The measure of a single angle of deviation on a regular octagon is 45 degrees.
<h3>Polygons</h3>
An octagon is a shape with 8 sides and 8 angles. The sum of an interior angle of an octagon is 1080 degrees.
<h3>Point of interseection</h3>
The point where the intersection of lines meets forms an angle of 45 degrees. Hence based on the given question, we can conclude that the measure of a single angle of deviation on a regular octagon is 45 degrees.
Learn more on polygons here: brainly.com/question/1487036
Shelly and her friends would equal 5 people so you take 138.60 and divided by 5 your answer is 27.72
Answer
x = 1
Explanation:
Given the following equation
![\begin{gathered} (2x+2)^{\frac{1}{2}}=\text{ -2} \\ \text{According to the law of indicies} \\ x^{\frac{1}{2}}\text{ = }\sqrt[]{x} \\ (2x+2)^{\frac{1}{2}}\text{ = }\sqrt[]{(2x\text{ + 2)}} \\ \text{Step 1: Take the square of both sides} \\ \sqrt[]{(2x\text{ + 2) }}\text{ = -2} \\ \sqrt[]{(2x+2)^2}=-2^2 \\ 2x\text{ + 2 = 4} \\ \text{Collect the like terms} \\ 2x\text{ = 4 - 2} \\ 2x\text{ = 2} \\ \text{Divide both sides by 2} \\ \frac{2x}{2}\text{ = }\frac{2}{2} \\ x\text{ = 1} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%282x%2B2%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Ctext%7B%20-2%7D%20%5C%5C%20%5Ctext%7BAccording%20to%20the%20law%20of%20indicies%7D%20%5C%5C%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7Bx%7D%20%5C%5C%20%282x%2B2%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7B%282x%5Ctext%7B%20%2B%202%29%7D%7D%20%5C%5C%20%5Ctext%7BStep%201%3A%20Take%20the%20square%20of%20both%20sides%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%282x%5Ctext%7B%20%2B%202%29%20%7D%7D%5Ctext%7B%20%3D%20-2%7D%20%5C%5C%20%5Csqrt%5B%5D%7B%282x%2B2%29%5E2%7D%3D-2%5E2%20%5C%5C%202x%5Ctext%7B%20%2B%202%20%3D%204%7D%20%5C%5C%20%5Ctext%7BCollect%20the%20like%20terms%7D%20%5C%5C%202x%5Ctext%7B%20%3D%204%20-%202%7D%20%5C%5C%202x%5Ctext%7B%20%3D%202%7D%20%5C%5C%20%5Ctext%7BDivide%20both%20sides%20by%202%7D%20%5C%5C%20%5Cfrac%7B2x%7D%7B2%7D%5Ctext%7B%20%3D%20%7D%5Cfrac%7B2%7D%7B2%7D%20%5C%5C%20x%5Ctext%7B%20%3D%201%7D%20%5Cend%7Bgathered%7D)
Therefore, x = 1
Before we start answering the question, let's define the compound interest formula:
Where:
<span>'A'</span> is the amount of money in dollars
'P' is the principal amount of money in dollars
'r' is the interest rate (decimal)
'n' is the number of times interest is compounded per year
't' is the time in years
<span>
(A) Find Principal Amount</span><u /><span><u>Given:</u>
</span>A = 12,000
P = ?
r = 0.08
n = 2 (semiannually)
t = 5
Now we plug our values in and solve:



∴ You would have to deposit $8106.77 in order to have $12,000 in 5 years from now.
(B) Find Principal AmountSame given values as above, with the exception of 't' which is now 10 instead of 5.



∴ You would have to deposit $5476.64 in order to have $12,000 in 10 years from now.
Hope this helps!