![y= ax^{2} -8x-3](https://tex.z-dn.net/?f=y%3D%20ax%5E%7B2%7D%20-8x-3)
1.
the line of symmetry is x=2, means that the x coordinate of the vertex is x=2.
the point x=2 is the midpoint of the roots
![x_1](https://tex.z-dn.net/?f=x_1)
and
![x_2](https://tex.z-dn.net/?f=x_2)
.
so
![\frac{x_1+x_2}{2}=2 ](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%3D2%0A%20)
![x_1+x_2=4](https://tex.z-dn.net/?f=x_1%2Bx_2%3D4)
Remark: in the x-axis, if c is the midpoint of a and b, then
![c= \frac{a+b}{2}](https://tex.z-dn.net/?f=c%3D%20%5Cfrac%7Ba%2Bb%7D%7B2%7D%20)
2.
since
![x_1](https://tex.z-dn.net/?f=x_1)
and
![x_2](https://tex.z-dn.net/?f=x_2)
are roots
![a(x_1)^{2} -8(x_1)-3=0](https://tex.z-dn.net/?f=a%28x_1%29%5E%7B2%7D%20-8%28x_1%29-3%3D0)
and
![a(x_2)^{2} -8(x_2)-3=0](https://tex.z-dn.net/?f=a%28x_2%29%5E%7B2%7D%20-8%28x_2%29-3%3D0)
3.
equalizing:
![a(x_1)^{2} -8(x_1)-3=a(x_2)^{2} -8(x_2)-3](https://tex.z-dn.net/?f=a%28x_1%29%5E%7B2%7D%20-8%28x_1%29-3%3Da%28x_2%29%5E%7B2%7D%20-8%28x_2%29-3)
![a(x_1)^{2} -8(x_1)=a(x_2)^{2} -8(x_2)](https://tex.z-dn.net/?f=a%28x_1%29%5E%7B2%7D%20-8%28x_1%29%3Da%28x_2%29%5E%7B2%7D%20-8%28x_2%29)
![a(x_1)^{2}-a(x_2)^{2} =8(x_1) -8(x_2)](https://tex.z-dn.net/?f=a%28x_1%29%5E%7B2%7D-a%28x_2%29%5E%7B2%7D%20%3D8%28x_1%29%20-8%28x_2%29)
in the left side factorize a, in the left side factorize 8:
![a[(x_1)^{2}-(x_2)^{2}] =8(x_1 -x_2)](https://tex.z-dn.net/?f=a%5B%28x_1%29%5E%7B2%7D-%28x_2%29%5E%7B2%7D%5D%20%3D8%28x_1%20-x_2%29)
in the right side use the difference of squares formula:
![a(x_1 -x_2)(x_1 +x_2) =8(x_1 -x_2)](https://tex.z-dn.net/?f=a%28x_1%20-x_2%29%28x_1%20%2Bx_2%29%20%3D8%28x_1%20-x_2%29)
simplify by
![(x_1 -x_2)](https://tex.z-dn.net/?f=%28x_1%20-x_2%29)
![a(x_1 +x_2) =8](https://tex.z-dn.net/?f=a%28x_1%20%2Bx_2%29%20%3D8)
substitute
![(x_1 +x_2)](https://tex.z-dn.net/?f=%28x_1%20%2Bx_2%29)
with 4:
![a*4 =8](https://tex.z-dn.net/?f=a%2A4%20%3D8)
a=2
Answer: C)2
Answer:
50 lbs of food
Step-by-step explanation:
If you add 5 lions that eat 250 pounds of food a day, all you need to do is divide to get your answer
The complete question describes the use of word problems to represent inequalities. The $21 means that there is a limit to the number of stops she can take using the train.
The inequality that represents this scenario is:
![5 + 2.75x \le 21](https://tex.z-dn.net/?f=5%20%2B%202.75x%20%5Cle%2021)
From the complete question, we have the following parameters:
Initial Fee = $5
Rate per stop = $2.75
Amount = $21
The inequality that represents the scenario is as follows:
Initial Fee + Rate * Number of stops <= Amount
We use <= because the total charges must not exceed the amount.
Let the number of stops be x.
The above formula becomes
![5 + 2.75 * x \le 21](https://tex.z-dn.net/?f=5%20%2B%202.75%20%2A%20x%20%5Cle%2021)
![5 + 2.75x \le 21](https://tex.z-dn.net/?f=5%20%2B%202.75x%20%5Cle%2021)
Read more at:
brainly.com/question/16061085