Answer:
165 different teams of 3 students can be formed for competitions
Step-by-step explanation:
Combinations of m elements taken from n in n (m≥n) are called all possible groupings that can be made with the m elements so that:
- Not all items fit
- No matter the order
- Elements are not repeated
That is, a combination is an arrangement of elements where the place or position they occupy within the arrangement does not matter. In a combination it is interesting to form groups and their content.
To calculate the number of combinations, the following expression is applied:

It indicates the combinations of m objects taken from among n objects, where the term "n!" is called "factorial of n" and is the multiplication of all the numbers that go from "n" to 1.
In this case:
Replacing:

Solving:

being:
- 3!=3*2*1=6
- 8!=8*7*6*5*4*3*2*1=40,320
- 11!=39,916,800
So:

C= 165
<u><em>165 different teams of 3 students can be formed for competitions</em></u>
Answer:
f(x) = x³+2x²-16x-32
Step-by-step explanation:
f(x) = 0 when x = -4, -2, 4
So these are the roots
Factors are (x+4)(x+2)(x-4)
f(x) = [(x+4)(x-4)](x+2)
f(x) = (x²-16)(x+2)
f(x) = x³+2x²-16x-32
If two triangles are similar, that means their side lengths are proportional, so we get the equation

Thus x = 13.6.
Hope that helped!
One over fifthteen...................................