Answer:
1/10
13/100
4/5
12/25
3/10
63/100
3/5
51/200
2/9
5/11
To prove the last 2 recurring ones:
0.222222... = x
10x = 10 * 0.22222... = 2.222222....
Notice how the decimal part of 10x is the same as for x:
10x - x = 2.2222222... - 0.222222... = 2
10x - x = 9x = 2
x = 2/9
Same procedure for the other one but times by 100 instead:
x = 0.454545...
100x = 45.454545...
100x - x = 45.454545... - 0.454545... = 45
100x - x = 99x = 45
x = 45/99 = 5/11
The greatest common factor of 14x-24 is 2. So it would be 7x - 12
Answer:
Step 1:
To find ordered pair solutions, you could create an x and y graph and fill out the x side. Then, plug in an x number to get your y number and graph the ordered pairs to see if they give you a straight line. I'm going to use these numbers: -1, 0, 1, and 2.

![\left[\begin{array}{ccc}-1&?\\0&?\\1&?\\2&?\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26%3F%5C%5C0%26%3F%5C%5C1%26%3F%5C%5C2%26%3F%5Cend%7Barray%7D%5Cright%5D)
Now, let's plug in -1 into the equation first to see what we get for y.

-5 is our y if x was -1.
We do the same for the other three numbers.



Step 2:
With all that done, we can now fill out our table and graph the points.

![\left[\begin{array}{ccc}-1&-5\\0&3\\1&11\\2&19\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-5%5C%5C0%263%5C%5C1%2611%5C%5C2%2619%5Cend%7Barray%7D%5Cright%5D)
If you graph these points on graph paper / a graphing website, you will see that these points go in a straight line. If you are given an ordered pair already (for example: (3,5)), then all you have to do is plug in the x into the equation (3) and see if the outcome is true (5).

Since they don't equal each other, then (3,5) is false.
Here is the graph for the table above. I hope I helped you!
The formula for the distance from a point (x, y, z) to the plane ax +by +cz +d = 0 is this:
.. distance = |ax +by +cz +d|/√(a^2 +b^2 +c^2)
For your point and plane, that is
.. distance = |-8 -2*7 -4*6 -8|/√(1^2 +2^2 +4^2)
.. = 54/√21
.. = (18/7)√21