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Blababa [14]
2 years ago
10

Convert the following repeating decimal to a fraction in simplest form .53

Mathematics
1 answer:
galben [10]2 years ago
5 0

9514 1404 393

Answer:

  53/99

Step-by-step explanation:

When an n-digit repeat begins at the decimal point, the repeating digits can be placed over an equal number of 9s to make a fraction. Sometimes, that fraction can be reduced to lower terms.

  0.\overline{53}=\boxed{\dfrac{53}{99}}

__

If the repeat does not start at the decimal point, the conversion can be done as follows.

For a number x with a decimal fraction that has n digits repeating, multiply by 10^n, subtract x and then divide by (10^n -1).

The fraction will be ...

  (x·10^n -x)/(10^n -1) . . . where x has n repeating digits in the decimal fraction

Here, that looks like ...

  x=0.\overline{53}\\100x=53.\overline{53}\\100x-x=53.\overline{53}-0.\overline{53}=53\\99x=53\\x=\dfrac{53}{99}

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Phoebe, andy and polly share €270
jeka94

Answer:

Polly=30

Andy=60

Phoebe=180

Step-by-step explanation:

Polly=x

Andy=2x

Phoeby 3(2x)=6x

x+2x+6x=270

9x=270

x=30

Polly=x=30

Andy = 2x=60

Phoebe=6x=180

7 0
3 years ago
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lana66690 [7]

Answer:

Step-by-step explanation:

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5 0
2 years ago
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Naomi pays $1.50 each time she rides the city bus. She has already ridden the bus 18 times so far this year. The expression repr
klio [65]

Answer:

$27

Step-by-step explanation:

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5 0
3 years ago
Sharon was going through the financial records of her company. The profit earned by the company, p(t), over time t, in years, fo
FromTheMoon [43]
For this case what we must do is find a quadratic function that is already factored.
 This is because in the factored quadratic equations, it is easier to observe the zeros of the function.
 In this case, the zeros of the function represent the time at which the company did not make any profit.
 We have the following equation:
 p (t) = 40 (t - 3) (t + 2) (t - 5) (t + 3)
 We observed that there was no gain in:
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 The other roots are discarded because they are negative
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a.p (t) = 40 (t - 3) (t + 2) (t - 5) (t + 3)
5 0
3 years ago
Jacob leaves his summer cottage and drives home. After
krok68 [10]

Answer:

A linear relationship can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If this line passes through the points (a, b) and (c, d) then the slope can be written as:

a = (a - c)/(b - d)

Here y will represent the distance between Jacob and his house, and the variable x represents the time that he has ben driving.

In this case, we know that after driving for 5 hours, he is 112km from home.

Then we can write this point as (5h, 112km)

We also know that after 7 hours he is 15km from home.

Then we can write this point as (7h, 15km)

Then the slope of this function will be:

a = (15km - 112km)/(7h - 5h) = -48.5 km/h

Then the equation is:

y = -(48.5 km/h)*x + b

To find the value of b, we can replace the values of one of the points, for example in the point (7h, 15km)

This means that we need to replace x by 12h, and y by 15km, then we get:

15km = -( 48.5 km/h)*7h + b

15km + ( 48.5 km/h)*7h = b = 354.5 km

then the equation will be:

y = (-48.5 km/h)*x + 354.5 km

Now we want to answer: How long had Jacob been driving when he was 209 km from  home?

Then we need to only replace y by 209km, and solve for x:

209km = (-48.5 km/h)*x + 354.5 km

209km - 354.5 km = (-48.5 km/h)*x

-145.5km =  (-48.5 km/h)*x

-145.5km/( -48.5 km/h) = x = 3h

So he is 209km away from his home after driving for 3 hours.

6 0
3 years ago
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