NASA uses a launch clock to measure time before and after lift-off. It takes 2 hours and 15 minutes of preparations on base, 20 minutes to travel to the launch pad, and 40 minutes of pre-launch checks once in the spacecraft. When should the astronauts begin preparation? –3 hours 15 minutes, because all the preparation times add to 3 hours and 15 minutes –3 hours 35 minutes, because all the preparation times add to 3 hours and 35 minutes –2 hours 35 minutes, because all the preparation times add to 2 hours and 35 minutes –2 hours 15 minutes, because all the preparation times add to 2 hours and 15 minute

chase is right because he already been to the swings and he know how far it will be to get there

step-by-step explanation:

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

(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