36 feet okay it is 36 feet of the area
12,089 is less than 12,098
The first choice is the correct one.
5 yellow marbles out of total of 17 marbles so 5/17
Answer:
k = -8
Step-by-step explanation:
The location of P is ...
P = (2A+B)/3 = (2·2+5, 2·1-8)/3 = (3, -2)
Putting this point into the equation for the line, we have ...
2(3) -(-2) +k = 0
8 +k = 0
k = -8
By induction:
It's true for
![n=1](https://tex.z-dn.net/?f=n%3D1)
, since
![1\cdot2\cdot3](https://tex.z-dn.net/?f=1%5Ccdot2%5Ccdot3)
clearly contains a factor of 3.
Suppose it's true for
![n=k](https://tex.z-dn.net/?f=n%3Dk)
, that
![k(k+1)(k+2)](https://tex.z-dn.net/?f=k%28k%2B1%29%28k%2B2%29)
is divisible by 3. Then
![(k+1)(k+2)(k+3)=\dfrac{k(k+1)(k+2)(k+3)}k=\dfrac{3m(k+3)}k](https://tex.z-dn.net/?f=%28k%2B1%29%28k%2B2%29%28k%2B3%29%3D%5Cdfrac%7Bk%28k%2B1%29%28k%2B2%29%28k%2B3%29%7Dk%3D%5Cdfrac%7B3m%28k%2B3%29%7Dk)
where
![m](https://tex.z-dn.net/?f=m)
is an integer. This reduces to
![\dfrac{3m(k+3)}k=3m+9\dfrac mk](https://tex.z-dn.net/?f=%5Cdfrac%7B3m%28k%2B3%29%7Dk%3D3m%2B9%5Cdfrac%20mk)
and both terms are clearly multiples of 3. We know that
![\dfrac mk](https://tex.z-dn.net/?f=%5Cdfrac%20mk)
is an integer since we had set
![m=k(k+1)(k+2)](https://tex.z-dn.net/?f=m%3Dk%28k%2B1%29%28k%2B2%29)
previously, which implies
![m](https://tex.z-dn.net/?f=m)
is a multiple of
![k](https://tex.z-dn.net/?f=k)
. So the statement is true.