![(\frac{g}{f})(3)=\frac{-13}{21}\\](https://tex.z-dn.net/?f=%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-13%7D%7B21%7D%5C%5C)
2/3 will not be included in the domain of g/f
Step-by-step explanation:
Given functions are:
![g(x) =-2x^2+5\\f(x)=9x-6](https://tex.z-dn.net/?f=g%28x%29%20%3D-2x%5E2%2B5%5C%5Cf%28x%29%3D9x-6)
We have to calculate (f/g)(x) first
The steps will be as follows:
![(\frac{g}{f})(x)=\frac{g(x)}{f(x)}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bg%7D%7Bf%7D%29%28x%29%3D%5Cfrac%7Bg%28x%29%7D%7Bf%28x%29%7D)
Putting the values of functions
![(\frac{g}{f})(x)=\frac{-2x^2+5}{9x-6}\\We\ have\ to\ find\ the\ value\ of\ (\frac{g}{f})(x)\ at\ 3\\So,\\(\frac{g}{f})(3)=\frac{-2(3)^2+5}{9(3)-6}\\(\frac{g}{f})(3)=\frac{-2(9)+5}{27-6}\\(\frac{g}{f})(3)=\frac{-18+5}{27-6}\\(\frac{g}{f})(3)=\frac{-13}{21}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bg%7D%7Bf%7D%29%28x%29%3D%5Cfrac%7B-2x%5E2%2B5%7D%7B9x-6%7D%5C%5CWe%5C%20have%5C%20to%5C%20find%5C%20the%5C%20value%5C%20of%5C%20%28%5Cfrac%7Bg%7D%7Bf%7D%29%28x%29%5C%20at%5C%203%5C%5CSo%2C%5C%5C%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-2%283%29%5E2%2B5%7D%7B9%283%29-6%7D%5C%5C%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-2%289%29%2B5%7D%7B27-6%7D%5C%5C%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-18%2B5%7D%7B27-6%7D%5C%5C%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-13%7D%7B21%7D)
Domain of g/f:
![(\frac{g}{f})(x)=\frac{-2x^2+5}{9x-6}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bg%7D%7Bf%7D%29%28x%29%3D%5Cfrac%7B-2x%5E2%2B5%7D%7B9x-6%7D)
The function will be undefined if the denominator is zero.
To find the domain we will put the denominator equal to zero
So,
![9x-6=0\\Adding\ 6\ on\ both\ sides\\9x-6+6=0+6\\9x=6\\Dividing\ both\ sides\ by\ 9\\\frac{9x}{9}=\frac{6}{9}\\x=\frac{2}{3}](https://tex.z-dn.net/?f=9x-6%3D0%5C%5CAdding%5C%206%5C%20on%5C%20both%5C%20sides%5C%5C9x-6%2B6%3D0%2B6%5C%5C9x%3D6%5C%5CDividing%5C%20both%5C%20sides%5C%20by%5C%209%5C%5C%5Cfrac%7B9x%7D%7B9%7D%3D%5Cfrac%7B6%7D%7B9%7D%5C%5Cx%3D%5Cfrac%7B2%7D%7B3%7D)
Hence, the function will be undefined on x=2/3 so 2/3 will not be included in the domain of (f/g)(x)
<u>Answer:</u>
![(\frac{g}{f})(3)=\frac{-13}{21}\\](https://tex.z-dn.net/?f=%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-13%7D%7B21%7D%5C%5C)
2/3 will not be included in the domain of g/f
Keywords: Domain, Operations on Functions
Learn more about functions at:
#LearnwithBrainly
Answer:
![m](https://tex.z-dn.net/?f=m%3C49%2F12)
Step-by-step explanation:
we are given
![y = 3x^2+7x+m](https://tex.z-dn.net/?f=y%20%3D%203x%5E2%2B7x%2Bm)
To find x-intercept means we have to find zeros
and for finding zeros , we will use quadratic formula
and we have it has two x-intercepts
so, it's discriminant must be greater than 0
so, we will find discriminant
![D = \sqrt{b^2-4ac}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7Bb%5E2-4ac%7D)
now, we can compare with
![y=ax^2+bx+c\\y=3x^2+7x+m](https://tex.z-dn.net/?f=y%3Dax%5E2%2Bbx%2Bc%5C%5Cy%3D3x%5E2%2B7x%2Bm)
and then we can find a , b and c
a = 3, b = 7, c = m
now, we can find D
![D = \sqrt{7^2-4*3*m} \\D=\sqrt{49-12m}](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B7%5E2-4%2A3%2Am%7D%20%5C%5CD%3D%5Csqrt%7B49-12m%7D)
It has two x-intercepts
so,
![D = \sqrt{49-12m}>0](https://tex.z-dn.net/?f=D%20%3D%20%5Csqrt%7B49-12m%7D%3E0)
now, we can solve for m
![49-12m>0\\12m](https://tex.z-dn.net/?f=49-12m%3E0%5C%5C12m%3C49%5C%5Cm%3C49%2F12)
Answer:
56.5
Step-by-step explanation:
Since you are rounding to the tenths place, you look at the number to the right of it, aka the thousandths place.
If the number in the thousandth place is 5 or greater than the number in the tenths place becomes a number higher, or If the number in the thousandth place is 4 or less, than you keep the number in the tenths place the same.
Since the 6 is greater than 4, the 4 in the tenths place becomes a 5
Answer: A) Stratified random sampling
Step-by-step explanation:
Since , the researchers divided college students into the four classes (freshman, sophomore, junior, and senior) and then took a random sample of students from each class.
That means each category is participating in the sample.
It means , they used stratified sampling method where each class denotes a strata.
- <em>Stratified random sampling</em><em> is a kind of random sampling technique in which the researcher divides the whole population into some finite number of groups also known as strata , the he randomly pick individuals from each strata to make a sample. </em>
Here , each category participates in researcher's analysis.
Hence, the correct answer is A) Stratified random sampling .
Answer:
17.928666
Step-by-step explanation:
2.394*7.489