Answer:
Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.
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)
Answer:
geometric
arithmetic
arithmetic
Step-by-step explanation:
1.
4/9,4/3,4,12,36
Multiply each term by 3 to get the next term. There is a common ratio between terms, so it geometric.
2.
0,1,2,3,4,5,6
Add 1 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.
3.
-10,-6,-2,2,6,10
Add 4 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.
Answer:
Pretty sure you put the wrong picture on this question, but the answer to the one you put is A
Step-by-step explanation:
A1=8
common ratio=r
sum of 6 terms
S=a1+a2+a3+...+a6
=a1(1+r+r^2+...+r^5)
=a1(r^6-1)/(r-1)
but we're given S=74648
=>
8(r^6-1)/(r-1)=74648
Cross multiply and solve for r (by trial and error)
r^6-1=9331(r-1)
r=6
so
a(3)=a1*r^(3-1)
=8*(6^2)
=288
