One day, i decide to run to the park. on the way there, i run at a rate of x^2 miles per hour for 3 hours. on the way back, i take the same path and jog at a slower rate of 16 - 4x miles per hour so that it takes me 4 hours to get home. given that x > 0, what is x? express your answer as a common fraction.

8/3

Step-by-step explanation:

Since we know that the distance that I traveled to the park and the distance that I traveled to get back home are the same, and that distance = rate x time, we have that

(x^2)(3)=(16-4x)(4)

3x^2=64-16x

3x^2+16x-64=0

(3x-8)(x+8)=0

Solving this equation, we get the solutions x=8/3 and x=-8. Since x must be positive, we have x=8/3.

(-1,-0.5)

step-by-step explanation:

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: