Answer:
or 
Step-by-step explanation:
We use casework on when
and when
.
For the first case,
, we add 9 to both sides to get
.
Dividing both sides by 3 gives

For the second case,
, we add 9 to both sides to get
.
Dividing both sides by 3 gives
.
Checking both cases, we plug in
and
.
For the first case, we have
, which satisfies the equation.
For the second case, we have
, which also satisfies the equation.
This gives us two solutions to the equation;
and
.
25% of 40 is 10 so it would be $40+10 for the price so that should be 50. Markup=profit/cost*100
Answer:
70 years
Step-by-step explanation:
35 years before Christ and then another 35 years after: 35 + 35 = 70 years
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
The measure of B’C’ is 18 inches