Dilate line f by a scale factor of one half with the center of dilation at the origin to create line f'. where are points a' and b' located after dilation, and how are lines f and f' related?

the locations of a' and b' are a' (0, 2) and b' (0, 0); lines f and f' intersect at point a.
the locations of a' and b' are a' (0, 1) and b' (1, 0); lines f and f' are parallel.
the locations of a' and b' are a' (0, 0) and b' (2, 0); lines f and f' intersect at point b.
the locations of a' and b' are a' (0, 2) and b' (2, 0); lines f and f' are the same line.

The locations of A' and B' are A' (0, 1) and B' (1, 0); lines f and f' are parallel.

Step-by-step explanation:

Dilate A and B by one half.

Dilate point A:

(0,2)   0 × 0.5 = 0     2 × 0.5 = 1

A' = (0,1)

Dilate point B:

(2,0)   2 × 0.5 = 1     0 × 0.5 = 0

B' = (1,0)

If you draw a line connecting A' and B' it would be line f'.

This line would be parallel to line f. This is because they do not intersect and they have the same slope.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

27

step-by-step explanation: