Answer:
y=9.25
Step-by-step explanation:
![4-(2x+4)=5\\-2x-4=1\\-2x=5\\x=-2.5](https://tex.z-dn.net/?f=4-%282x%2B4%29%3D5%5C%5C-2x-4%3D1%5C%5C-2x%3D5%5C%5Cx%3D-2.5)
Put it back into the equation,
![4-(2x+4)=5\\4-(2(-2.5)+4)=5\\4-(-5+4)=5\\4-(-1)=5\\5=5](https://tex.z-dn.net/?f=4-%282x%2B4%29%3D5%5C%5C4-%282%28-2.5%29%2B4%29%3D5%5C%5C4-%28-5%2B4%29%3D5%5C%5C4-%28-1%29%3D5%5C%5C5%3D5)
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Answer:
k=32
Step-by-step explanation:
Given the points:
![A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$.](https://tex.z-dn.net/?f=A%20%3D%20%284%2C-1%29%24%2C%20%24B%20%3D%20%286%2C2%29%24%2C%20and%20%24C%20%3D%20%28-1%2C2%29%24.)
The first step is to find the <u>Centroid</u> of the triangle.
Centroid, X
![=\left(\dfrac{x_1+x_2+x_3}{3} ,\dfrac{y_1+y_2+y_3}{3} \right)\\=\left(\dfrac{4+6+(-1)}{3} ,\dfrac{-1+2+2}{3} \right)\\=\left(\dfrac{9}{3} ,\dfrac{3}{3} \right)=(3,1)](https://tex.z-dn.net/?f=%3D%5Cleft%28%5Cdfrac%7Bx_1%2Bx_2%2Bx_3%7D%7B3%7D%20%2C%5Cdfrac%7By_1%2By_2%2By_3%7D%7B3%7D%20%5Cright%29%5C%5C%3D%5Cleft%28%5Cdfrac%7B4%2B6%2B%28-1%29%7D%7B3%7D%20%2C%5Cdfrac%7B-1%2B2%2B2%7D%7B3%7D%20%5Cright%29%5C%5C%3D%5Cleft%28%5Cdfrac%7B9%7D%7B3%7D%20%2C%5Cdfrac%7B3%7D%7B3%7D%20%5Cright%29%3D%283%2C1%29)
Next, let P be a point (x,y)
Using the <u>distance formula, </u>
<u />
<u />
<u />
On Substitution into: ![PA^2 + PB^2 + PC^2 = 3PX^2 + k](https://tex.z-dn.net/?f=PA%5E2%20%2B%20PB%5E2%20%2B%20PC%5E2%20%3D%203PX%5E2%20%2B%20k)
![(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
![\\LHS: x^2-8x+16+y^2+2y+1+x^2-12x+36+y^2\\-4y+4+x^2+2x+1+y^2-4y+4\\=3x^2-18x+3y^2-6y+62](https://tex.z-dn.net/?f=%5C%5CLHS%3A%20x%5E2-8x%2B16%2By%5E2%2B2y%2B1%2Bx%5E2-12x%2B36%2By%5E2%5C%5C-4y%2B4%2Bx%5E2%2B2x%2B1%2By%5E2-4y%2B4%5C%5C%3D3x%5E2-18x%2B3y%5E2-6y%2B62)
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:
![3x^2-18x+3y^2-6y+62=3x^2+3y^2-18x-6y+30+k\\k=3x^2-18x+3y^2-6y+62-3x^2-3y^2+18x+6y-30\\k=3x^2-3x^2+3y^2-3y^2-18x+18x+62-30\\k=32](https://tex.z-dn.net/?f=3x%5E2-18x%2B3y%5E2-6y%2B62%3D3x%5E2%2B3y%5E2-18x-6y%2B30%2Bk%5C%5Ck%3D3x%5E2-18x%2B3y%5E2-6y%2B62-3x%5E2-3y%5E2%2B18x%2B6y-30%5C%5Ck%3D3x%5E2-3x%5E2%2B3y%5E2-3y%5E2-18x%2B18x%2B62-30%5C%5Ck%3D32)
11.16 repeat only the six is repeating
Based on the given details you have given, the total amount of money that you will have will be measured in dollars ($). Since the given value is also in dollars which is $2, therefore, the total amount of money you will have is also in dollars which is 250 x $2 is $500 in total. Hope this answers the question.