Rectangle abcd with coordinates a(1,1), b(4,1), c(4,2) and d(1,2) dilates with respect to the origin to give rectangle a’b’c’d’. if a’b’=6 what is the scale factor of the dilation?

a: 6
b: 3
c: 2
d: 1/2
e: 4

Option C.

Step-by-step explanation:

You need to find the distance AB with the formula for calculate the distance between two points:

Then, substituting the coordinates of the points A(1,1) and B(4,1), you get:

You know that A'B'=6, then the scale factor of dilation can be calculated with:

Substituting values, you get:

This matches with the option C.

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.