The path of the ball is an illustration of absolute equation.
The equation of the path is: ![y =- \frac{12}7|x- 4.8| + 6.4](https://tex.z-dn.net/?f=y%20%3D-%20%5Cfrac%7B12%7D7%7Cx-%204.8%7C%20%2B%206.4)
The given parameters are:
--- the vertex (i.e. the point where the ball hits the wall)
![(x_1,y_1) = (2,1.6)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%282%2C1.6%29)
![(x_2,y_2) = (7.6,1.6)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%287.6%2C1.6%29)
An absolute function is represented as:
![y = a |x - h| + k](https://tex.z-dn.net/?f=y%20%3D%20a%20%7Cx%20-%20h%7C%20%2B%20k)
Substitute ![(h,k) = (4.8,6.4)](https://tex.z-dn.net/?f=%28h%2Ck%29%20%3D%20%284.8%2C6.4%29)
![y = a |x - 4.8| + 6.4](https://tex.z-dn.net/?f=y%20%3D%20a%20%7Cx%20-%204.8%7C%20%2B%206.4)
Substitute
for x and y
![1.6 = a|2 - 4.8| + 6.4](https://tex.z-dn.net/?f=1.6%20%3D%20a%7C2%20-%204.8%7C%20%2B%206.4)
![1.6 = a|- 2.8| + 6.4](https://tex.z-dn.net/?f=1.6%20%3D%20a%7C-%202.8%7C%20%2B%206.4)
Remove absolute bracket
![1.6 = 2.8a + 6.4](https://tex.z-dn.net/?f=1.6%20%3D%202.8a%20%2B%206.4)
Collect like terms
![2.8a = -6.4+1.6](https://tex.z-dn.net/?f=2.8a%20%3D%20-6.4%2B1.6)
![2.8a =- 4.8](https://tex.z-dn.net/?f=2.8a%20%3D-%204.8)
Solve for a
![a =-\frac{4.8}{2.8}](https://tex.z-dn.net/?f=a%20%3D-%5Cfrac%7B4.8%7D%7B2.8%7D)
Simplify
![a =-\frac{12}{7}](https://tex.z-dn.net/?f=a%20%3D-%5Cfrac%7B12%7D%7B7%7D)
Substitute
in ![y = a |x - 4.8| + 6.4](https://tex.z-dn.net/?f=y%20%3D%20a%20%7Cx%20-%204.8%7C%20%2B%206.4)
![y =- \frac{12}7|x- 4.8| + 6.4](https://tex.z-dn.net/?f=y%20%3D-%20%5Cfrac%7B12%7D7%7Cx-%204.8%7C%20%2B%206.4)
Hence, the equation of the path is: ![y =- \frac{12}7|x- 4.8| + 6.4](https://tex.z-dn.net/?f=y%20%3D-%20%5Cfrac%7B12%7D7%7Cx-%204.8%7C%20%2B%206.4)
See attachment for graph that models the path
Read more about absolute equations at:
brainly.com/question/2166748
The answer is C.
Since here taxable income is over $77,100 and below $160,850, her tax is $15,698.75 + [.28*($95,000 - $77,100)].
Tax = $15,698.75 + [.28*($17,900)]<span>.
= </span>$15,698.75 + [$5012]<span>.
=</span><span> $</span><span>20,710.75
Thank you for posting this question. Please feel free to ask me more.</span>
I would probably distribute 15 with the parentheses 15x 9860 which is 147,900 then you would add 6997+147,900
Y= 154187
If it is 50 pages in an hour, half an hour would be 25 pages, and if it is 40 pages in an hour it would be 20 pages in half an hour, the answer is 5 pages more in half hour