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Darya [45]
3 years ago
11

Prove algebraically that 0.5 recurring = 5/9

Mathematics
1 answer:
ad-work [718]3 years ago
3 0

Answer and Step-by-step explanation:

We want to prove that 0.5555... = 5/9.

First, let's set 0.555... equal to x:

x = 0.555...

Now multiply this by 10:

10x = 5.555...

Now subtract the original from this new one:

   10x = 5.555...

-       x = 0.555...

______________

     9x = 5

Note that we could cancel all the recurring terms because they were the same for both 5.555... and 0.555... since the 5's go up to infinity.

We now have 9x = 5, so divide both sides by 9:

x = 5/9, as desired

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Mardi received an inheritance of $40,000. She invested part at 9% and the rest at 12%. Her total annual income from the investme
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Answer:

She invested $30,000 at 9%

Step-by-step explanation:

Let the amount invested per percentage be $x and $y respectively

Total investment is 40,000

This means that;

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Now for her income;

9/100 * x = 9x/100

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Now;

9x/100 + 12y/100 = 3,900

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we solve both simultaneously

From i, y = 40,000-x

Substitute this into ii

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x = 90,000/3

x = $30,000

5 0
3 years ago
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