The vertex form:
![y=a(x-h)^2+k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E2%2Bk)
(h,k) - the coordinates of the vertex
![y-13=2(x+4)^2 \\ y=2(x+4)^2+13 \\ y=2(x-(-4))^2+13 \\ \\ h=-4 \\ k=13](https://tex.z-dn.net/?f=y-13%3D2%28x%2B4%29%5E2%20%5C%5C%0Ay%3D2%28x%2B4%29%5E2%2B13%20%5C%5C%0Ay%3D2%28x-%28-4%29%29%5E2%2B13%20%5C%5C%20%5C%5C%0Ah%3D-4%20%5C%5C%20k%3D13)
The coordinates of the vertex are
(-4,13).
Answer:
Equation 1: 14t + 61s = 150
Equation 2: 14t + 25s = 78
Use Elimination (x)
(-1) (14t + 25s) = (78) (-1)
-14t - 25s = -78
14t + 61s = 150
+ -14t - 25s = -78
--------------------------
36s = 72
s = 2
Salad costs $2
Then find t
14t + 61(2) = 150
14t + 122 = 150
14t = 28
t = 2
Sandwich costs $2
Answer:
r = ![\sqrt{11}](https://tex.z-dn.net/?f=%5Csqrt%7B11%7D)
Step-by-step explanation:
So we need to complete the square for both parts of the equation
First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6
So first we can complete the square for x² + 2x
To do so we need to use
to figure out the number we need to add to both sides
In this case our b is 2, so substituting this in we get ![(\frac{2}{2} )^{2} =(1)^{2} =1](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%7D%7B2%7D%20%29%5E%7B2%7D%20%3D%281%29%5E%7B2%7D%20%3D1)
Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1
Now we can follow the same steps to complete the square for y² + 4y
Here our b is 4, so substituting this in we get ![(\frac{4}{2} )^{2}=(2)^{2} =4](https://tex.z-dn.net/?f=%28%5Cfrac%7B4%7D%7B2%7D%20%29%5E%7B2%7D%3D%282%29%5E%7B2%7D%20%3D4)
Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4
Now condensing everything we have (x + 1)² + (y + 2)² = 11
The formula for a circle is (x - h)² + (y - k)² = r²
In our equation we have r² = 11
To find the radius we need to take the square root of both sides
to get r = ![\sqrt{11}](https://tex.z-dn.net/?f=%5Csqrt%7B11%7D)
7..
49 can be equally divided by seven, which means there would be 9 red roses in each center piece. And 63 can be equally divided by 7 which means there would by 7 white roses in each center piece.
hope this helps