12k-2+6k
find like terms and put them next to each other
12k+6k-2
combine like terms
18k-2
C
Answer:
Hello,
Step-by-step explanation:
![A=(1,2)\\B=(0,-1)\\\overrightarrow{AB}=((0,-1)-(1,2)=(-1,-3)\ ||\overrightarrow{AB}||^2=1+9=10\\\overrightarrow{BC}=((3,-2)-(0,-1)=(3,-1)\ ||\overrightarrow{BC}||^2=9+1=10\\\\Triangle\ is\ isosceles.\\\\\overrightarrow{AB}.\overrightarrow{BC}=(-1,-3)*\left[\begin{array}{c}3\\-1\end{array}\right] =-3+3=0\\\\Triangle \ is\ right.\\\\](https://tex.z-dn.net/?f=A%3D%281%2C2%29%5C%5CB%3D%280%2C-1%29%5C%5C%5Coverrightarrow%7BAB%7D%3D%28%280%2C-1%29-%281%2C2%29%3D%28-1%2C-3%29%5C%20%7C%7C%5Coverrightarrow%7BAB%7D%7C%7C%5E2%3D1%2B9%3D10%5C%5C%5Coverrightarrow%7BBC%7D%3D%28%283%2C-2%29-%280%2C-1%29%3D%283%2C-1%29%5C%20%7C%7C%5Coverrightarrow%7BBC%7D%7C%7C%5E2%3D9%2B1%3D10%5C%5C%5C%5CTriangle%5C%20is%5C%20isosceles.%5C%5C%5C%5C%5Coverrightarrow%7BAB%7D.%5Coverrightarrow%7BBC%7D%3D%28-1%2C-3%29%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%5C%5C-1%5Cend%7Barray%7D%5Cright%5D%20%3D-3%2B3%3D0%5C%5C%5C%5CTriangle%20%5C%20is%5C%20right.%5C%5C%5C%5C)
The question is asking which formula will give the results
1, 9, 36, 100, 225, ...
for k values of
1, 2, 3, 4, 5, ...
You can try them out to see.
A) for k=2, gives 2*3/2 = 3 . . . not 9
B) for k=1, gives 2^3/3 = 8/3 . . . not 1
C) for k=2, gives (2^2*3^2)/4 = 9 . . . . looks promising
D) for k=1, gives 1*2^3/5 = 8/5 . . . not 1
Selection C is the only viable choice. (And the correct one.)