The three dots after the 777 indicate that the pattern repeats forever. Specifically the 7s go on forever (the 1 does not repeat and its only listed one time)
Let
x = 0.1777...
The goal is to find the value of x in terms of a fraction of whole numbers (eg like 2/3 or 4/5)
The trick is to somehow get the decimal portion that goes on forever to go away. We will do this through subtraction. But first, we need to do a bit of side work.
Multiply both sides of the equation above by 10
x = 0.1777...
10*x = 10*0.1777...
10x = 1.777...
Notice how this moves the decimal over 1 spot to the right
Then go back to the original equation for x and multiply both sides by 100
x = 0.1777...
100*x = 100*0.1777...
100x = 17.777...
Now the decimal is moved over two spots to the right
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In summary so far, we have
10x = 1.777...
100x = 17.777...
If we subtract 100x - 10x then we'll have
100x - 10x = (17.777...) - (1.777...)
90x = 16
The decimal portion 777... cancels out when we subtract. This is because the terms line up perfectly and subtract to 0
The last few steps is to solve 90x = 16 for x. We divide both sides by 90 and then reduce as much as possible
90x = 16
90x/90 = 16/90
x = 16/90
x = 8/45
Therefore the final answer is the fraction 8/45
I recommend you use a calculator to confirm that 8/45 will have the decimal form of 0.1777...
Note: your calculator may round the last digit from 7 to an 8
Answer:
y=(5/6)x
Step-by-step explanation:
its how much it rises over how much it runs. so it goes up 5 and to the right 6
<span>Creo que estás en el lugar equivocado</span>
ANSWER:
A. 32 - 3x
This is as the sum of 7 and 25 is 32 so:
7 + 25 = 32
As well as 4x subtracted by 7x being - 3x so:
4x - 7x = - 3x
When we combine this together, we get:
= 32 - 3x
Therefore, Option A must be the answer.
Hope this helps! :)
Have a lovely day! <3