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vampirchik [111]
3 years ago
9

Convert the repeating decimal to an improper fraction or mixed number. Include your work in your final answer. \(3.\overline{152

}\)
Mathematics
1 answer:
Lera25 [3.4K]3 years ago
8 0

Answer:

Assuming the repetitive part is 152, i.e. the original repeating decimal is

A=3.152152152....

then  

1000A=3152.152152152152....

subtract A

1000A-A=3152.152152....-3.152152152....

999A=3149

A=3149/999=3+152/999=3 152/999

Therefore

3.152152152.... = 3149/999 or 3 152/999

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Two passenger train, A and B, 450 km apart, star to move toward each other at the same time and meet after 2hours.
likoan [24]

Let v be the speed of train A, and let's set the origin in the initial position of train A. The equations of motion are

\begin{cases}s_A(t) = vt\\s_B(t) = -\dfrac{8}{7}vt+450\end{cases}

where s_A,\ s_B are the positions of trains A and B respectively, and t is the time in hours.

The two trains meet if and only if s_A=s_B, and we know that this happens after two hours, i.e. at t=2

\begin{cases}s_A(2) = 2v\\s_B(2) = -\dfrac{16}{7}v+450\end{cases}\implies 2v = -\dfrac{16}{7}v+450

Solving this equation for v we have

2v = -\dfrac{16}{7}v+450 \iff \dfrac{30}{7}v=450 \iff v=\dfrac{450\cdot 7}{30} = 105

So, train A is travelling at 105 km/h. This implies that train B travels at

105\cdot \dfrac{8}{7} = 15\cdot 8=120 \text{ km/h}

5 0
3 years ago
Evaluate t-u/v, when t=-1,u=-3 and v=1/2
mars1129 [50]

Answer:

5

Step-by-step explanation:

t-u/v

substitute (-1) - (-3)/(1/2)

divide     (-1) - (-6)

simplify   (-1) + 6

add         5

3 0
3 years ago
(a)(−(−b))(−c) HELP PLEASE
Liono4ka [1.6K]

Answer:

No photo?

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Your EZ Pass account begins with $80. It costs you $4/day. Write an equation
vivado [14]

Answer:

The equation is A(d) = 80 - 4d

Step-by-step explanation:

Linear function:

A linear function for the amount of money in an account after t days is given by:

A(d) = A(0) - md

In which A(0) is the initial value and m is the daily cost.

Your EZ Pass account begins with $80. It costs you $4/day.

This means that A(0) = 80, m = 4

So

A(d) = A(0) - md

A(d) = 80 - 4d

7 0
3 years ago
Which of the following are possible values of r?<br><img src="https://tex.z-dn.net/?f=%20%7Br%7D%5E%7B2%20%7D%20%20%3D%20%20%5Cf
marshall27 [118]

Answer:

r=\frac{\sqrt{3} }{4}    and    r=-\frac{\sqrt{3} }{4}

Step-by-step explanation:

when you solve for r in the given equation, you need to apply the square root property, which gives positive and negative answers (both should therefore be considered):

r^2=\frac{3}{16} \\r=+/-\sqrt{\frac{3}{16}} \\r=+/-\frac{\sqrt{3} }{4}

then you need to include these two possible solutions:

r=\frac{\sqrt{3} }{4}    and    r=-\frac{\sqrt{3} }{4}

5 0
3 years ago
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