The gym has eleven different types of machines in the weight room. geoff has time to use only three of them this afternoon. how many different combinations of machines can geoff choose from to use?

Here the key word is combination, i.e. the order of using the machines is not important, it's the choice of the three machines.

One way to calculate:
first machine: 11 choices
second machine : 10 choices
third machine: 9 choices
Total number of ways in order: 11*10*9
But there are 6=3! ways the three machines could be ordered
so the combination is actually 11*10*9/(3*2*1)=165

Another way:
The number of combinations of r choices taken from n objects is
n!/(r!(n-r)!)
=11!/(3!(8!))
=165 
as before.

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle