Answer:
k=32
Step-by-step explanation:
Given the points:
The first step is to find the <u>Centroid</u> of the triangle.
Centroid, X
Next, let P be a point (x,y)
Using the <u>distance formula, </u>
<u />
<u />
<u />
On Substitution into: 
![(x-4)^2+(y-(-1))^2+(x-6)^2+(y-2)^2+(x-(-1))^2+(y-2)^2=3[(x-3)^2+(y-1)^2]+k](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%28y-%28-1%29%29%5E2%2B%28x-6%29%5E2%2B%28y-2%29%5E2%2B%28x-%28-1%29%29%5E2%2B%28y-2%29%5E2%3D3%5B%28x-3%29%5E2%2B%28y-1%29%5E2%5D%2Bk)
Let us simplify the LHS first
Also, the Right Hand Side
![RHS:3[(x-3)^2+(y-1)^2]+k\\=3[x^2-6x+9+y^2-2y+1]+k\\=3x^2-18x+27+3y^2-6y+3+k\\=3x^2+3y^2-18x-6y+30+k](https://tex.z-dn.net/?f=RHS%3A3%5B%28x-3%29%5E2%2B%28y-1%29%5E2%5D%2Bk%5C%5C%3D3%5Bx%5E2-6x%2B9%2By%5E2-2y%2B1%5D%2Bk%5C%5C%3D3x%5E2-18x%2B27%2B3y%5E2-6y%2B3%2Bk%5C%5C%3D3x%5E2%2B3y%5E2-18x-6y%2B30%2Bk)
Therefore:
Answer:
Step-by-step explanation:
8.18
I think this is asking what power when the first number given is raised to it will equal the number within the parentheses. So, for example, the answer to the first question would be 5 because 2^5 = 32. 10^3 = 1000, so the answer is 3, and so on.
The third one I think btw if you get mad at this person
