Answer:
At first, we have 3 expressions that are equal.
This is not true.
Answer:
Step-by-step explanation:
Given is a triangle RST and another triangle R'S'T' tranformed from RST
Vertices of RST are (0, 0), (negative 2, 3), (negative 3, 1).
Vertices of R'S'T' are (2, 0), (0, negative 3), (negative 1, negative 1).
Comparing the corresponding vertices we find that x coordinate increased by 2 while y coordinate got the different sign.
This indicates that there is both reflection and transformation horizontally to the right by 2 units
So first shifted right by 2 units so that vertices became
(2,0) (0,3) (-1,1)
Now reflected on the line y=0 i.e. x axis
New vertices are
(2,0) (0,-3) (-1,-1)
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:
1308
Step-by-step explanation:
multply
109 by 12
giving you 1,309
equation: 109×12
Answer:
lol nah <3
Step-by-step explanation:
i would try and help, but not with that trump pfp my dude
