Answer:
24,192.
Step-by-step explanation:
The first number must be one of 2,3,4,5,6,7,8 or 9. That is 8 possibilities.
The number of permutations of the other 4 numbers is 9P4
= 9! / (9-4)!
= 3024
Now we multiply by the 8:
3024 * 8
= 24,192.
Answer:
55
Step-by-step explanation:
Divide both sides by 3.14 to get d by itself.
172.7 / 3.14 = 55 = d
Since g(h(x))=h(g(x))= x, hence functions h and g are inverses of each other
Given the functions expressed as:
![h(x) =\sqrt{2x+2}\\g(x)\frac{x^2-2}{2} \\](https://tex.z-dn.net/?f=h%28x%29%20%3D%5Csqrt%7B2x%2B2%7D%5C%5Cg%28x%29%5Cfrac%7Bx%5E2-2%7D%7B2%7D%20%20%5C%5C)
In order to check whether they are inverses of each other, we need to show that h(g(x)) = g(h(x))
Get the composite function h(g(x))
![h(g(x))=h(\frac{x^2-2}{2} )\\h(g(x))=\sqrt{2(\frac{x^2-2}{2} )+2}\\h(g(x))=\sqrt{x^2-2+2} \\h(g(x))=\sqrt{x^2}\\h(g(x))=x](https://tex.z-dn.net/?f=h%28g%28x%29%29%3Dh%28%5Cfrac%7Bx%5E2-2%7D%7B2%7D%20%29%5C%5Ch%28g%28x%29%29%3D%5Csqrt%7B2%28%5Cfrac%7Bx%5E2-2%7D%7B2%7D%20%29%2B2%7D%5C%5Ch%28g%28x%29%29%3D%5Csqrt%7Bx%5E2-2%2B2%7D%20%5C%5Ch%28g%28x%29%29%3D%5Csqrt%7Bx%5E2%7D%5C%5Ch%28g%28x%29%29%3Dx)
Get the composite function g(h(x))
![g(h(x))=\frac{(\sqrt{2x+2} )^2-2}{2} \\g(h(x))=\frac{2x+2-2}{2}\\g(h(x))=\frac{2x}{2}\\g(h(x))=x](https://tex.z-dn.net/?f=g%28h%28x%29%29%3D%5Cfrac%7B%28%5Csqrt%7B2x%2B2%7D%20%29%5E2-2%7D%7B2%7D%20%5C%5Cg%28h%28x%29%29%3D%5Cfrac%7B2x%2B2-2%7D%7B2%7D%5C%5Cg%28h%28x%29%29%3D%5Cfrac%7B2x%7D%7B2%7D%5C%5Cg%28h%28x%29%29%3Dx)
Since g(h(x))=h(g(x))= x, hence functions h and g are inverses of each other
Learn more on inverse functions here; brainly.com/question/14391067
Answer:
4/2
Step-by-step explanation:
Rise/Run
4/2
12 + 0.35X = 20.05
12 + 0.35X - 12 = 20.05 - 12
0.35X = 8.05
0.35X/0.35 = 8.05/0.35
X = 23
Hope this helps!!