It is 6 sq. units. I hope you do well. Have a wonderful day.
Answer:
5
Step-by-step explanation:
Plug in x = 2 into the equation 2x + 1
2x + 1
2 * 2 + 1
4 + 1
5
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:
3:4
Step-by-step explanation:
This is basically asking you to simplify the values and find the lowest ratio that compares their sizes. Starting with 27:36, you simplify. You could divide by 3, but 9 also works. Dividing both by 9 gives you 3:4, which is the most simplified answer.
Answer:
45 mins
Step-by-step explanation:
Estimated time it would take to visit with each client = fraction of time required for one client x 60 minutes
3/4 x 60 = 45 minutes
time it would take to visit with 7 clients = 7 x 45 minutes = 5hours 25 mins
