Quadrilateral abcd is dilated to produce quadrilateral a′b′c′d′ with a scale factor of n. if the area of abcd is r, what is the area of a’b’c’d’

The area of the quadrilateral a'b'c'd' is

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x----> the area of the dilated quadrilateral a'b'c'd'

y----> the area of the original quadrilateral abcd

we have

substitute the values

------> area of the quadrilateral a'b'c'd'

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.