Lyla is planning on riding his bike no more than 65 miles during the week. She has already ridden 17 miles. Write and solve an inequality to find how many more miles she can ride. Then interpret the solution.

17 + m ≤ 65

Step-by-step explanation:

Maximum distance = 65 miles

Number of miles already ridden = 17

Expression to represent how many more miles, 'm' she can ride ;

Number of miles already ridden + m ≤ maximum distance

17 + m ≤ 65

m ≤ 65 - 17

m ≤ 48

The amount of additional miles Lyla can ride is at most 48 miles

answer: 88

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