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Llana [10]
3 years ago
11

Express the following repeating decimal as a fraction in simplest form.

Mathematics
1 answer:
Ivenika [448]3 years ago
4 0

Answer:

0.\overline{369} = \frac{41}{111}

Step-by-step explanation:

x = 0.369369369...

10x = 3.69369369...

100x = 36.9369369...

1000x = 369.369369...

1000x - x = 369

999x = 369

x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}

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Nearest hundred thousand 700,00 what is the exact number
coldgirl [10]
It`s either 100,000 because there is only four 0`s making it 70,000 or it`s 700,000 and you made a mistake of not typing that last zero in which case the question would be pointless to ask because the answer is in the question.
6 0
3 years ago
Wildlife conservationists are concerned that the deer population might not be constant across the National Forest. The scientist
tankabanditka [31]

Answer

9 deer per square- mile

Step-by-step explanation:.

7 0
3 years ago
Given that x and y are positive integers, solve the equation x² - 4y² = 13​
zvonat [6]
<h3>Answer:  x = 7 and y = 3</h3>

=====================================================

Explanation:

Apply the difference of squares rule

x² - 4y² = 13

x² - (2y)² = 13

(x - 2y)(x + 2y) = 13

Since x and y are positive integers, this means x-2y and x+2y are both integers as well.

The value 13 is prime. Its only factors are 1 and 13

Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:

  • A) x-2y = 1 and x+2y = 13
  • B) x-2y = 13 and x+2y = 1

----------------

Let's consider case A

We have this system of equations

\begin{cases}x-2y = 1\\x+2y = 13\end{cases}

Add the equations straight down

  • x+x becomes 2x
  • -2y+2y becomes 0y = 0 which goes away
  • 1+13 becomes 14

Therefore we have 2x = 14 solve to x = 7

From here, plug this into either equation to solve for y

x-2y = 1

7 - 2y = 1

-2y = 1-7

-2y = -6

y = -6/(-2)

y = 3

You should get the same result if you used x+2y = 13

----------------

Since we've found that x = 7 and y = 3, notice how case B is not possible

Example:  x-2y = 13 becomes 7-2(3) = 13 which is false.

Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.

-----------------

Let's check those x and y values in the original equation

x² - 4y² = 13

7² - 4*(3)² = 13

49 - 4(9) = 13

49 - 36 = 13

13 = 13

The answer is confirmed.

4 0
2 years ago
2
Kamila [148]
The first one is y=16
3 0
3 years ago
The answer is A I just need help working it out
nordsb [41]
STU + STR = 180
8x + STR = 180 [ STU = 8x ]
STR = 180 - 8x

STR = SRT [ RS ≈ ST ]

Now, In ΔSRT,
we have, RST = 7x - 54, STR = SRT = 180-8x
Their sum is 180, as it constitutes a triangle.

7x-54 + 2(180-8x) = 180
7x - 54 + 360 - 16x = 180
 306 - 9x = 180
9x = 306 - 180
9x = 306 - 180
x = 126/9
x = 14

So, option A is your answer.

Hope this helps!

5 0
3 years ago
Read 2 more answers
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