6 choose 2
6C2 = 6!/(2!(6-2)!)
=6!/(2!4!)
=6•5/2
=15
The answer is 15 ways.
Answer:
b
Step-by-step explanation:
8-7-6-5-4-3-2-1-0-234 567 8 8
Answer:
Step-by-step explanation:
<u>Answer:</u>
Option C. The given system has two solutions.
<u>Solution:
</u>
The given equations are,
![y = -x + 1](https://tex.z-dn.net/?f=y%20%3D%20-x%20%2B%201)
![y = -x^2 + 4x-2](https://tex.z-dn.net/?f=y%20%3D%20-x%5E2%20%2B%204x-2)
From the equation we can say,
![-x+1 = -x^2+ 4x-2](https://tex.z-dn.net/?f=-x%2B1%20%3D%20-x%5E2%2B%204x-2)
![\Rightarrow-x^{2}+4 x-2+x-1=0](https://tex.z-dn.net/?f=%5CRightarrow-x%5E%7B2%7D%2B4%20x-2%2Bx-1%3D0)
![\Rightarrow-x^{2}+5 x-3=0](https://tex.z-dn.net/?f=%5CRightarrow-x%5E%7B2%7D%2B5%20x-3%3D0)
We know that the quadratic formula to solve this,
x has two values which are
Here, a = (-1), b = 5 , c = -3
So, ![x=\frac{(-5+\sqrt{(5)^{2}-4 x(-1)} \times(-3))}{2 \times(-1)}=\frac{(-5+\sqrt{25-12})}{-2}=\frac{(-5+\sqrt{13})}{-2}=\frac{(5-\sqrt{13})}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%28-5%2B%5Csqrt%7B%285%29%5E%7B2%7D-4%20x%28-1%29%7D%20%5Ctimes%28-3%29%29%7D%7B2%20%5Ctimes%28-1%29%7D%3D%5Cfrac%7B%28-5%2B%5Csqrt%7B25-12%7D%29%7D%7B-2%7D%3D%5Cfrac%7B%28-5%2B%5Csqrt%7B13%7D%29%7D%7B-2%7D%3D%5Cfrac%7B%285-%5Csqrt%7B13%7D%29%7D%7B2%7D)
Again ![x=\frac{(5+\sqrt{13})}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%285%2B%5Csqrt%7B13%7D%29%7D%7B2%7D)
Hence, x has two solutions.