The diagram shows the lengths of corresponding sides of similar triangles a'b'c' and abc. which expression gives the perimeter of a'b'c'?

options:
a) 4(4 + b + c)
b) 2(a + b + c)
c) 4(a + b + c)
d) 8(a + b + c)

The correct answer option is b) 2(a + b + c).

Step-by-step explanation:

We are given two similar triangles A'B'C' and ABC with the lengths of their corresponding sides.

From the diagram, we can see that side a = 4 in triangle ABC while its corresponding side is 8 which means that triangle A'B'C' is twice the size of ABC.

So we can write the following expression for the perimeter of A'B'C':

2(a + b + 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.