Dilate line f by a scale factor of 3 with the center of dilation at the origin to create line . where are points a' and b' located after dilation, and how are lines and related?
the locations of a and b' are a' (0, 2) and b' (6, 0), lines fand f intersect at point a.
the locations of a and b' are a' (0.6) and b' (2, 0); lines and
intersect at point b.
the locations of a and b' are a' (0, 2) and b' (2, 0), lines and f are the same line.
the locations of a' and b' are a (0, 6) and b' (6, 0), lines fand fare parallel.

The locations of A' and B' are A' (0, 6) and B' (6, 0), lines f and f' are

parallel ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- A dilation is a transformation that changes the size of a line segment.  

- It can become larger or smaller

- The scale factor, measures how much larger or smaller  

 the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- The image of any point (x , y) by dilation about the origin by scale

 factor k is (kx , ky)

- The line NOT passing through the center of the dilation is parallel to

  its image

* Lets solve the problem

- Line f has two points A (0 , 2) and B (2 , 0)

- Line f dilate by scale factor 3 with center of dilation at the origin

- f' is the image of line f after dilation has points A' and B' whose the

  images of A and B after dilation

∵ The scale factor is 3

∵ A = (0 , 2) and B = (2 , 0)

∴ A' = (0 × 3 , 2 × 3) = (0 , 6)

∴ B' = (2 × 3 , 0 × 3) = (6 , 0)

∴ Points A' and B' located at (0 , 6) and (6 , 0)

∵ Line f NOT passes through the origin point (center of dilation)

∴ Line f is parallel to its image f'

∴ Lines f and f' are parallel

* The locations of A' and B' are A' (0, 6) and B' (6, 0), lines f and f'

  are parallel

D    The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

Step-by-step explanation: i just took the test so it is right

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752