explain why. (2 points: 1 for the answer, 1 for the explanation) 7. Confirm or disprove Emma's work by using two other points from the slope of the downhill hike. (1 point)

8. What does the slope tell you about the rate of change in elevation during descent? (1 point for identifying the rate of change)

Step-by-step explanation:

Pair of points (x, y):

Slope formula:

Calculate the slope:

(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