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:
x = 3
Step-by-step explanation:
3(10-x)=21
30-3x=21
-30 -30
-3x=-9
x=3
Answer:
16
Step-by-step explanation:
We can use the Pythagorean theorem to find the height
a^2 + b^2 = c^2 with a and b legs and c the hypotenuse
The triangle is a right triangle with legs GH and FG and hypotenuse FH
FG^2 + GH^2 = FH^2
FG ^2 + 12^2 = 20^2
FG^2 +144 = 400
Subtract 144 from each side
FG^2 +144-144 = 400-144
FG^2 =256
Take the square root of each side
sqrt(FG^2) =sqrt(256)
FG = 16
Answer:-17x+6
Step-by-step explanation:
-15x-2x+6
-17x+6
There is no x value as there is no solution. I plugged into desmos cause it didnt make sense at first then it showed me that it has no solution.
