Answer:
f^-1(x) = (x-1)/-3
Step-by-step explanation:
Invert equation:
Describe X in original function:
multiplied by -3
add 1
Reverse order:
subtract 1
divide by -3
Answer:
42 miles
Step-by-step explanation:
If it's a constant 12 miles per hour then it would be
12 mph x 3 hours = 36
then you would add that with the 1/2 hour for
12 mph x 1/2 hours = 6
36 + 6 = 42 miles traveled
Answer:
b= -0.1
Step-by-step explanation:
Answer: The road, crucifix/cross, sidewalks, railroads, and so much more.
Step-by-step explanation: Roads are parallel so that everyone can get to the same place in different lanes. This is important because lines that aren't parallel will inevitably meet, meaning that a highway would eventually merge its two lanes. This happens, but most of the highway is parallel. The same is true of sidewalks and railroads. The crucifix/cross is a Christian symbol, and while I'm not Christian, I'm sure it's important to a lot of people who are.
<u>Part a)</u>
Given the expression
![54m^3n\:+\:81m^4n^2](https://tex.z-dn.net/?f=54m%5E3n%5C%3A%2B%5C%3A81m%5E4n%5E2)
Apply exponent rule: ![a^{b+c}=a^ba^c](https://tex.z-dn.net/?f=a%5E%7Bb%2Bc%7D%3Da%5Eba%5Ec)
∵ ![m^4n^2=m^3mnn](https://tex.z-dn.net/?f=m%5E4n%5E2%3Dm%5E3mnn)
Rewrite 81 as 3 · 27
Rewrite 54 as 2 · 27
![=2\cdot \:27m^3n+3\cdot \:27m^3mnn](https://tex.z-dn.net/?f=%3D2%5Ccdot%20%5C%3A27m%5E3n%2B3%5Ccdot%20%5C%3A27m%5E3mnn)
Factor out the common term: 27m³n
Therefore,
![54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn=27m^3n\left(2+3mn\right)](https://tex.z-dn.net/?f=54m%5E3n%5C%3A%2B%5C%3A81m%5E4n%5E2%3D54m%5E3n%2B81m%5E3mnn%3D27m%5E3n%5Cleft%282%2B3mn%5Cright%29)
<u>Part B)</u>
Given the expression
![15x^2y^3z+25x^3y^2z+35x^2y^2z](https://tex.z-dn.net/?f=15x%5E2y%5E3z%2B25x%5E3y%5E2z%2B35x%5E2y%5E2z)
Apply exponent rule: ![a^{b+c}=a^ba^c](https://tex.z-dn.net/?f=a%5E%7Bb%2Bc%7D%3Da%5Eba%5Ec)
![15x^2y^3z+25x^3y^2z+35x^2y^2z=15x^2y^2yz+25x^2xy^2z+35x^2y^2z](https://tex.z-dn.net/?f=15x%5E2y%5E3z%2B25x%5E3y%5E2z%2B35x%5E2y%5E2z%3D15x%5E2y%5E2yz%2B25x%5E2xy%5E2z%2B35x%5E2y%5E2z)
Rewrite as
![=3\cdot \:5y^2x^2zy+5\cdot \:5y^2x^2zx+7\cdot \:5y^2x^2z](https://tex.z-dn.net/?f=%3D3%5Ccdot%20%5C%3A5y%5E2x%5E2zy%2B5%5Ccdot%20%5C%3A5y%5E2x%5E2zx%2B7%5Ccdot%20%5C%3A5y%5E2x%5E2z)
Factor out common term 5y²x²z
![=5y^2x^2z\left(3y+5x+7\right)](https://tex.z-dn.net/?f=%3D5y%5E2x%5E2z%5Cleft%283y%2B5x%2B7%5Cright%29)
Therefore,
![15x^2y^3z+25x^3y^2z+35x^2y^2z=5y^2x^2z\left(3y+5x+7\right)](https://tex.z-dn.net/?f=15x%5E2y%5E3z%2B25x%5E3y%5E2z%2B35x%5E2y%5E2z%3D5y%5E2x%5E2z%5Cleft%283y%2B5x%2B7%5Cright%29)