ANSWER
x=11
EXPLANATION
We want to solve the equation:
![\sqrt{x - 2} + 8 = x](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20-%202%7D%20%20%2B%208%20%3D%20x)
Add -8 to both sides:
![\sqrt{x - 2} = x - 8](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20-%202%7D%20%3D%20x%20-%208)
Square both sides of the equation to get:
![(\sqrt{x - 2} )^{2} =( x - 8)^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bx%20-%202%7D%20%29%5E%7B2%7D%20%3D%28%20x%20-%208%29%5E%7B2%7D%20)
![x - 2 = {x}^{2} - 16x + 64](https://tex.z-dn.net/?f=x%20-%202%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20-%2016x%20%2B%2064)
Rewrite in the form ax² +bx+c=0
![{x}^{2} - 16x - x + 64 + 2 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20-%2016x%20-%20x%20%2B%2064%20%2B%202%20%3D%200)
![{x}^{2} - 17x + 66 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20-%2017x%20%2B%2066%20%3D%200)
Factor to get,
![(x - 11)(x - 6) = 0](https://tex.z-dn.net/?f=%28x%20-%2011%29%28x%20-%206%29%20%3D%200)
This implies that,
![x = 11 \: or \: x = 6](https://tex.z-dn.net/?f=x%20%3D%2011%20%5C%3A%20or%20%5C%3A%20x%20%3D%206)
Checking for extraneous solutions.
When x=6, the original equation becomes,
![\sqrt{6- 2} + 8 = 6](https://tex.z-dn.net/?f=%5Csqrt%7B6-%202%7D%20%20%2B%208%20%3D%206)
![\sqrt{4 } + 8 = 6](https://tex.z-dn.net/?f=%20%5Csqrt%7B4%20%7D%20%20%2B%208%20%3D%206)
2+8= 6 is not true.
x=6 is an extraneous solution.
When x=11, the original equation becomes,
![\sqrt{11- 2} + 8 = 11](https://tex.z-dn.net/?f=%20%5Csqrt%7B11-%202%7D%20%20%2B%208%20%3D%2011)
![\sqrt{9} + 8 = 11](https://tex.z-dn.net/?f=%5Csqrt%7B9%7D%20%20%2B%208%20%3D%2011)
![3 + 8 = 11](https://tex.z-dn.net/?f=3%20%2B%208%20%3D%2011)
This is true, hence x=11 is the only solution.
Z varies inversely as w ⇒ z*w=k
when z=7 and w=8 ⇒ 7*8=56=k
when w=14 ⇒ z*14=56
⇒z=56/14
⇒ z=4
The answer is the first option: it has the same domain as the function f(x) = - √(-x).
The domain is the set of x-values for which the function is defined.
The square root function is defined only for zero and positve values.
- x is positive when x negative.
So the domain for - √(-x) and √(-x) are the same: x less than or equal to zero.
D Train= 600 miles in 4 hours
C Train= 320 miles in 4 hours
600-320= 280 miles they would be apart ❤️