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Leto [7]
3 years ago
8

Rodrigo surveyed some students at his school about their favorite professional sports,

Mathematics
1 answer:
Lunna [17]3 years ago
8 0
The answer is 1 in 15
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Derive the equation of the parabola with a focus at (-5,5) and a directix of y = -1
Paladinen [302]

Answer:

D

Step-by-step explanation:

From any point (x, y) on the parabola the focus and directrix are equidistant

Using the distance formula

\sqrt{(x+5)^2+(y-5)^2} = | y + 1 |

Squaring both sides

(x + 5)² + (y - 5)² = (y + 1)^2 , that is

(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides

(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify

y² + 2y + 1 - y² + 10y - 25 = (x + 5)²

12y - 24 = (x + 5)² ← factor left side

12(y - 2) = (x + 5)² ← divide both sides by 12

y - 2 = \frac{1}{12} (x + 5)² ← add 2 to both sides

y = \frac{1}{12} (x + 5)² + 2

or

f(x) = \frac{1}{12} (x + 5)² + 2 → D

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Common factor of 12/15
Evgesh-ka [11]
The gcf of 12/15 is 3 (simplest terms is 4/5)
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