The equation t^2=a^3 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 twice the mean distance from the sun as planet x, by what factor is the orbital period increased? a. 2^1/3. b. 2^1/2. c. 2^2/3. d. 2^3/2

for the points

step-by-step explanation:

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.