<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.
To estimate round up if its 5 and up round down if its 4 and below
80 - 30 = 50
50
Answer:
540
Step-by-step explanation:
Answer:
1) d
2) b
3) b
Step-by-step explanation:
Hope it helps plz give brainliest! :D
Answer:
![\huge{ \fbox{ \tt{12}}}](https://tex.z-dn.net/?f=%20%5Chuge%7B%20%5Cfbox%7B%20%5Ctt%7B12%7D%7D%7D)
Step-by-step explanation:
![\underline{ \sf{Given}} : \sf a=6, \: b=3 \: and \: c=2](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Csf%7BGiven%7D%7D%20%3A%20%5Csf%20a%3D6%2C%20%5C%3A%20%20b%3D3%20%5C%3A%20%20and%20%20%5C%3A%20c%3D2)
![\underline{ \sf{To \: find }} : \sf{Value \: of \: the \: given \: expression}](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Csf%7BTo%20%5C%3A%20find%20%7D%7D%20%20%3A%20%20%20%5Csf%7BValue%20%5C%3A%20of%20%5C%3A%20the%20%5C%3A%20given%20%5C%3A%20expression%7D)
![\underline{ \underline{ \mathfrak{Let's \: solve}}} :](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%7B%20%5Cmathfrak%7BLet%27s%20%5C%3A%20solve%7D%7D%7D%20%3A%20)
![\bigstar{ \tt{ \: c \: ( \: b \: + \: a \: ) - \: a}}](https://tex.z-dn.net/?f=%20%5Cbigstar%7B%20%5Ctt%7B%20%5C%3A%20c%20%5C%3A%20%28%20%5C%3A%20b%20%5C%3A%20%20%2B%20%20%5C%3A%20a%20%5C%3A%20%29%20-%20%20%5C%3A%20a%7D%7D)
Plug the values of a , b and c
![\mapsto{ \tt{ \: 2 \: ( \: 3 \: + \: 6 \: ) \: - \: 6}}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Ctt%7B%20%5C%3A%202%20%5C%3A%20%28%20%5C%3A%203%20%5C%3A%20%20%2B%20%20%5C%3A%206%20%5C%3A%20%29%20%5C%3A%20%20-%20%20%5C%3A%206%7D%7D)
![\text{Step \: 2} : \sf{ \: Add \: the \: numbers : 6 \: and \: 3}](https://tex.z-dn.net/?f=%20%5Ctext%7BStep%20%5C%3A%202%7D%20%3A%20%5Csf%7B%20%5C%3A%20Add%20%5C%3A%20the%20%5C%3A%20numbers%20%3A%206%20%5C%3A%20and%20%5C%3A%203%7D)
![\mapsto{ \sf{ \: 2 \: * \: 9 \: - \: 6 \: }}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7B%20%5C%3A%202%20%5C%3A%20%2A%20%5C%3A%209%20%5C%3A%20%20-%20%20%5C%3A%206%20%5C%3A%20%7D%7D)
![\text{Step \: 3 \: } : \sf{ \: Multiply \: the \: numbers : 9 \: and \: 2}](https://tex.z-dn.net/?f=%20%5Ctext%7BStep%20%5C%3A%203%20%5C%3A%20%7D%20%3A%20%5Csf%7B%20%5C%3A%20Multiply%20%5C%3A%20the%20%5C%3A%20numbers%20%3A%209%20%5C%3A%20and%20%5C%3A%202%7D)
![\mapsto{ \sf{18 - 6}}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7B18%20-%206%7D%7D)
![\text{Step \: 4 \:} : \sf{Subtract \: 6 \: from \: 18}](https://tex.z-dn.net/?f=%20%5Ctext%7BStep%20%5C%3A%204%20%5C%3A%7D%20%3A%20%20%5Csf%7BSubtract%20%5C%3A%206%20%5C%3A%20from%20%5C%3A%2018%7D)
![\mapsto{ \sf{ \: 12}}](https://tex.z-dn.net/?f=%20%5Cmapsto%7B%20%5Csf%7B%20%5C%3A%2012%7D%7D)
Note : Just follow the PEMDAS rule ( See attached picture )
Hope I helped!
Best regards! :D
~![\sf{TheAnimeGirl}](https://tex.z-dn.net/?f=%20%5Csf%7BTheAnimeGirl%7D)