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: It will take 7 stages for all 19,530 families to be called.
In the first stage, only 5 families are called.
In the second stage, we would have 5 x 5 = 25 families being called.
In the third stage, we would have 5 x 5 x 5 = 125 families being called.
We can use exponents to finish the list and see when our goal is reached.
4th stage: 5^4 = 625
5th stage: 5^5 = 3125
6th stage: 5^6 = 15625
7th stage: 5^7 = 78,125
Step-by-step explanation:
It's a question of trigonometry.
You need to remember that tangent (tan) stands for Perpendicular / Base.
So, tan P = QR / PR
By Pythagoras Theorem,
34² = 30² + x²
x² = 34² - 30²
x² = 1156 - 900
x² = 256
x = 16
Now, placing the values,
tan P = 30 / 16
tan P = 1.875
HOPE IT HELPS ^_^
Multiply the price by (1 + sales tax).
85 x (1+0.07)
85 x 1.07 = 90.95
He will pay $90.95
The answer would be the first one or 3y2, this is because it goes into each term evenly enough to simplify it.
