Answer:
x = -10
y = -13
Step-by-step explanation:
-6(y + 3) + 4y = 8
-6y - 18 + 4y = 8
-2y - 18 = 8
+ 18 + 18
-2y (÷ -2) = 26 (÷ -2)
y = -13
x = -13 + 3
x = -10
The equation of a circle in standard form is
![(x - h)^2 + (y - k)^2 = r^2](https://tex.z-dn.net/?f=%20%28x%20-%20h%29%5E2%20%2B%20%28y%20-%20k%29%5E2%20%3D%20r%5E2%20)
where (h, k) is the center of the circle, and r is the radius if the circle.
We need to find the radius and center of the circle.
We are given a diameter, so to find the center, we need the midpoint of the diameter.
M = ((-6 + 6)/2, (6 + (-2))/2) = (0, 2)
The center is (0, 2).
To find the radius, we find the length of the given diameter and divided by 2.
![d = \sqrt{(-6 - 6)^2 + (6 - (-2))^2)}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%28-6%20-%206%29%5E2%20%2B%20%286%20-%20%28-2%29%29%5E2%29%7D%20)
![d = \sqrt{144 + 64}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B144%20%2B%2064%7D%20)
![d = \sqrt{208}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B208%7D%20)
![r = \dfrac{d}{2} = \dfrac{\sqrt{208}}{2} = \dfrac{\sqrt{208}}{\sqrt{4}} = \sqrt{52}](https://tex.z-dn.net/?f=%20r%20%3D%20%5Cdfrac%7Bd%7D%7B2%7D%20%3D%20%5Cdfrac%7B%5Csqrt%7B208%7D%7D%7B2%7D%20%3D%20%5Cdfrac%7B%5Csqrt%7B208%7D%7D%7B%5Csqrt%7B4%7D%7D%20%3D%20%5Csqrt%7B52%7D%20)
![(x - 0)^2 + (y - 2)^2 = (\sqrt{52})^2](https://tex.z-dn.net/?f=%20%28x%20-%200%29%5E2%20%2B%20%28y%20-%202%29%5E2%20%3D%20%28%5Csqrt%7B52%7D%29%5E2%20)
Imagine that this curve is a roller coaster. A dot on the roller coaster would be a car for a person to sit in, so to speak. As this car moves to the right, the car ultimately moves downward. So this means that as x gets larger, y gets smaller. Put another way: as x approaches infinity, f(x) approaches negative infinity.
Similarly, we can move the other way to work our way to the left. Moving to the left has us go up this time. As x approaches negative infinity, f(x) approaches positive infinity
These two facts point to choice B as the final answer
Answer:
36 in
Step-by-step explanation:
The ratio of proportionality between the two similar triangles is 1:6, which you can find by dividing the corresponding side length measures from each triangle (3/18 = 4/24). Then you can set up a proportion:
1/6 = 6/x, which you can solve to get x = 36
7 batches. There is 12 cookies in a dozen so multiply 8×12 to get 96 cookies. 96 Is the total cookies you need to make. So if you divide 96 by the 14 to see how many batches you must make. you will get a number of 6.85... so you must round up to 7.