Answer:
The value of the function is 2 when x=-4 or x=0.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Slope Formula = (y2-y1)/(x2-x1)
6)
(-8-6)/(0--8)
= -14/8
= -7/4
7) (17-14)/(-20-12)
-3/32
8) (-14-0)/(16--11)
-14/27
9) (-16-10)/(22-7)
-26/15
10) (-13--7)/(0-14)
-6/-14
= 3/7
How many samples of 3 apples can be drawn from the crate?you have 26 apples in total so you can choose 3 apples from 26 in 26C3 ways...i.e 26 combination 3 ways...i.e. 2600...
How many samples of 3 can be drawn in which all 3 are rotten?there are 7 rotten apples in total...so one can choose 3 rotten apples from 7 in 7C3 ways...7 combination 3 ways...ie 35 ways...
How many samples of 3 can be drawn in which there are 2 good apples and one rotten apple?one wishes to choose 3 apples in total from a total of 27...out of that 26, 7 are rotten...How many ways can he choose 2 good AND 1 bad apple: since there are 7 rotten apples, there are 19 good apples thus one can choose 2 good apples from 19 in 19C2...and one can choose 1 bad apple from 7 in 7C1...so one can choose 2 good and 1 rotten apple in 19C2 x 7C1 = 171 x7 = 1197 ways or samples
To find the zeros of a quadratic fiunction given the equation you can use the next quadratic formula after equal the function to 0:
![\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20ax%5E2%2Bbx%2Bc%3D0%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5Cend%7Bgathered%7D)
For the given function:
![f(x)=2x^2-10x-3](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E2-10x-3)
![x=\frac{-(-10)\pm\sqrt[]{(-10)^2-4(2)(-3)}}{2(2)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-10%29%5Cpm%5Csqrt%5B%5D%7B%28-10%29%5E2-4%282%29%28-3%29%7D%7D%7B2%282%29%7D)
![x=\frac{10\pm\sqrt[]{100+24}}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B100%2B24%7D%7D%7B4%7D)
![\begin{gathered} x=\frac{10\pm\sqrt[]{124}}{4} \\ \\ x=\frac{10\pm\sqrt[]{2\cdot2\cdot31}}{4} \\ \\ x=\frac{10\pm\sqrt[]{2^2\cdot31}}{4} \\ \\ x=\frac{10\pm2\sqrt[]{31}}{4} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B124%7D%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B2%5Ccdot2%5Ccdot31%7D%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B10%5Cpm%5Csqrt%5B%5D%7B2%5E2%5Ccdot31%7D%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B10%5Cpm2%5Csqrt%5B%5D%7B31%7D%7D%7B4%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
![\begin{gathered} x_1=\frac{10}{4}+\frac{2\sqrt[]{31}}{4} \\ \\ x_1=\frac{5}{2}+\frac{\sqrt[]{31}}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x_1%3D%5Cfrac%7B10%7D%7B4%7D%2B%5Cfrac%7B2%5Csqrt%5B%5D%7B31%7D%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20x_1%3D%5Cfrac%7B5%7D%7B2%7D%2B%5Cfrac%7B%5Csqrt%5B%5D%7B31%7D%7D%7B2%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} x_2=\frac{10}{4}-\frac{2\sqrt[]{31}}{4} \\ \\ x_2=\frac{5}{2}-\frac{\sqrt[]{31}}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x_2%3D%5Cfrac%7B10%7D%7B4%7D-%5Cfrac%7B2%5Csqrt%5B%5D%7B31%7D%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20x_2%3D%5Cfrac%7B5%7D%7B2%7D-%5Cfrac%7B%5Csqrt%5B%5D%7B31%7D%7D%7B2%7D%20%5Cend%7Bgathered%7D)
Then, the zeros of the given quadratic function are:
![\begin{gathered} x=\frac{5}{2}+\frac{\sqrt[]{31}}{2} \\ \\ x_{}=\frac{5}{2}-\frac{\sqrt[]{31}}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D%5Cfrac%7B5%7D%7B2%7D%2B%5Cfrac%7B%5Csqrt%5B%5D%7B31%7D%7D%7B2%7D%20%5C%5C%20%20%5C%5C%20x_%7B%7D%3D%5Cfrac%7B5%7D%7B2%7D-%5Cfrac%7B%5Csqrt%5B%5D%7B31%7D%7D%7B2%7D%20%5Cend%7Bgathered%7D)
Answer: Third option