Answer:
See below
Step-by-step explanation:
if b^2 - 4ac is greater than 0 then there are 2 answers that are not equal to each other, but both are real.
If b^2 - 4ac = 0 then you have two real answers that are equal
The real problem is what happens when b^2 - 4ac is less than 0? In this case the answer is a complex number of the form
a + bi
a - bi
where i is the square root of - 1
Answer:
1320 ways
Step-by-step explanation:
To solve we need to use permutations and factorials. If we wanted to find where they would all place 1-12, we would do 12!
12! is the same as 12x11x10x9x8... etc
But in this problem, we are only looking for the top 3.
We can set up a formula
![\frac{n!}{(n-r)!}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
N is the number of options that are available and r represents the amount we are choosing
In this case, we have 12 teams so n=12
We are looking for the top 3 so r=3
![\frac{12!}{(12-3)!}](https://tex.z-dn.net/?f=%5Cfrac%7B12%21%7D%7B%2812-3%29%21%7D)
![\frac{12!}{9!}](https://tex.z-dn.net/?f=%5Cfrac%7B12%21%7D%7B9%21%7D)
We expand the equation and cancel out
![\frac{12x11x10x9x8x7x6x5x4x3x2}{9x8x7x6x5x4x3x2}](https://tex.z-dn.net/?f=%5Cfrac%7B12x11x10x9x8x7x6x5x4x3x2%7D%7B9x8x7x6x5x4x3x2%7D)
Notice how both sides can cancel out every number 9 and below
That leaves us with 12x11x10
1320 ways
Answer
6 hours and 25 mins Tell me if I’m wrong
The correct answer is 2 pi