Hans is using frequent flier miles to fly to a location 450 miles away, but the airline he is using still charges $15.89 for fees and taxes and $0.17 to redeem each mile. In the equation below, x represents the distance Hans is flying, and y represents the cost of the trip. y = $0.17x + $15.89 How much did Hans pay for his trip?

Given :

Hans is using frequent flier miles to fly to a location 450 miles away, but the airline he is using still charges $15.89 for fees and taxes and $0.17 to redeem each mile.

In the equation below, x represents the distance Hans is flying, and y represents the cost of the trip. y = $0.17x + $15.89 1)

To Find :

How much did Hans pay for his trip.

Solution :

x = 450 miles.

Putting value of x in equation 1 we get :

y = $(0.17×450 + 15.89)

y = $(76.5+15.89)

y = $92.39

Therefore, Hans will pay $92.39 for his trip.

Hence, this is the required solution.

(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