Mathematics

Mathematics, 24.08.2019 06:00, rsanchez1226

Which statement is not always true?
a. the sum of a rational number and an irrational number is irrational.
b. the sum of two rational numbers is rational.
c. the product of two irrational numbers is irrational.
d. the product of two rational numbers is rational.

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Mathematics, 03.08.2019 03:30, dkdk31

Below is a proof showing that the sum of a rational number and an irrational number is an irrational number. let a be a rational number and b be an irrational number. assume that a + b = x and that x is rational. then b = x – a = x + (–a). x + (–a) is rational because however, it was stated that b is an irrational number. this is a contradiction. therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number. in conclusion, the sum of a rational number and an irrational number is irrational. which of the following best completes the proof? it is the sum of two rational numbers. it is the sum of two irrational numbers. it represents a non-terminating, non-repeating decimal. its terms cannot be combined.

Answers: 1

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Mathematics, 18.09.2019 21:00, erickamurillo9929

Below is a proof showing that the sum of a rational number and an irrational number is an irrational number. let a be a rational number and b be an irrational number. assume that a + b = x and that x is rational. then b = x – a = x + (–a). x + (–a) is rational because however, it was stated that b is an irrational number. this is a contradiction. therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number. in conclusion, the sum of a rational number and an irrational number is irrational. which of the following best completes the proof? it is the sum of two rational numbers. it is the sum of two irrational numbers. it represents a non-terminating, non-repeating decimal. its terms cannot be combined.

Answers: 1

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Mathematics, 18.10.2019 19:00, noahdwilke

Below is a proof showing that the sum of a rational number and an irrational number is an irrational number. let a be a rational number and b be an irrational number. assume that a + b = x and that x is rational. then b = x – a = x + (–a). x + (–a) is rational because however, it was stated that b is an irrational number. this is a contradiction. therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number. in conclusion, the sum of a rational number and an irrational number is irrational. which of the following best completes the proof? it is the sum of two rational numbers. it is the sum of two irrational numbers. it represents a non-terminating, non-repeating decimal. its terms cannot be combined.

Answers: 3

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Mathematics, 12.11.2019 22:31, 12311724

Astudent memorized the statement the product of any rational number and any irrational number is irrational. label this statement as true or false, and explain your reasoning. a) true. for example, 3 ·5 is irrational, 7 · 2 3 is irrational, and (π)·(−4) is irrational. b) false. suppose an irrational times a rational = rational, then irrational = rational rational . this means irrational = rational, which is a contradiction.thus an irrational times a rational = rational. c) true. suppose an irrational times a rational = rational, then irrational = rational rational . this means irrational = rational, which is a contradiction.thus an irrational times a rational = irrational. d) false. the rational number cannot be zero. suppose an irrational times a nonzero rational = rational, then irrational = rational nonzero rational . this means irrational = rational, which is a contradiction. thus an irrational times a nonzero rational = irrational.

Answers: 1

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