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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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Nine times the sum of a number and 4 is 2
Anna11 [10]

Answer(s):

If you are asking for the equation, it's 9(x+4)=2

However, if you're asking for the value of x as well, it's -34/9

Step by Step:

1) First we must find the equation. In your question, the unknown number is x. Therefore we can know that "the sum of a number and 4" is (x+4). Since we are multiplying this sum by 9, we can put the 9 in front of this expression to multiply it--getting 9(x+4). And since we know it "is 2" we can say that 9(x+4)=2.

2) Now, we have to solve the equation, 9(x+4) = 2

3) We can start by distributing, 9x+36 = 2

4) Now let's move 36 to the right by subtracting from both sides, 9x = -34

5) To isolate x, let's divide both sides by 9, x = -34/9

6) Our fraction answer can't be simplified, so we get x = -34/9

7 0
3 years ago
Besides phone numbers, what are the other categorical variables in your survey? (The survey asks for family size, the kind of pe
Firdavs [7]

Answer:

I believe it would be C.

Step-by-step explanation:

8 0
3 years ago
??????????????????????
never [62]

Answer:

I belive the answer would be the first one. 2^28 x 3^20 x 9^4

Step-by-step explanation:

This is becasue you need to multiply the power on the outside of the parenthesis, (4).     7 times itself 4 times is 28, 5 times itself 4 times is 20, and then use the 4 for the 9. Hope this helps!

7 0
3 years ago
Nathan invests money in an account paying simple interest. He invests $180 and no money is added or removed from the investment.
sweet-ann [11.9K]
I think this question is technically asking
196.20 is what percent of 180, if so it would be 109%

https://www.percentagecal.com/answer/180-is-what-percent-of-196
5 0
3 years ago
Read 2 more answers
What is the equation 9+10​
Aliun [14]
9+10=19 it’s an addition problem and the sum is 19
3 0
3 years ago
Read 2 more answers
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