check the pictured below.
now, notice that APB is just a flat-line and therefore those two angles there add up to 180°.
also notice that since ∡ACB is 90°, then those two angles add up to that much.
![\bf \stackrel{\measuredangle ACP}{(3x+2y)}+\stackrel{\measuredangle BCP}{(3x+4y)}=90\implies 6x+6y=90\implies \stackrel{\textit{common factor}}{6(x+y)}=90 \\\\\\ x+y=\cfrac{90}{6}\implies x+y=15\implies \boxed{x=15-y} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Cmeasuredangle%20ACP%7D%7B%283x%2B2y%29%7D%2B%5Cstackrel%7B%5Cmeasuredangle%20BCP%7D%7B%283x%2B4y%29%7D%3D90%5Cimplies%206x%2B6y%3D90%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bcommon%20factor%7D%7D%7B6%28x%2By%29%7D%3D90%0A%5C%5C%5C%5C%5C%5C%0Ax%2By%3D%5Ccfrac%7B90%7D%7B6%7D%5Cimplies%20x%2By%3D15%5Cimplies%20%5Cboxed%7Bx%3D15-y%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill)
![\bf \stackrel{\measuredangle APC}{(7x+3)}+\stackrel{\measuredangle BPC}{(16y)}=180\implies 7x+16y=177\implies 7\left( \boxed{15-y} \right)+16y=177 \\\\\\ 105-7y+16y=177\implies 9y=72\implies y=\cfrac{72}{9}\implies \blacktriangleright y=8 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \measuredangle BPC=16(8)\implies \measuredangle BPC=128](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Cmeasuredangle%20APC%7D%7B%287x%2B3%29%7D%2B%5Cstackrel%7B%5Cmeasuredangle%20BPC%7D%7B%2816y%29%7D%3D180%5Cimplies%207x%2B16y%3D177%5Cimplies%207%5Cleft%28%20%5Cboxed%7B15-y%7D%20%5Cright%29%2B16y%3D177%0A%5C%5C%5C%5C%5C%5C%0A105-7y%2B16y%3D177%5Cimplies%209y%3D72%5Cimplies%20y%3D%5Ccfrac%7B72%7D%7B9%7D%5Cimplies%20%5Cblacktriangleright%20y%3D8%20%5Cblacktriangleleft%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Cmeasuredangle%20BPC%3D16%288%29%5Cimplies%20%5Cmeasuredangle%20BPC%3D128)
The annual number of cases can be modeled using a quadratic equation y = 14x2 – 9x + 1. the variable x represents the number of years after 2008. the variable y represents the number of pertussis cases in year x. according to the equation, in what year can the county be expected to have 2,619 cases of pertussis?
Perpendicular lines is e
Angle is c
Line segment is a
Parallel lines is h
Circles is f
The correct answer is D.
The symbol you are looking at is sigma, which means sum of all. Because the number on the bottom is 1 and the top is 6, these are the start and end numbers for our n value. Therefore, it means to add together all of the values of your expression (n -3), for all of the values with n equaling between 1 and 6. So let's plug in all of the numbers for n they ask for and see what we have.
1
1 - 3 = -2
2
2 - 3 = -1
3
3 - 3 = 0
4
4 - 3 = 1
5
5 - 3 = 2
6
6 - 3 = 3
Now, when we add all of these numbers up, we look for the answer.
-2 + -1 + 0 + 1 + 2 + 3 = 3
This is the answer we see in D