Is this on a graph if so you need to explain futher
Answer:
(x + 4)² + (y + 5)² = 73
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 4, - 5), thus
(x - (- 4))² + (y - (- 5))² = r², that is
(x + 4)² + (y + 5)² = r²
The radius is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (4, - 2)
r =
= ![\sqrt{8^2+3^2}](https://tex.z-dn.net/?f=%5Csqrt%7B8%5E2%2B3%5E2%7D)
=
=
⇒ r² = 73, thus
(x + 4)² + (y + 5)² = 73 ← equation of circle
4th 2nd 3rd 1st I think thats the order.
Answer:
Infinite Amount of Solutions
Step-by-step explanation:
Step 1: Write out equation
2a + 6 = 2a + 5 + 1
Step 2: Combine like terms
2a + 6 = 2a + 6
Here we see that we have the same slope and same y-intercept or the same equation. When this happens, our solution set is infinite amount of solutions, as any value <em>a</em> can be plugged in and would be true.
Answer:
Part a) ![n=-8.017176](https://tex.z-dn.net/?f=n%3D-8.017176)
Part b) ![n=9.700465](https://tex.z-dn.net/?f=n%3D9.700465)
Step-by-step explanation:
Part a) we have
![9^{(n+10)}+3=81](https://tex.z-dn.net/?f=9%5E%7B%28n%2B10%29%7D%2B3%3D81)
Solve for n
Subtract 3 both sides
![9^{(n+10)}+3-3=81-3](https://tex.z-dn.net/?f=9%5E%7B%28n%2B10%29%7D%2B3-3%3D81-3)
![9^{(n+10)}=78](https://tex.z-dn.net/?f=9%5E%7B%28n%2B10%29%7D%3D78)
take log both sides
![log[9^{(n+10)}]=log[78]](https://tex.z-dn.net/?f=log%5B9%5E%7B%28n%2B10%29%7D%5D%3Dlog%5B78%5D)
![(n+10)log[9]=log[78]](https://tex.z-dn.net/?f=%28n%2B10%29log%5B9%5D%3Dlog%5B78%5D)
![(n+10)=log[78]/log[9]](https://tex.z-dn.net/?f=%28n%2B10%29%3Dlog%5B78%5D%2Flog%5B9%5D)
----> using a calculator
![n=-8.017176](https://tex.z-dn.net/?f=n%3D-8.017176)
Part b) we have
![11^{(n-8)}-5=54](https://tex.z-dn.net/?f=11%5E%7B%28n-8%29%7D-5%3D54)
Solve for n
Adds 5 both sides
![11^{(n-8)}-5+5=54+5](https://tex.z-dn.net/?f=11%5E%7B%28n-8%29%7D-5%2B5%3D54%2B5)
![11^{(n-8)}=59](https://tex.z-dn.net/?f=11%5E%7B%28n-8%29%7D%3D59)
take log both sides
![log[11^{(n-8)}]=log[59]](https://tex.z-dn.net/?f=log%5B11%5E%7B%28n-8%29%7D%5D%3Dlog%5B59%5D)
![(n-8)log[11]=log[59]](https://tex.z-dn.net/?f=%28n-8%29log%5B11%5D%3Dlog%5B59%5D)
![(n-8)=log[59]/log[11]](https://tex.z-dn.net/?f=%28n-8%29%3Dlog%5B59%5D%2Flog%5B11%5D)
----> using a calculator
![n=9.700465](https://tex.z-dn.net/?f=n%3D9.700465)