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topjm [15]
3 years ago
5

3 friends went to the movies. the total cost of all three ticket 15. each friend spent $6 at the concession stand.including the

price of the ticket how much did each friend spend
Mathematics
2 answers:
olya-2409 [2.1K]3 years ago
4 0
$11 because you do 15 divided by 3 the add 6

Vlad1618 [11]3 years ago
4 0
15 divided by 3 is 5 plus 6 so it's 11 :)) hope I helped
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Let $A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$. There exists a point $X$ and a constant $k$ such that for any point $P$,
goldfiish [28.3K]

Answer:

k=32

Step-by-step explanation:

Given the points:

A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$.

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)

Next, let P be a point (x,y)

Using the <u>distance formula, </u>\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}<u />

<u />PA^2=(x-4)^2+(y-(-1))^2\\PB^2=(x-6)^2+(y-2)^2\\PC^2=(x-(-1))^2+(y-2)^2\\PX^2=(x-3)^2+(y-1)^2\\<u />

On Substitution into: PA^2 + PB^2 + PC^2 = 3PX^2 + k

(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

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

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

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

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3 years ago
Area = ___ square units​
4vir4ik [10]

Answer:

9 square units

Step-by-step explanation:

Area of a square = base * height

= 3*3

= 9

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