Find the GCF of 80 and 32.
I'd start by identifying possible integer factors of both 80 and 32:
80: {1,2,4,5,8,10,16,20, 40, 80}
32: {1, 2,4, 8, 16, 32}
Working backwards, we see that the first factor that is represented in both lists is 16. Is 80 evenly divisible by 16? Yes; the quotient is 5.
Is 32 evenly divisible by 16? Yes; the quotient is 2.
You could writet 80 + 32 as 16(5 + 2). This is a product equal to 112, just as 80 + 32 = 112.
Regarding the functions in this problem, it is found that:
a) The verbal description of the inverse is: Take the third root, subtract by 5 and divide by 3.
b) The formulas are:
c) The compositions result in x, hence they are inverses.
<h3>How to obtain the inverse function?</h3>
The original function is described as follows:
- Take the third power: (3x + 5)³.
Hence the function is:
y = (3x + 5)³.
To obtain the inverse functions, we exchange x and y and then isolate y, hence:
x = (3y + 5)³
![\sqrt[3]{x} = \sqrt[3]{(3y+5)^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%20%3D%20%5Csqrt%5B3%5D%7B%283y%2B5%29%5E3%7D)
![3y + 5 = \sqrt[3]{x}](https://tex.z-dn.net/?f=3y%20%2B%205%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
![3y = \sqrt[3]{x} - 5](https://tex.z-dn.net/?f=3y%20%3D%20%5Csqrt%5B3%5D%7Bx%7D%20-%205)
![y = \frac{\sqrt[3]{x} - 5}{3}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B%5Csqrt%5B3%5D%7Bx%7D%20-%205%7D%7B3%7D)
![f^{-1}(x) = \frac{\sqrt[3]{x} - 5}{3}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Cfrac%7B%5Csqrt%5B3%5D%7Bx%7D%20-%205%7D%7B3%7D)
The verbal description of the inverse is:
- Take the third root. sqrt[3](x).
- Subtract by 5: sqrt[3](x) - 5.
The compositions are given as follows:
More can be learned about inverse functions at brainly.com/question/11735394
#SPJ1
Answer:
y = -2x
Step-by-step explanation:
Answer:
Oceans and the Sun.
Step-by-step explanation:
Lakes and the sun is also a good answer, but the question is asking which interact the <em>most</em>, which is the ocean and sun.
We can also rule out the moon since it has nothing to do with the water cycle, so the last two options are also wrong.