The equation 7^2=a^2 shows the relationship between a planet’s orbital period, t, and the planet’s mean distance from the sun, a, in astronomical units, au. if planet y is k times the mean distance from the sun as planet x, by what factor is the orbital period increased?

The period of Y increases by a factor of with respect to the period of X

Step-by-step explanation:

The equation shows the relationship between the orbital period of a planet, T, and the average distance from the planet to the sun, A, in astronomical units, AU. If planet Y is k times the average distance from the sun as planet X, at what factor does the orbital period increase?  

For the planet Y:  

For planet X:  

To know the factor of aumeto we compared with

We know that the distance "a" from planet Y is k times larger than the distance from planet X to the sun. So:  

So

Then, the period of Y increases by a factor of with respect to the period of X

19

step-by-step explanation:

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18