Use the change-of-basis identity,

to write

Use the product-to-sum identity,

to write

Redistribute the factors on the left side as

and simplify to

Now expand the right side:

Simplify and rewrite using the logarithm properties mentioned earlier.





(C)
Answer:
160
Step-by-step explanation:
800 gallons in 5 days. The days is the denominator and the gallons are the numerator, whatever you do the the bottom you do to the top, so you divide the denominator by 5 and the numerator by 5 and you get 160 gallons per day. If you want to know how your answer is right, multiply 160 by 5
Answer:
10x+15
Step-by-step explanation:
area of the two rectangles combined is one big rectangle
area of rectange= base*height
base length: 2x+3
height: 5
(2x+3)*5
=(2x*5)+(3*5)
=10x+15
Answer:
B: Permutation; Number of ways = 60
Step-by-step explanation:
First we have to decide if this is a problem of permutation or combination. The rule is:
- If the order matters, permutations will be used
- If order does not matter, combinations will be used
In this problem, they order of awarding the medals matters, so this is a permutation problem.
We have to award 3 medals among 5 runners. So this can be done in 5P3 ways:

Therefore, there are 60 ways to award the medal. Therefore, the correct answer is B.