Answer:
2000
Step-by-step explanation:
Khan academy answer
Answer:
Step-by-step explanation:
1. Replace F(x) with y.
2. Interchange x and y in y = 2x + 1: x = 2y + 1
3. Solve this result for y: 2y = x - 1, or y = (x - 1)/2
4. Replace y with:
-1
F (x):
-1 x - 1
F (x) = -----------
2
I don’t get what you mean. Reword it
Answer:
- 80 restaurant purchased meals are eaten in a restaurant
- 31 meals are eaten in a car
- 60 meals are eaten at home
Step-by-step explanation:
Let us suppose r be the total number of meals eaten in a restaurant
Let us suppose c be the total number of meals eaten in a car
Let us suppose h be the total number of meals eaten in a home
- The total number of meals eaten in a restaurant, in a car or at home is given as 163. Hence,
![r + c + h = 171.....[A]](https://tex.z-dn.net/?f=r%20%2B%20c%20%2B%20h%20%3D%20171.....%5BA%5D)
- The total number meals eaten in a car or at home exceeds the number eaten in a restaurant by 11. Hence,
![c + h = r + 11.....[B]](https://tex.z-dn.net/?f=c%20%2B%20h%20%3D%20r%20%2B%2011.....%5BB%5D)
- Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. Hence,
![r = h + 20.....[C]](https://tex.z-dn.net/?f=r%20%3D%20h%20%2B%2020.....%5BC%5D)
Substituting Equation [B] into [A],
![r + c + h = 171.....[A]](https://tex.z-dn.net/?f=r%20%2B%20c%20%2B%20h%20%3D%20171.....%5BA%5D)
![r + r + 11 = 171](https://tex.z-dn.net/?f=r%20%2B%20r%20%2B%2011%20%3D%20171)
![2r + 11 = 171](https://tex.z-dn.net/?f=2r%20%2B%2011%20%3D%20171)
![2r = 160](https://tex.z-dn.net/?f=2r%20%3D%20160)
![r = 80](https://tex.z-dn.net/?f=r%20%3D%2080)
Putting
in ![r = h + 20.....[C]](https://tex.z-dn.net/?f=r%20%3D%20h%20%2B%2020.....%5BC%5D)
![80 = h + 20](https://tex.z-dn.net/?f=80%20%3D%20h%20%2B%2020)
![h = 60](https://tex.z-dn.net/?f=h%20%3D%2060)
Putting
and
in ![r + c + h = 171.....[A]](https://tex.z-dn.net/?f=r%20%2B%20c%20%2B%20h%20%3D%20171.....%5BA%5D)
![80 + c + 60 = 171](https://tex.z-dn.net/?f=80%20%2B%20c%20%2B%2060%20%3D%20171)
![c = 171 - 60 - 80](https://tex.z-dn.net/?f=c%20%3D%20171%20-%2060%20-%2080)
![c = 31](https://tex.z-dn.net/?f=c%20%3D%2031)
Therefore,
- 80 restaurant purchased meals are eaten in a restaurant
- 31 meals are eaten in a car
- 60 meals are eaten at home
Verification:
![r + c + h = 171](https://tex.z-dn.net/?f=r%20%2B%20c%20%2B%20h%20%3D%20171)
Putting
,
and
in ![r + c + h = 171](https://tex.z-dn.net/?f=r%20%2B%20c%20%2B%20h%20%3D%20171)
![80 + 31 + 60 = 171](https://tex.z-dn.net/?f=80%20%2B%2031%20%2B%2060%20%3D%20171)
![171 = 171](https://tex.z-dn.net/?f=171%20%3D%20171)
<em>Keywords: number, equation</em>
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Answer:
- domain: x ∉ {-4, 3}
- range: y ∉ {1}
- horizontal asymptote: y=1
- vertical asymptote: x=3
Step-by-step explanation:
The expression reduces to ...
![\dfrac{x^2+9x+20}{x^2+x-12}=\dfrac{(x+4)(x+5)}{(x+4)(x-3)}=\dfrac{x+5}{x-3}\quad (x\ne-4)](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%2B9x%2B20%7D%7Bx%5E2%2Bx-12%7D%3D%5Cdfrac%7B%28x%2B4%29%28x%2B5%29%7D%7B%28x%2B4%29%28x-3%29%7D%3D%5Cdfrac%7Bx%2B5%7D%7Bx-3%7D%5Cquad%20%28x%5Cne-4%29)
The domain is limited to values of x where the expression is defined. It is undefined where the denominator is zero, at x=-4 and x=3. The graph of the expression has a "hole" at x=4, where the numerator and denominator factors cancel.
- the domain is all real numbers except -4 and +3
The function approaches the value of 1 as x gets large in magnitude, but it cannot take on the value of 1.
- the range is all real numbers except 1
As discussed in 'range', there is a horizontal asymptote at y=1. That is the value you would get if you were to determine the quotient of the division:*
(x+5)/(x-3) = 1 + (8/(x-3)) . . . . quotient is 1
There is a vertical asymptote at the place where the denominator is zero in the simplified expression: x = 3.
- vertical asymptote at x=3; horizontal asymptote at y=1
_____
* For some rational functions, the numerator has a higher degree than the denominator. In those cases, the quotient may be some function of x. The "end behavior" of the expression will match that function. (Sometimes it is a "slant asymptote", sometimes a higher-degree polynomial.)