Algebra probability ***
you have 6 friends who want to go to a concert with you, but you only have room in your car for 2 of them. to avoid accusations of favoritism, you have your friends draw straws: there are 4 long and 2 short straws, and the short straws win. how many possible pairs of friends could be chosen in this way?

15 possible pairs of friends could be chosen in this way.

Step-by-step explanation:

Given : You have 6 friends who want to go to a concert with you, but you only have room in your car for 2 of them. To avoid accusations of favoritism, you have your friends draw straws: There are 4 long and 2 short straws, and the short straws win.

To find : How many possible pairs of friends could be chosen in this way?  

Solution :

Total number of friends = 6

The space in the car is for 2 person.

Since, the order doesn't matter we have to choose 2 people out of 6 so we apply combination.

As There are 4 long and 2 short straws, and the short straws win.

i.e. that 2 friends were chosen.

So, Possible ways to find the pairs of friends is

Solving,

Therefore, 15 possible pairs of friends could be chosen in this way.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15