There would be 12 people at the party!
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Hope this helps!
Answer:
About 110.6
Step-by-step explanation:
The sine of an angle is the length of the opposite side divided by the length of the hypotenuse.

Hope this helps!
Answer: OPTION C.
Step-by-step explanation:
Given the following expression:

You can simplify this expression applying these steps:
First step: You must apply Distributive property:
Second step: You need to add the like terms.
Then, you get:
You can observe that this simplified expression matches with the expression provided in Option C.