Sum/difference:
Let
This means that
Now, assume that is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.
The answer is going to be 750.00 because first I converted the percent into a decimal
r/100=5%/100=0.05 per year
A=500(1+(0.05x10))=750
A=750.00
Start by taking out a common factor.
x^10
x^10(x^6 - 2x^5 - x^4 + 4x^3 - x^2 - 2x + 1) = 0
So far we know that D won't work.
x - 1 is a factor because putting 1 in for the xs in the expression inside the brackets gives 0 Now you need to do a division. I'm going to assume you can do that.
Using division, I get
x^5 - x^4 - 2x^3 + 2x^2 + x - 1 Now divide x - 1 into this mess again. You get
x^4 - 2x^2 + 1 which factors into
(x^2 - 1)(x^2 - 1) which factors into
(x - 1)(x + 1)(x - 1)(x + 1) = 0
The first two divisions add (x -1)(x - 1)
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So we have (x - 1) with a multiplicity of 4 and (x + 1) with a multiplicity of 2
or x = 1 with a multiplicity of 4 and x = -1 with a multiplicity of 2 and x = 0
with a multiplicity of 10
That's the answer.
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C <<<< ===== Answer.
Hey there.I believe the answer is D.I hope this helps.