Given:
The measure of three sides of a triangle are 8, 7 and 14.
To find:
The measure of the angle opposite the side of length 8.
Solution:
According to the Law of Cosine:

Let a=8, b=7 and c=14, then by using Law of Cosine, we get



Taking cos inverse on both sides.



Therefore, the measure of the angle opposite the side of length 8 is 22.6 degrees.
Tony’s backpack can carry weight up to 22 but not more that that
If the variable n represents the total weight carried by tony
Then ; n less than or equal to (n=1+3+3b
=4+3b
Where b represents book
4+3b is less or equal to 22
3b is less or equal to 18
b is less or equal to 6
Therefore Tony’s backpack cannot carry more than 6 books
The common ratio of 2, 10/3, 50/9 is 
<u>Solution:</u>
Given, series of elements are 
We have to find the common ratio of the above given series.
We know that, common ratio of an G.P is division of any number in that series with the previous number of the series.
So, now take
and 2


Hence, the common ratio of the given series is 
Answer:
Step-by-step explanation:
To find the least number of party favors, we have to consider the number of guests.
In this case, there are two possibilities—6 or 8.
For 6: 6, 12, 18, 24 (Add 6 to each number)
For 8: 8, 16, 24 (Add 8 to each number)
Now in both series, the least number (that is in common) is 24. Hence, Madison should make at least 24 party favors.