![f(x)=\quad 2{ x }^{ 2 }+3x+5](https://tex.z-dn.net/?f=f%28x%29%3D%5Cquad%202%7B%20x%20%7D%5E%7B%202%20%7D%2B3x%2B5)
Let's called the input 'z'
When we plug 'z' in the function we get ;
![f(z)=\quad 2{ z }^{ 2 }+3z+5](https://tex.z-dn.net/?f=f%28z%29%3D%5Cquad%202%7B%20z%20%7D%5E%7B%202%20%7D%2B3z%2B5)
And we know that, this is equal to 19, so ;
![2{ z }^{ 2 }+3z+5=\quad 19](https://tex.z-dn.net/?f=2%7B%20z%20%7D%5E%7B%202%20%7D%2B3z%2B5%3D%5Cquad%2019)
Let's rearrange the equation.
![2{ z }^{ 2 }+3z+5=\quad 19\\ \\ 2{ z }^{ 2 }+3z=\quad 19-5\\ \\ 2{ z }^{ 2 }+3z=\quad 14\\ \\ 2{ z }^{ 2 }+3z-14=\quad 0](https://tex.z-dn.net/?f=2%7B%20z%20%7D%5E%7B%202%20%7D%2B3z%2B5%3D%5Cquad%2019%5C%5C%20%5C%5C%202%7B%20z%20%7D%5E%7B%202%20%7D%2B3z%3D%5Cquad%2019-5%5C%5C%20%5C%5C%202%7B%20z%20%7D%5E%7B%202%20%7D%2B3z%3D%5Cquad%2014%5C%5C%20%5C%5C%202%7B%20z%20%7D%5E%7B%202%20%7D%2B3z-14%3D%5Cquad%200)
So we have a quadratic equation here.
We'll use this formula to solve it :
![\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2a }](https://tex.z-dn.net/?f=%5Cfrac%20%7B%20-b%5Cpm%20%5Csqrt%20%7B%20%7B%20b%20%7D%5E%7B%202%20%7D-4ac%20%7D%20%20%7D%7B%202a%20%7D%20)
The formula is used in equation formed like this :
![a{ x }^{ 2 }+bx+c=0](https://tex.z-dn.net/?f=a%7B%20x%20%7D%5E%7B%202%20%7D%2Bbx%2Bc%3D0)
In our equation,
a=2 , b=3 and c=-14
Let's plug in the values in the formula to solve,
![a=2\quad b=3\quad c=-14\\ \\ \frac { -3\pm \sqrt { 9-(4\cdot 2\cdot -14) } }{ 4 } \\ \\ \frac { -3\pm \sqrt { 9-(-112) } }{ 4 } \\ \\ \frac { -3\pm \sqrt { 9+112 } }{ 4 } \\ \\ \frac { -3\pm \sqrt { 121 } }{ 4 } \\ \\ \frac { -3\pm 11 }{ 4 }](https://tex.z-dn.net/?f=a%3D2%5Cquad%20b%3D3%5Cquad%20c%3D-14%5C%5C%20%5C%5C%20%5Cfrac%20%7B%20-3%5Cpm%20%5Csqrt%20%7B%209-%284%5Ccdot%202%5Ccdot%20-14%29%20%7D%20%20%7D%7B%204%20%7D%20%5C%5C%20%5C%5C%20%5Cfrac%20%7B%20-3%5Cpm%20%5Csqrt%20%7B%209-%28-112%29%20%7D%20%20%7D%7B%204%20%7D%20%5C%5C%20%5C%5C%20%5Cfrac%20%7B%20-3%5Cpm%20%5Csqrt%20%7B%209%2B112%20%7D%20%20%7D%7B%204%20%7D%20%5C%5C%20%5C%5C%20%5Cfrac%20%7B%20-3%5Cpm%20%5Csqrt%20%7B%20121%20%7D%20%20%7D%7B%204%20%7D%20%5C%5C%20%5C%5C%20%5Cfrac%20%7B%20-3%5Cpm%2011%20%7D%7B%204%20%7D%20)
So,
![z=\quad \frac { -3+11 }{ 4 } \quad ,\quad \frac { -3-11 }{ 4 } \\ \\ z=\quad \frac { 8 }{ 4 } \quad ,\quad \frac { -14 }{ 4 } \\ \\ z=\quad 2,\quad -\frac { 7 }{ 2 }](https://tex.z-dn.net/?f=z%3D%5Cquad%20%5Cfrac%20%7B%20-3%2B11%20%7D%7B%204%20%7D%20%5Cquad%20%2C%5Cquad%20%5Cfrac%20%7B%20-3-11%20%7D%7B%204%20%7D%20%5C%5C%20%5C%5C%20z%3D%5Cquad%20%5Cfrac%20%7B%208%20%7D%7B%204%20%7D%20%5Cquad%20%2C%5Cquad%20%5Cfrac%20%7B%20-14%20%7D%7B%204%20%7D%20%5C%5C%20%5C%5C%20z%3D%5Cquad%202%2C%5Cquad%20-%5Cfrac%20%7B%207%20%7D%7B%202%20%7D%20)
So the input can be both, 2 and
Answer:
![y = 32 - \frac{1}{2}x](https://tex.z-dn.net/?f=y%20%3D%2032%20-%20%5Cfrac%7B1%7D%7B2%7Dx)
Step-by-step explanation:
Given
---- not 52
![Students = x](https://tex.z-dn.net/?f=Students%20%3D%20x)
![Remainder = y](https://tex.z-dn.net/?f=Remainder%20%3D%20y)
--- not z
Required
The equation for y
The remainder y is calculated as:
![y = Cups - Students * Each\\](https://tex.z-dn.net/?f=y%20%3D%20Cups%20-%20Students%20%2A%20Each%5C%5C)
1% would be £60
3% would be £180
0.5% would be £30
3.5% would be £210
103.5% would be £6210
Answer:
D. ![\frac{45a^{16}c^{34}}{b^{27}}](https://tex.z-dn.net/?f=%5Cfrac%7B45a%5E%7B16%7Dc%5E%7B34%7D%7D%7Bb%5E%7B27%7D%7D)
Step-by-step explanation:
Here you are...
Hope this helps! Brainliest would be much appreciated! Have a great day! :)