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:
90+3+6/10+5/100
Step-by-step explanation:
Watch this vid to see how to multiply: https://www.khanacademy.org/math/arithmetic/fractions/multiplying_fractions/v/multiplying-fractions
The value of dividing x^2-3x+9 by x-2 is x + 3
<h3>Ways of dividing polynomials</h3>
There are several ways to divide polynomial functions; some of these ways include
- By factorization
- By long division
- By synthetic division
- By using technology such as graph
<h3>How to divide the polynomials?</h3>
The expression for the polynomial division is given as:
x^2-3x+9/x-2
To divide polynomial functions, we make use of the division by factorization method
Start by expanding the numerator of the polynomial division
x^2-3x+9/x-2 = x^2 + 3x - 6x + 9/x-2
Factorize the equation
x^2-3x+9/x-2 = x(x + 3) - 2(x + 3)/x - 2
Factor out x + 3 from the numerator
x^2-3x+9/x-2 = (x- 2)(x + 3)/x - 2
Cancel out the common factors
x^2-3x+9/x-2 = x + 3
Hence, the value of dividing x^2-3x+9 by x-2 is x + 3
Read more about polynomial division at:
brainly.com/question/25289437
#SPJ1
Answer:
There would be 216 possible outcomes
Step-by-step explanation: