Mathematics, 22.02.2020 02:28 stoog7352

Which of the following is an example of why irrational numbers are not closed under addition?
StartRoot 4 EndRoot + StartRoot 4 EndRoot = 2 + 2 = 4, and 4 is not irrational
One-half + one-half = 1, and 1 is not irrational
StartRoot 10 EndRoot + (negative StartRoot 10 EndRoot) = 0, and 0 is not irrational
–3 + 3 = 0, and 0 is not irrational

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Answer from: lucerogd170

Option C: $\sqrt{10} +(-\sqrt{10})=0$ is an example of why irrational numbers are not closed under addition.

Explanation:

For a irrational number to be closed under addition, the sum of two numbers of an irrational number must also be an irrational.

Option A : $\sqrt{4} +\sqrt{4} =2+2=4$ and 4 is not irrational.

From the expression, we can see that $\sqrt{4}$ is a rational number because it results in a rational number. That is, $\sqrt{4}=2$

Thus, Option A is not the correct answer.

Option B : $\frac{1}{2} +\frac{1}{2} =1$ and 1 is not irrational.

From the expression, we can see that $\frac{1}{2}$ is a rational number.

Hence, the addition of two rational numbers results in a rational number.

Thus, Option B is not the correct answer.

Option C : $\sqrt{10} +(-\sqrt{10})=0$ and 0 is not irrational.

From the expression, we can see that $\sqrt{10}$ is an irrational number because it is a non - terminating decimal number.

Hence, the addition of two irrational number is a rational number.

Therefore, the irrational numbers are not closed under addition because the addition of irrational numbers does not result in a irrational number.

Thus, Option C is the correct answer.

Option D : -3+3=0 and 0 is not irrational.

From the expression, we can see that 3 is a rational number.

Hence, the addition of two rational numbers results in a rational number.

Thus, Option D is not the correct answer.

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

6 spoons of sugar for every 21 cups of flour

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Which of the following is an example of why irrational numbers are not closed under addition?
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