Answer:
![\{-4, -1, 0, 2, 7\}](https://tex.z-dn.net/?f=%5C%7B-4%2C%20-1%2C%200%2C%202%2C%207%5C%7D)
Step-by-step explanation:
The domain of the function is the set of all possible inputs for the function. Therefore, the set of all possible inputs is
.
You have a system of equations
![\left \{ {{y = -x^2+2x-9} \atop {y =-6x+6}} \right.](https://tex.z-dn.net/?f=%20%5Cleft%20%5C%7B%20%7B%7By%20%3D%20-x%5E2%2B2x-9%7D%20%5Catop%20%7By%20%3D-6x%2B6%7D%7D%20%5Cright.%20)
.
1. Substitude right side of second equation into the left side of the first equation:
![-6x+6=-x^2+2x-9](https://tex.z-dn.net/?f=-6x%2B6%3D-x%5E2%2B2x-9)
.
2. Solve this equation:
![x^2-2x+9-6x+6=0, \\ x^2-8x+15=0, \\ D=(-8)^2-4\cdot 1\cdot 15=64-60=4, \\ \sqrt{D}=2, \\ x_{1,2}=\dfrac{8\pm 2}{2 } =3,5](https://tex.z-dn.net/?f=x%5E2-2x%2B9-6x%2B6%3D0%2C%20%5C%5C%20x%5E2-8x%2B15%3D0%2C%20%5C%5C%20D%3D%28-8%29%5E2-4%5Ccdot%201%5Ccdot%2015%3D64-60%3D4%2C%20%20%5C%5C%20%5Csqrt%7BD%7D%3D2%2C%20%20%5C%5C%20x_%7B1%2C2%7D%3D%5Cdfrac%7B8%5Cpm%202%7D%7B2%20%20%7D%20%3D3%2C5)
.
3. Find y:
for
![x_1=3, y_1=-6\cdot 3+6=-18+6=-12](https://tex.z-dn.net/?f=x_1%3D3%2C%20y_1%3D-6%5Ccdot%203%2B6%3D-18%2B6%3D-12)
,
for
![x_2=5, y_2=-6\cdot 5+6=-30+6=-24](https://tex.z-dn.net/?f=x_2%3D5%2C%20y_2%3D-6%5Ccdot%205%2B6%3D-30%2B6%3D-24)
.
4. The solutions of the system are: (3,-12) and (5,-24).
Answer: Correct choice is A.
If you subtract Betty's time for the swim, 27.948 seconds, from Nancy's time, 28.004 seconds, you will find that Betty was faster than Nancy by 0.056 seconds. She would be considered the winner of the 50-meter freestyle swim.
Reflection across the y-axis