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!
Mel should use the least common multiple to solve the problem
<u>Solution:</u>
Given, Mel has to put the greatest number of bolts and nuts in each box so each box has the same number of bolts and the same number of nuts.
We have to find that should Mel use the greatest common factor or the least common multiple to solve the problem?
He should use least common multiple.
Let us see an example, suppose 12 bolts and nuts are to be fit in 6 boxes.
Then, if we took H.C.F of 12 and 6, it is 6, which means 6 bolts and nuts in each box, but, after filling 2 boxes with 6 bolts and nuts, there will be nothing left, which is wrong as remaining boxes are empty.
So the remaining method to choose is L.C.M.
Hence, he should use L.C.M method.
Answer:
x = 4
x = -1
Step-by-step explanation:
Length(l)= 2w
Width(w)= w
Area(A) = l*w
A= 128 ft²
128= l*w
128= (2w)w
2w²= 128
w²= 64
w=√64= 8 ft
w= 8 ft
length(l)= 2w
l=2(8)
l=16 ft
P= 2l+2w
P=2(16)+2(8)= 32+16= 48ft
P= 48ft
Answer:
The Perimeter of this rectangle is 48 feet.
Leave any questions you still have in the comments below please! Thank you! Hope this helped! :)
