Answer:
![\large\boxed{A.\ (x+6)^2+(y+10)^2=20}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BA.%5C%20%28x%2B6%29%5E2%2B%28y%2B10%29%5E2%3D20%7D)
Step-by-step explanation:
The standard form of an equation of a circle:
![(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 of a circle (-8, -6) and (-4, -14).
The midpoint of a 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%2C%5C%20%5Cdfrac%7By_1%2By_2%7D%7B2%7D%5Cright%29)
Substitute:
![x=\dfrac{-8+(-4)}{2}=\dfrac{-12}{2}=-6\\\\y=\dfrac{-6+(-14)}{2}=\dfrac{-20}{2}=-10](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-8%2B%28-4%29%7D%7B2%7D%3D%5Cdfrac%7B-12%7D%7B2%7D%3D-6%5C%5C%5C%5Cy%3D%5Cdfrac%7B-6%2B%28-14%29%7D%7B2%7D%3D%5Cdfrac%7B-20%7D%7B2%7D%3D-10)
We have h = -6 and k = -10.
The radius is the distance between a center and the point on a circumference of a circle.
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 (-6, -10) and (-8, -6):
![r=\sqrt{(-8-(-6))^2+(-6-(-10))^2}=\sqrt{(-2)^2+4^2}=\sqrt{4+16}=\sqrt{20}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%28-8-%28-6%29%29%5E2%2B%28-6-%28-10%29%29%5E2%7D%3D%5Csqrt%7B%28-2%29%5E2%2B4%5E2%7D%3D%5Csqrt%7B4%2B16%7D%3D%5Csqrt%7B20%7D)
Finally we have
![(x-(-6))^2+(y-(-10))^2=(\sqrt{20})^2\\\\(x+6)^2+(y+10)^2=20](https://tex.z-dn.net/?f=%28x-%28-6%29%29%5E2%2B%28y-%28-10%29%29%5E2%3D%28%5Csqrt%7B20%7D%29%5E2%5C%5C%5C%5C%28x%2B6%29%5E2%2B%28y%2B10%29%5E2%3D20)
Answer: y(t) = 600(0.921)^t
Step-by-step explanation:
Given:
Percentage yearly reduction = 7.9%
Initial mass m = 600 mg
time in years = t
An exponential function with yearly decay rate to determine the final mass of the substance is given as:
y(t) = m(f)^t
y(t) = final mass in milligram
m = 600
f = final mass fraction = 1 - 0.079 = 0.921
f = 0.921
Therefore, the exponential function is given as;
y(t) = 600(0.921)^t
Answer:
−5r+5
Step-by-step explanation:
Let's simplify step-by-step.
−5−5r+10
=−5+−5r+10
Combine Like Terms:
=−5+−5r+10
=(−5r)+(−5+10)
=−5r+5
Hope this helped <3
Answer:
Step-by-step explanation:
![\frac{9}{10} - \frac{13}{18} \\ \\ = \frac{9 \times 9}{10 \times 9} - \frac{13 \times 5}{18 \times 5} \\ \\ = \frac{81}{90} - \frac{65}{90} \\ \\ = \frac{81 - 65}{90}\\ \\ = \frac{16}{90} \\ \\ = \frac{8}{45} \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B9%7D%7B10%7D%20%20-%20%20%5Cfrac%7B13%7D%7B18%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%5Cfrac%7B9%20%5Ctimes%209%7D%7B10%20%5Ctimes%209%7D%20%20-%20%20%5Cfrac%7B13%20%5Ctimes%205%7D%7B18%20%5Ctimes%205%7D%20%5C%5C%20%20%20%5C%5C%20%20%3D%20%5Cfrac%7B81%7D%7B90%7D%20%20-%20%20%5Cfrac%7B65%7D%7B90%7D%20%20%5C%5C%20%20%20%5C%5C%20%3D%20%20%5Cfrac%7B81%20-%2065%7D%7B90%7D%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B16%7D%7B90%7D%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B8%7D%7B45%7D%20%20%5C%5C%20)