Answer:
14/45
Step-by-step explanation:
So we have the fraction:
![0.3\bar1=0.31111...](https://tex.z-dn.net/?f=0.3%5Cbar1%3D0.31111...)
We can do this algebraically. Follow to following steps:
Let's let this number equal to n. Thus:
![0.31111...=n](https://tex.z-dn.net/?f=0.31111...%3Dn)
Since there is only 1 digit repeating, let's multiply everything by 10. So:
![3.1111...=10n](https://tex.z-dn.net/?f=3.1111...%3D10n)
Now, subtract n from both sides:
![3.1111-n=10n-n](https://tex.z-dn.net/?f=3.1111-n%3D10n-n)
On the left, substitute the number for n. On the right, combine like terms:
![3.1111...-0.31111...=9n](https://tex.z-dn.net/?f=3.1111...-0.31111...%3D9n)
All of the 1s will cancel. So:
![3.1-0.3=9n](https://tex.z-dn.net/?f=3.1-0.3%3D9n)
Subtract:
![2.8=9n](https://tex.z-dn.net/?f=2.8%3D9n)
Divide both sides by 9:
![n=2.8/9](https://tex.z-dn.net/?f=n%3D2.8%2F9)
Remove the decimal by multiplying both sides by 10:
![n=28/90](https://tex.z-dn.net/?f=n%3D28%2F90)
Reduce:
![n=14/45](https://tex.z-dn.net/?f=n%3D14%2F45)
And we're done!
Use a calculator to check:
![14/45\stackrel{\checkmark}{=}0.31111...](https://tex.z-dn.net/?f=14%2F45%5Cstackrel%7B%5Ccheckmark%7D%7B%3D%7D0.31111...)
Answer:
A)$ 45
B) $105
Step-by-step explanation:
Bag and a belt cost $255
Let bag = x
Let belt = y
X+y= 255 equation 1
Let total money be z first
Remaining money= z-255
X-30 = z-255
Y +15 = z-255
Equating the left side of the equation
X+30 = y+15
X-y= 45 equation 2
Solving simultaneously
X+y= 255
X-y= 45
2x = 300
X= 150
If x= 150
150-y= 45
150-45= y
105=y
Bag = $150
Belt = $105
Bag Is 150-105 more than the belt
150-105= $45
Distance between the two cities:
453 - 333 = 120 miles.
Rest area is 2/3 of the way:
120 x 2/3 = 240/3 = 80 miles.
Divide the miles to the rest stop by his speed:
80 miles/ 60 miles per hour = 1 and 1/3 hours as a fraction. 1.3333 as a decimal( round as needed.
( 1 hour and 20 minutes)
Answer:
the graph will start at y1 and go down 1 and right 2 for every point.
Step-by-step explanation: since the x is negative you know that the graph is going to be negative so from left to right it will be going from top to bottom. next you look at the 1/2 which just states that every point on that line will will be 1 down and two right from the previous point. now you look at the +1 which just says that the graph will cross the y axis a 1.