Remember that the equation of a circle is:
![(x - h)^{2} + (y - k)^{2} = r^{2}](https://tex.z-dn.net/?f=%28x%20-%20h%29%5E%7B2%7D%20%2B%20%28y%20-%20k%29%5E%7B2%7D%20%3D%20%20r%5E%7B2%7D%20)
Where (h, k) is the center and r is the radius.
We need to get the equation into that form, and find k.
![x^{2} - 6x + y^{2} - 10y = 56](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20-%206x%20%2B%20%20y%5E%7B2%7D%20-%2010y%20%3D%2056)
Complete the square. We must do this for x² - 6x and y² - 10y separately.
x² - 6x
Divide -6 by 2 to get -3.
Square -3 to get 9. Add 9,
x² - 6x + 9
Because we've added 9 on one side of the equation, we have to remember to do the same on the other side.
![x^{2} - 6x + 9 + y^{2} - 10y = 65](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20-%206x%20%2B%209%20%2B%20y%5E%7B2%7D%20-%2010y%20%3D%2065)
Now factor x² - 6x + 9 to get (x - 3)² and do the same thing with y² - 10y.
y² - 10y
Divide -10 by 2 to get -5.
Square -5 to get 25.
Add 25 on both sides.
![(x - 3)^{2}+ y^{2} - 10y + 25= 90](https://tex.z-dn.net/?f=%20%28x%20-%203%29%5E%7B2%7D%2B%20y%5E%7B2%7D%20-%2010y%20%2B%2025%3D%2090)
Factor y² - 10y + 25 to get (y - 5)²
![(x - 3)^{2}+ (y - 5)^{2} = 90](https://tex.z-dn.net/?f=%20%28x%20-%203%29%5E%7B2%7D%2B%20%28y%20-%205%29%5E%7B2%7D%20%3D%2090)
Now our equation is in the correct form. We can easily see that h is 3 and k is 5. (not negative because the original equation has -h and -k so you must multiply -1 to it)
Since (h, k) represents the center, (3, 5) is the center and 5 is the y-coordinate of the center.
The answer is D. Because when use the slope formula m=5.
Answer:
{x| 43 ≤ x ≤ 47} where x = Sean's speed (in mph)
Step-by-step explanation:
Sean is taking driver's ed. The instructor asked him to stay within 2 miles of the posted speed limits. The current speed limit is 45 mph.
So, the maximum speed which Sean can reach is, (45 + 2) mph
=47 mph
and, the minimum speed which Sean can reach is, (45 - 2) mph
=43 mph
so, {x| 43 ≤ x ≤ 47} where x = Sean's speed (in mph)
Answer:
1 = 1.3
3 = 3.3
0 = 40
Step-by-step explanation:
i tried my best, hope u get a good score !