The standard form: Ax + By = C
3x - y = -6 YES - A = 3, B = -1, C = -6
3x + y = 6 YES - A = 3, B = 1, C = 6
x + 6y = 9 YES - A = 1, B = 6, C = 9
x - 6y = -9 YES - A = 1, B = -6, C = -9
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Answer:
$150
Step-by-step explanation:
$100 + 100% = $200 in the first year
$200 - 25% = $150 in the second year
Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
Answer:
6
Step-by-step explanation:
You have to find what to multiply by to get to the next term
-30 ÷ -5 = 6
- 180 ÷ -30 = 6
therfore the common ratio is 6
