Answer:
The students can be paired up in 654,729,075 ways
Step-by-step explanation:
The 20 people can organize themselves in a line. The first and second people can make up a pair, the 2nd and 3rd can do the same. This can be done until all 20 of them have a pair. This will be done in 20! ways
If the two people in a pair swap positions. In mathematics, it is considered as a different arrangement. This can be done 
since there are 10 pairs We will have to divide by this.
If the 10 pairs can swap places with each other, it will form another pair. As a matter of fact, the 10 pairs can swap pairs with each other all they like. This can be done in 10! ways. we will also have to divide by this.
Hence the total number of ways = 
Answer:
Step-by-step explanation:
Write a system of equations to model the situation. Add the equations to eliminate the y-term and then solve for x. Substitute the value for x into one of the original equations to find y. Check your answer by substituting x = 8 and y = 2 into the original system.
Answer:
Step-by-step explanation:
Given
Required
Possible values of k
The general quadratic equation is:
Subtract and
Factorize:
Rewrite as:
Compare the above equation to:
For the equation to have two distinct solution, the following must be true:
So, we have:
Expand
Rewrite as:
Expand
Factorize
Factor out k + 6
Split:
or 
So:
or k 
To make the above inequality true, we set:
or 
So, the set of values of k is:
Answer:
I would say 32 but I'm so sorry if it's wrong
Answer:
A line is increasing if it goes up from left to right. The slope is positive, i.e. m > 0 {\displaystyle m>0} .
A line is decreasing if it goes down from left to right. The slope is negative, i.e. m < 0 {\displaystyle m<0} .
If a line is horizontal the slope is zero. This is a constant function.
If a line is vertical the slope is undefined (see below).
