Question
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Suppose that p & q are nonzero rational numbers and z is an irrational number. Which of the following would be rational? Select TWO answers.
(2 points)
Responses
the sum of q and z
the sum of q and z
the sum of p and q
the sum of p and q
the product of p and q
the product of p and q
the product of p and z
the product of p and z
the difference of p and z
the difference of p and z
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Suppose that p & q are nonzero rational numbers and z is an irrational number. Which of the following would be rational? Select TWO answers.
(2 points)
Responses
the sum of q and z
the sum of q and z
the sum of p and q
the sum of p and q
the product of p and q
the product of p and q
the product of p and z
the product of p and z
the difference of p and z
the difference of p and z
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Answers
GPT-4o mini
To determine which of the provided options would be rational, let's analyze each one:
1. **The sum of q and z**: Since q is a rational number and z is an irrational number, their sum (q + z) is irrational.
2. **The sum of p and q**: Both p and q are rational numbers, so their sum (p + q) is rational.
3. **The product of p and q**: Both p and q are rational numbers, so their product (p * q) is rational.
4. **The product of p and z**: p is a rational number and z is an irrational number. The product (p * z) is irrational.
5. **The difference of p and z**: p is a rational number and z is an irrational number. The difference (p - z) is irrational.
Based on this analysis, the two options that are rational are:
- The sum of p and q
- The product of p and q
1. **The sum of q and z**: Since q is a rational number and z is an irrational number, their sum (q + z) is irrational.
2. **The sum of p and q**: Both p and q are rational numbers, so their sum (p + q) is rational.
3. **The product of p and q**: Both p and q are rational numbers, so their product (p * q) is rational.
4. **The product of p and z**: p is a rational number and z is an irrational number. The product (p * z) is irrational.
5. **The difference of p and z**: p is a rational number and z is an irrational number. The difference (p - z) is irrational.
Based on this analysis, the two options that are rational are:
- The sum of p and q
- The product of p and q