Triangles ABC and DEF are mathematically similar. The area of triangles ABC is 34cm^2. Calculate the area of triangle DEF.

First of all, what are similar shapes? Well, two shapes are similar if you can turn one into the other by moving, rotating, flipping, or scaling. That means you can make one shape bigger or smaller. In this case, we know that triangles ABC and DEF are mathematically similar. The area of triangles ABC is , so we need to know the area of triangle DEF.

From math, let's call the scaling factor, so we know that for any similar figures, the ratio of the areas of any are in proportion to . In other words, if is the area of triangle ABC, and is the area of triangle DEF, then we can write the following relationship:

So we have a relationship between the area of triangle ABC and DEF.

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

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.