So much stuff at once...
I'm only going to give you the information needed to do this.
All of these involve the 4 main exponent laws.
1) Multiplying.
When you multiply two 'numbers' that share the same base, you add exponents and keep the base the same. (ex. 4g²(4g⁴) = 4g²⁺⁴ = 4g⁶)
2) Dividing.
When you divide two 'numbers' that share the same base, you subtract exponents and keep the base the same. (ex. 3a⁷ / 3a⁴ = 3a⁷⁻³ = 3a³)
3) To the power of 1.
Anything to the power of 1 is the same. (ex. 5a¹ = 5a)
4) To the power of 0.
Anything to the power of 0 = 1. (ex. 2d⁰ = 2(1) = 2)
This should help.
Given:
27y and 54y³
To find:
The highest common factor (HCF) using prime factorization.
Solution:
We have,
27y and 54y³
Using the prime factorization, we get
Now, the common prime factors are 3, 3, 3 and y. So,
Therefore, the highest common factor of the given terms is 27y.
Let's interpret this equation. If we have that a runner has 0 races under his belt, he completes the race in 38.1 min. We have that the slope is -1.2 min/race and the intercept at n=0 is 38.1 min. Hence, for every race, the duration of the run decreases by 1.2 min (or increases by -1.2 min).
Lets derive that. Suppose a runner that has run n races, runs once more.
The difference of times is:
(-1.2(n+1)+38.1)-(-1.2n+38.1)=-1.2(n+1)-(-1.2n)= -1.2n-1.2+1.2n=1.2 minutes.
Hence, the correct answer is the first.
Answer:
69% increase (nice)
Step-by-step explanation:
2900 / 4200 = .69047
Round up the answer to nearest hundredth
.69
turn it into a percentage
69%
Answer:
80% of 65
Step-by-step explanation:
Hope it will help you.