65124 rounded to the nearest thousand
2 answers:
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An equation of the form ax+by+c=0, where x, y are variable, and a, b, c are numbers, is called a "linear equation"
the reason we call it linear, is that all solutions (x, y) to this equation, when plotted in the x-y axis, form a line.
To draw this line, 2 points are enough, that is 2 solutions (x, y) of the equation.
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-2x+5y-10=0 is a linear equation (a=-2, b=5, c=-10)
to find 2 solutions, we set x or y any value we want, and solve for the other
for example:
let x=0,
then
-2x+5y-10=0 becomes 5y-10=0, so y=2
this gives us the solution (0, 2)
another example; set y=0
then -2x+5y-10=0 becomes -2x-10=0; -2x=10 so x=-5
thus another solution is (-5, 0)
Draw these 2 points, and join them with a line, as shown in the figure.
the reason we call it linear, is that all solutions (x, y) to this equation, when plotted in the x-y axis, form a line.
To draw this line, 2 points are enough, that is 2 solutions (x, y) of the equation.
-------------------------------------------------------------------------------------------------
-2x+5y-10=0 is a linear equation (a=-2, b=5, c=-10)
to find 2 solutions, we set x or y any value we want, and solve for the other
for example:
let x=0,
then
-2x+5y-10=0 becomes 5y-10=0, so y=2
this gives us the solution (0, 2)
another example; set y=0
then -2x+5y-10=0 becomes -2x-10=0; -2x=10 so x=-5
thus another solution is (-5, 0)
Draw these 2 points, and join them with a line, as shown in the figure.
Answer: A) Yes, because the number can be written as the quotient of two integers
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Explanation:
Any repeating decimal can be expressed as a fraction of two integers.
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Optional section:
Here's a proof showing how the given number can be expressed as a fraction
Let x = 0.020020200202002...
The block of digits "02002" repeats forever.
Multiply both sides by 10^5 = 100,000 to move the decimal over 5 spots to the right.
The equation
x = 0.020020200202002...
will turn into
100000x = 2002.0200202002...
We have this system of equations
Subtracting said equations leads to
100,000x - x = 99,999x on the left
2002.0200202002... - 0.0200202002... = 2002 on the left
Note how the decimal portions line up perfectly to cancel out when we subtract
After those two subtractions, we end up with the equation
99,999x = 2002
Divide both sides by 99,999 and we isolate x
x = 2002/(99,999)
Use your calculator to find that,
2002/(99,999) = 0.02002020020202...
which helps confirm our answer.