Answer:
Step-by-step explanation:
<u>Given vertices of a triangle:</u>
- A(4, 12), B(14, 6), and C(-6, 2)
Let the circumcenter is point M(x, y)
We know that the circumcenter is equidistant from each of the vertices.
<u>Use distance formula:</u>
- AM = √(x - 4)² + (y - 12)²
- BM = √(x - 14)² + (y - 6)²
- CM = √(x + 6)² + (y - 2)²
<u>All three distances are equal:</u>
- AM = BM = CM ⇒ AM² = BM² = CM² ⇒
- (x - 4)² + (y - 12)² = (x - 14)² + (y - 6)² = (x + 6)² + (y - 2)²
<u>Square of each:</u>
- AM² = x² - 8x + 16 + y² - 24y + 144 = x² + y² - 8x - 24y + 160
- BM² = x² - 28x + 196 + y² - 12y + 36 = x² + y² - 28x - 12y + 232
- CM² = x² + 12x + 36 + y² - 4y + 4 = x² + y² + 12x - 4y + 40
<u>Comparing the squares, we get following system:</u>
- -8x- 24y + 160 = -28x - 12y + 232 ⇒ 20x - 12y = 72 ⇒ 5x - 3y = 18
- - 8x - 24y + 160 = 12x - 4y + 40 ⇒ 20x + 20y = 120 ⇒ x + y = 6
<u>Solve by substitution, x = 6 - y:</u>
- 5(6 - y) - 3y = 18
- 30 - 8y = 18
- 8y = 12
- y = 1.5
<u>Find x:</u>
So the circumcenter is M(4.5, 1.5)
30 members....21 girls and 9 boys
ratio of girls to boys is : 21/9 which reduces to 7/3 or 7:3 or 7 to 3
Answer:
No matter if you are on Earth, the moon or just chilling in space, your mass does not change. But your weight depends on the gravity force; you would weigh less on the moon than on Earth, and in space you would weigh almost nothing at all. Where ever you are, your mass will always stay the same.
Answer:
4 pints
Step-by-step explanation:
30 quarts ÷ 15 kids = 2 quarts per kid
there are 2 pints in a quart so..
2 quarts per kid x 2 pints per quarter = 4 pints
