Answer:
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Answer:
The graph is attached; it is the graph of f(x) = x.
Step-by-step explanation:
Two functions are inverses if their composites form the function f(x) = x.
Take, for example, the function f(x) = 2x-4. We can write this as y=2x-4.
To find the inverse, we isolate x. To do this, first add 4 to each side:
y+4 = 2x-4+4
y+4 = 2x
Divide both sides by 2:
(y+4)/2 = 2x/2
y/2 + 4/2 = x
1/2y + 2 = x
Swap x and y, and the inverse is
y=1/2x+2
This can be written as g(x).
The composite of these two functions, f(g(x)), is:
f(1/2x+2) = 2(1/2x+2)-4
= 2(1/2x)+2(2)-4
=1x+4-4
= x
The composite of two functions is always f(x) = x.
This means the graph will have a slope of 1 and a y-intercept of 0.
Answer:
For 124 chirps per minute the temperature is 68 ºF.
For 68 chirps per minute the temperature is 54 ºF.
Step-by-step explanation:
Linear functions are those whose graph is a straight line. A linear function has the following form
![f(x)=b+mx](https://tex.z-dn.net/?f=f%28x%29%3Db%2Bmx)
b is the constant term or the y intercept. It is the value of the dependent variable when x = 0.
m is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.
We know that
- At 104 chirps per minute, the temperature is 63 ºF.
- At 176 chirps per minute, the temperature is 81 ºF.
This information can be converted to Cartesian coordinates (x, y). Where x = the number of chirps per minute and y = the temperature in ºF.
To find a linear function that let us find the outside temperature from how fast crickets chirp we must:
![m=\frac{y_2-y_1}{x_2-x_1}=\frac{81-63}{176-104}=\frac{1}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%3D%5Cfrac%7B81-63%7D%7B176-104%7D%3D%5Cfrac%7B1%7D%7B4%7D)
![81=\frac{1}{4}\cdot 104+b](https://tex.z-dn.net/?f=81%3D%5Cfrac%7B1%7D%7B4%7D%5Ccdot%20104%2Bb)
Solving for b
![b=81-\frac{1}{4} (176)=37](https://tex.z-dn.net/?f=b%3D81-%5Cfrac%7B1%7D%7B4%7D%20%28176%29%3D37)
Therefore, the linear function is
![y=\frac{1}{4} \cdot x+37](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B4%7D%20%5Ccdot%20x%2B37)
Now, using this linear function we can know the temperature when we know the chirps per minute:
For 124 chirps per minute the temperature is:
![y=\frac{1}{4} \cdot (124)+37=68](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B4%7D%20%5Ccdot%20%28124%29%2B37%3D68)
For 68 chirps per minute the temperature is:
![y=\frac{1}{4} \cdot (68)+37=54](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B4%7D%20%5Ccdot%20%2868%29%2B37%3D54)
Answer:
25
Step-by-step explanation:
175 ÷ 7 = 25
each child will get 25 stickers.