8m=2*2*2*m
36m^3=2*2*3*3*m*m*m
12=2*2*3
gcf=2*2
answer is 4
4 pounds (you need 3 2/6 pounds but if you can buy in whole pounds you need 4)
Answer:
The open spot? Sorry if I’m wrong
Step-by-step explanation:
Answer:
The statement is true.
Step-by-step explanation:
Let us assume that x is the required number.
Now, given that the number minus 3 is at most 12.
Hence, x - 3 ≤ 12
⇒ x ≤ 15 ......... (1)
And also given that 1 more than 2 times the number is at least 25.
Hence, 2x + 1 ≥ 25
⇒ 2x ≥ 24
⇒ x ≥ 12 .......... (2)
Therefore, from equations (1) and (2) we get the number must be greater than or equal to 12 or less than or equal to 15.
So, the statement is true. (Answer)
If

is an integer, you can use induction. First show the inequality holds for

. You have

, which is true.
Now assume this holds in general for

, i.e. that

. We want to prove the statement then must hold for

.
Because

, you have

and this must be greater than

for the statement to be true, so we require

for

. Well this is obviously true, because solving the inequality gives

. So you're done.
If you

is any real number, you can use derivatives to show that

increases monotonically and faster than

.