![f(x)=\dfrac{7x}{x-3}\\\\The\ domain:\\x-3\neq0\ \ \ \ |+3\\\\x\neq3](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B7x%7D%7Bx-3%7D%5C%5C%5C%5CThe%5C%20domain%3A%5C%5Cx-3%5Cneq0%5C%20%5C%20%5C%20%5C%20%7C%2B3%5C%5C%5C%5Cx%5Cneq3)
Answer: All real numbers except 3
Answer:
![x=-1,\frac{-1}{2}](https://tex.z-dn.net/?f=x%3D-1%2C%5Cfrac%7B-1%7D%7B2%7D)
Step-by-step explanation:
The following formula tells us that a quadratic equation can be solved:
which gives us the real and distinct roots
We have been given an equation:
![4x^2+6x+2=0](https://tex.z-dn.net/?f=4x%5E2%2B6x%2B2%3D0)
Here, on comparing it with general quadractic equation which is: ![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
Here, a=4,b=6 and c=2
On substituting the values in the formula to find D
![D=6^2-4(4)(2)](https://tex.z-dn.net/?f=D%3D6%5E2-4%284%29%282%29)
![D=36-32](https://tex.z-dn.net/?f=D%3D36-32)
![D=4](https://tex.z-dn.net/?f=D%3D4)
Now, to find x:
we have a formula:
![x=\frac{-b\pm\sqrt{D}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7BD%7D%7D%7B2a%7D)
On substituting the values we get:
![x=\frac{-6\pm\sqrt{4}}{2(4)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B4%7D%7D%7B2%284%29%7D)
![\x=frac{-6\pm2}{8}](https://tex.z-dn.net/?f=%5Cx%3Dfrac%7B-6%5Cpm2%7D%7B8%7D)
On simplification:
![x=\frac{-8}{8},\frac{-4}{8}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-8%7D%7B8%7D%2C%5Cfrac%7B-4%7D%7B8%7D)
![x=-1,\frac{-1}{2}](https://tex.z-dn.net/?f=x%3D-1%2C%5Cfrac%7B-1%7D%7B2%7D)
X = 3/4
So substitute x for 3/4 in <span> 2/3x
(3/4) x (2/3)
Now solve
</span>(3/4) x (2/3) = 1/2 or 0.5
114/6 = 19 parts per minute
19 * 15 = 285 parts
hope this helps.