The answer is B. Hope you get it.
Let's solve this problem step-by-step.
6+0.1x=0.15x+8
Step 1: Simplify both sides of the equation.
0.1x+6=0.15x+8
Step 2: Subtract 0.15x from both sides.
0.1x+6−0.15x=0.15x+8−0.15x
−0.05x+6=8
Step 3: Subtract 6 from both sides.
−0.05x+6−6=8−6
−0.05x=2
Step 4: Divide both sides by -0.05.
-0.05x/-0.05=2/-0.05
So, the answer for this problem is x=-40
Answer:
![\large\boxed{(x-2)^2+(y-1)^2=34}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%28x-2%29%5E2%2B%28y-1%29%5E2%3D34%7D)
Step-by-step explanation:
The equation of a circle in standard form:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
(h, k) - center
r - radius
We have the endpoints of the diameter: (-1, 6) and (5, -4).
Midpoint of diameter is a center of a circle.
The formula of a midpoint:
![\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7Bx_1%2Bx_2%7D%7B2%7D%3B%5C%20%5Cdfrac%7By_1%2By_2%7D%7B2%7D%5Cright%29)
Substitute:
![h=\dfrac{-1+5}{2}=\dfrac{4}{2}=2\\\\k=\dfrac{6+(-4)}{2}=\dfrac{2}{2}=1](https://tex.z-dn.net/?f=h%3D%5Cdfrac%7B-1%2B5%7D%7B2%7D%3D%5Cdfrac%7B4%7D%7B2%7D%3D2%5C%5C%5C%5Ck%3D%5Cdfrac%7B6%2B%28-4%29%7D%7B2%7D%3D%5Cdfrac%7B2%7D%7B2%7D%3D1)
The center is in (2, 1).
The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.
The formula of a distance between two points:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Substitute the coordinates of the points (2, 1) and (5, -4):
![r=\sqrt{(5-2)^2+(-4-1)^2}=\sqrt{3^2+(-5)^2}=\sqrt{9+25}=\sqrt{34}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%285-2%29%5E2%2B%28-4-1%29%5E2%7D%3D%5Csqrt%7B3%5E2%2B%28-5%29%5E2%7D%3D%5Csqrt%7B9%2B25%7D%3D%5Csqrt%7B34%7D)
Finally we have:
![(x-2)^2+(y-1)^2=(\sqrt{34})^2](https://tex.z-dn.net/?f=%28x-2%29%5E2%2B%28y-1%29%5E2%3D%28%5Csqrt%7B34%7D%29%5E2)
You need to add a -1
We can find this by setting up the equation like so
x + (-6) + 12 + 15 / 4 = 5
x + 21 = 20
x = 20 -21
x = -1
Now if we insert -1 where x is located in the equation, you will get a means of 5