The volume of a prism changes from 20 to 540 after a dilation. what was the scale factor of the dilation? 3 9 27 520

yes it's the first option, 3 is the scale factor. Took test got it right.

3 is the scale factor

Step-by-step explanation:

Whenever a geometrical figure is dilated by scale factor of 3, we will have perimeter to be dilated by same 3 units

Area by 3 square = 9 square units

and volume by 3 cube = 27 cubic units

Here original volume = 20

New volume = 540

Ratio = 540/20 = 27 = 3 cube

Hence scale factor is 3

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

but there’s no any figure there!