The number of dimes is 75 coins.
The number of nickels is 1 coin.
<u>Step-by-step explanation:</u>
It is given that,
A box contains 76 coins, only dimes and nickels.
- The 10 cent coin is called a dime.
- Let, the number of dimes be x.
- The 5 cent coin is called a nickel.
- Let, the number of nickels be y.
<u>This is represented by the system of equations :</u>
x + y = 76 -------(1)
10x + 5y = 4.90 ------(2)
Multiply eq (1) by 5 and subtract eq (2) from eq (1),
5x + 5y = 380
-<u>(10x + 5y = 4.90)</u>
<u>-5x = 375.1</u>
x = 375/5
x = 75 coins.
The number of dimes is 75 coins.
Substitute x=75 in eq (1),
y = 76 - 75
y = 1 coin.
The number of nickels is 1 coin.
The answer to that equation is {7,7}
Answer:
![\[3x+\frac{2}{3}\]](https://tex.z-dn.net/?f=%5C%5B3x%2B%5Cfrac%7B2%7D%7B3%7D%5C%5D)
Step-by-step explanation:
![\[f(x)=x-\frac{1}{3}\]](https://tex.z-dn.net/?f=%5C%5Bf%28x%29%3Dx-%5Cfrac%7B1%7D%7B3%7D%5C%5D)
![\[g(x)=3x+1\]](https://tex.z-dn.net/?f=%5C%5Bg%28x%29%3D3x%2B1%5C%5D)
Hence, ![\[(f o g)(x)=f(3x+1)\]](https://tex.z-dn.net/?f=%5C%5B%28f%20o%20g%29%28x%29%3Df%283x%2B1%29%5C%5D)
But, ![\[f(3x+1)=(3x+1)-\frac{1}{3}\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D%283x%2B1%29-%5Cfrac%7B1%7D%7B3%7D%5C%5D)
Simplifying,
![\[f(3x+1)=3x+(1-\frac{1}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%281-%5Cfrac%7B1%7D%7B3%7D%29%5C%5D)
= ![\[f(3x+1)=3x+(\frac{3-1}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%28%5Cfrac%7B3-1%7D%7B3%7D%29%5C%5D)
= ![\[f(3x+1)=3x+(\frac{2}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5C%5D)
Hence, ![\[(f o g)(x)=3x+(\frac{2}{3})\]](https://tex.z-dn.net/?f=%5C%5B%28f%20o%20g%29%28x%29%3D3x%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5C%5D)
Answer:
a) 7/10
b) There is no improper fraction form for this
Depends on how much space you have on your device
