Let us say that:
K = age of Kristen
B = age of Ben
From the problem, we make the equations:
eqtn 1: K + B = 32
eqtn 2: (K – 4) = 2 (B – 4)
Simplifying eqtn 2:
K – 4 = 2 B – 8
K = 2 B – 4
Plugging in this to eqtn 2:
(2 B – 4) + B = 32
3 B – 4 = 32
3 B = 36
B = 12
From eqtn 2:
K = 2 B – 4 = 2 (12) – 4 = 20
So Kristen is 20 while Ben is 12.
Answer:
Step-by-step explanation:
We know that time is distance over velocity, that is:
time = distance / velocity
t = d / v
Now from the given:
d / 460 + d / 500 = 4.8
Now we can find for d:
d = 4.8 / [1/460 + 1/500]
d = 1150 miles
So the time of each flight is:
flight = 1150 / 460 = 2.5 hours
<span>return flight = 1150 / 500 = 2.3 hours</span>
Answer:
Problem 9: -1/2
Problem 10: 1/5
Step-by-step explanation:
Problem 10: Label the given ln e^(1/5) as y = ln e^(1/5).
Write the identity e = e. Raise the first e to the power y and the second e to the power 1/5 (note that ln e^(1/5) = 1/5). Thus, we have:
e^y = e^(1/5), so that y = 1/5 (answer).
Problem 9: Let y = (log to the base 4 of) ∛1 / ∛8, or
y = (log to the base 4 of) ∛1 / ∛8, or
y = (log to the base 4 of) 1 /2
Write out the obvious:
4 = 4
Raise the first 4 to the power y and raise the second 4 to the power (log to the base 4 of) 1 /2. This results in:
4^y = 1/2. Solve this for y.
Note that 4^(1/2) = 2, so that 4^(-1/2) = 1/2
Thus, y = -1/2
Answer:
2 5/9
Step-by-step explanation:
2.5 repeating is 2 5/9 as a fraction (mixed number) or 23/9 (fraction)
