*HELP ASAP WILL MARK BRAINLIEST* Ignore if you don't know Geometry problem: Point D is the incenter of triangleABC, if DE=x^2 and DF= 20-8x, find each of the following

x = 2

DG = 4

Step-by-step explanation:

The thing to know about the incenter of a triangle, is that the segments to each side are equidistant. In other words, they are identical lengths.

This means that ED = FD = GD.

Which means:

DE = DF

x^2 = 20 - 8x

So we need to solve for X. I would solve this using factoring:

Subtract 20 from both sides.

x^2−20=−8x

Add 8x to both sides.

x^2−20+8x=0

Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

x^2+8x−20=0

Factor the left hand side by grouping. First, the left hand side needs to be rewritten as x^2+ax+bx−20. To find a and b, set up a system to be solved.

a+b=8 ab=1(−20)=−20

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product −20.

(−1,20) (−2,10) (−4,5)

Calculate the sum for each pair.

−1+20=19

−2+10=8

−4+5=1

The solution is the pair that gives sum 8.

a=−2 b=10

Rewrite x^2+8x−20 as (x^2−2x)+(10x−20).

(x^2−2x)+(10x−20)

Factor out x in the first and 10 in the second group.

x(x−2)+10(x−2)

Factor out common term x−2 by using distributive property.

(x−2)(x+10)

To find equation solutions, solve x−2=0 and x+10=0.

x = 2

x = −10

In this case, X is equal to 2 as the solution -10 doesn't make much sense given the context of the problem.

To find DG we just need to plug the solution back into one of the equations and solve:

20 - 8x

20 - 8(2)

20 - 16 = 4

DG = 4

step-by-step explanation:

my butt

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer