Answer: 
<u>Step-by-step explanation:</u>
It is given that θ is between 270° and 360°, which means that θ is located in Quadrant IV ⇒ (x > 0, y < 0). Furthermore, the half-angle will be between 135° and 180°, which means the half-angle is in Quadrant II ⇒ 
It is given that sin θ = 
⇒ y = -7 & hyp = 25
Use Pythagorean Theorem to find "x":
x² + y² = hyp²
x² + (-7)² = 25²
x² + 49 = 625
x² = 576
x = 24
Use the "x" and "hyp" values to find cos θ:
Lastly, input cos θ into the half angle formula:
Reminder: We previously determined that the half-angle will be negative.
9514 1404 393
Answer:
7.92 years
Step-by-step explanation:
We want to find t such that ...
3 = 2^(t/5)
where 2^(t/5) is the annual multiplier when doubling time is 5 years.
Taking logs, we have ...
log(3) = (t/5)log(2)
t = 5·log(3)/log(2) ≈ 7.92 . . . years
It will take about 7.92 years for the population to triple.
Answer:
x=12 and y=31
Step-by-step explanation:
First, ( 5x - 7 ) and ( 3x + 17 ) are alternate interior angles, which means they are congruent, or equal:
5x - 7 = 3x + 17
Add 7 to each side:
5x = 3x + 24
Subtract 3x from both sides:
2x = 24
Divide each side by 2:
x = 12
Now we can see that ( 5x - 7 ) and ( 4y + 3 ) are supplementary angles, which means they will add up to 180 degrees:
5x - 7 + 4y + 3 = 180
Substitute 12 in for x to solve for y:
5 ( 12 ) - 7 + 4y + 3 = 180
60 - 7 + 4y + 3 = 180
combine like terms:
( 60 + ( -7 ) + 3 ) + 4y = 180
56 + 4y = 180
Subtract 56 from each side:
4y = 124
Divide each side by 4:
y = 31
Will got 12 and John got 24.
You would set the equation as:
36=n+2n
Combine like terms
36=3n
Divide 3 from both sides
12=n
If you want to check it
12+2(12)=36
12+24=36
36=36
