303/4 - -929/8 -59/2
= 1299/8
Answer:
(a) Circle Q is 9.4 units to the center of circle P
(b) Circle Q has a smaller radius
Step-by-step explanation:
Given
![P:(x - 1)^2 + (y + 6)^2 = 9](https://tex.z-dn.net/?f=P%3A%28x%20-%201%29%5E2%20%2B%20%28y%20%2B%206%29%5E2%20%3D%209)
![Q:(x + 4)^2 + (y + 14)^2 = 4](https://tex.z-dn.net/?f=Q%3A%28x%20%2B%204%29%5E2%20%2B%20%28y%20%2B%2014%29%5E2%20%3D%204)
Solving (a): The distance between both
The equation of a circle is:
![(x - h)^2 + (y - k)^2 = r^2](https://tex.z-dn.net/?f=%28x%20-%20h%29%5E2%20%2B%20%28y%20-%20k%29%5E2%20%3D%20r%5E2)
Where
![Center: (h,k)](https://tex.z-dn.net/?f=Center%3A%20%28h%2Ck%29)
![Radius:r](https://tex.z-dn.net/?f=Radius%3Ar)
P and Q can be rewritten as:
![P:(x - 1)^2 + (y + 6)^2 = 3^2](https://tex.z-dn.net/?f=P%3A%28x%20-%201%29%5E2%20%2B%20%28y%20%2B%206%29%5E2%20%3D%203%5E2)
![Q:(x + 4)^2 + (y + 14)^2 = 2^2](https://tex.z-dn.net/?f=Q%3A%28x%20%2B%204%29%5E2%20%2B%20%28y%20%2B%2014%29%5E2%20%3D%202%5E2)
So, for P:
![Center = (1,-6)](https://tex.z-dn.net/?f=Center%20%3D%20%281%2C-6%29)
![r = 3](https://tex.z-dn.net/?f=r%20%3D%203)
For Q:
![Center = (-4,-14)](https://tex.z-dn.net/?f=Center%20%3D%20%28-4%2C-14%29)
![r = 2](https://tex.z-dn.net/?f=r%20%3D%202)
The distance between them is:
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2)
Where:
--- ![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
--- ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
So:
![d = \sqrt{(1 - -4)^2 + (-6 - -14)^2](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%281%20-%20-4%29%5E2%20%2B%20%28-6%20-%20-14%29%5E2)
![d = \sqrt{(5)^2 + (8)^2](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%285%29%5E2%20%2B%20%288%29%5E2)
![d = \sqrt{25 + 64](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B25%20%2B%2064)
![d = \sqrt{89](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B89)
![d = 9.4](https://tex.z-dn.net/?f=d%20%3D%209.4)
Solving (b): The radius;
In (a), we have:
--- circle P
--- circle Q
By comparison
![2 < 3](https://tex.z-dn.net/?f=2%20%3C%203)
<em>Hence, circle Q has a smaller radius</em>
Answer:
8
Step-by-step explanation:
7x+y=0
x+6y=5
x-y+4=8
4 + 2x = 16. First, we must subtract 4 from both sides.
2x = 12. Now, divide both sides by 2
x = 6.
Answer choice "a" is correct. You need to use subtraction and division to solve this equation.
Answer:
9 3/4
Step-by-step explanation:
9.5 is 9 2/4 in fraction form and 9 3/4 is greater than 9 2/4.