the equation for a parabola with focus (h, k+p) and directrix y=k-p is
so using your directrix y=-3, and knowing directrix is y=k-p, you have
-3=k-p.
similarly, knowing the focus is defined by (h,k+p) and your focus is (-5,-1)
you have the equation -1=k+p.
you now have a system of equations
which you can solve using any method, I will use elimination.
adding down
you now have k and can find p using either equation.
.
now you plug those in, getting the answer
The answer is B.
I hope this helps!
[-5] [7] [6] [10]
U is union thus list everything in A and B
Answer:
Step-by-step explanation:
Total cost for trip = 290 + 50 + 95*5 =290+50+ 475 = $ 815
Savings = $143
Money needed = 815 - 143 = $ 672
No. of driveways = 672/48 = 14
14 driveways must she shovel to have enough money to pay for the trip.
Answer:
Each goal gives 5 points and a penalty costs 7 points.
Step-by-step explanation:
Let a penalty cost = x points
And a goal gives = y points
Ben makes 7 goals and 2 penalties ending the game with 21 points,
7y - 2x = 21 --------(1)
Alyssa makes 10 goals and 8 penalties ending the game with (-6) points,
10y - 8x = -6
5y - 4x = -3 --------(2)
Equation (1) multiplied by 2, then subtracted from equation (2),
(5y - 4x) - 2(7y - 2x) = -3 - 2(21)
5y - 4x - 14y + 4x = -3 - 42
-9y = -45
y = 5
From equation (1)
7(5) - 2x = 21
35 - 2x = 21
2x = 35 - 21
2x = 14
x = 7
Therefore, each goal gives 5 points and a penalty costs 7 points.