The volume of a prism changes from 20 to 540 after a dilation. what was the scale factor of the dilation?

The scale factor is 3 : 1.

Step-by-step explanation:

We know that,

The scale factor of the dilation of a prism is the cube root of the ratio of the volume of resultant prism after dilation and the volume of the given prism,

Here, the volume of prism before dilation = 20 cube unit,

And, the volume of the prism after dilation = 540 cube unit,

Thus, by the above statement,

Hence, the scale factor is 3 : 1.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b