You and your friend are standing back-to-back. Your friend runs 8 feet forward, and then 6 feet right. At the same time, you run 4 feet forward, and then run 3 feet to the right. You stop and throw a football to your friend, who catches it. How far did you throw the football?

15 feet

Step-by-step explanation:

you and your friend basically formed two different triangles, and in order to determine the distance that the ball traveled we must calculate both hypotenuses:

triangle 1:

hypotenuse = √(8² + 6²) = √100 = 10 feet

triangle 2:

hypotenuse = √(4² + 3²) = √25 = 5 feet

total distance traveled by the ball = 10 + 5 = 15 feet

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2

a. 12.5 kg

step-by-step explanation:

f = ma

so

m = f/a = (2500 n)/(200 m/s²) = 12.5 kg

1 n = 1 kg·m/s²