.580 80 repeating as fraction
2 answers:
First off, we'll move the non-repeating part in the decimal to the left-side, by doing a division by a power of 10.
then we'll equate the value to some variable, and move the repeating part over to the left as well.
anyhow, the idea being, we can just use that variable, say "x" for the repeating bit, let's proceed,
and you can check that in your calculator.
then we'll equate the value to some variable, and move the repeating part over to the left as well.
anyhow, the idea being, we can just use that variable, say "x" for the repeating bit, let's proceed,
and you can check that in your calculator.
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Answer:
Step-by-step explanation:
The given system is:
Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.
This gives me the system:
We could solve the first equation for and replace the second
with that.
Let's do that.
Subtract on both sides:
So we are replacing the second in the second equation with
which gives us:
Now recall the first equation we arranged so that was the subject. I'm referring to
.
We can now find given that
using the equation
.
Let's do that.
with
:
So the solution is (8,-1).
We can check this point by plugging it into both equations.
If both equations render true for that point, then we have verify the solution.
Let's try it.
with
:
is a true equation so the "solution" looks promising still.
with
:
is also true so the solution has been verified since both equations render true for that point.
Now, recall Descartes Rule of Signs. Check the picture below.
the +x part, gives us the positive Real zeros, and it depends on how many times the sign changes from term to term, notice in the picture, it changed 3 times, so the positive real ones are 3, or 3-2, namely 1, so 3 or 1.
the negative real ones, come from using -x as the argument on f(x), and as you can see in the picture, there was only 1 sign change, meaning the negative real zeros are only 1.
since, based on the fundamental theorem of algebra the polynomial has 4 roots at most then,
3 positive real ones, and 1 negative real one, no complex ones
or
1 positive real one, and 1 negative real one, and 2 complex ones
bear in mind that complex always come in pairs, never alone.
the +x part, gives us the positive Real zeros, and it depends on how many times the sign changes from term to term, notice in the picture, it changed 3 times, so the positive real ones are 3, or 3-2, namely 1, so 3 or 1.
the negative real ones, come from using -x as the argument on f(x), and as you can see in the picture, there was only 1 sign change, meaning the negative real zeros are only 1.
since, based on the fundamental theorem of algebra the polynomial has 4 roots at most then,
3 positive real ones, and 1 negative real one, no complex ones
or
1 positive real one, and 1 negative real one, and 2 complex ones
bear in mind that complex always come in pairs, never alone.