The number r is irrational. Which statement about 7 + r is true? Choices: (A)7 + r is rational. (B)7 + r is irrational. (C)7 + r can be rational or irrational, depending on the value of r.

Evaluate Number Types: Evaluate the nature of the sum of a rational number and an irrational number. 7 is a rational number because it can be expressed as a fraction 7/1. r is given as an irrational number, which means it cannot be expressed as a fraction of two integers. The sum of a rational number and an irrational number is always irrational.Identify Rational and Irrational Numbers: Conclude the nature of 7 + r based on the evaluation. Since adding a rational number to an irrational number results in an irrational number, 7 + r is irrational.

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The number $r$ is irrational. Which statement about $7 + r$ is true? $\newline$ Choices: $\newline$ (A) $7 + r$ is rational. $\newline$ (B) $7 + r$ is irrational. $\newline$ (C) $7 + r$ can be rational or irrational, depending on the value of $r$ .

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Math Problems

Algebra 2

Classify rational and irrational numbers

Full solution

Q. The number

r

is irrational. Which statement about

7 + r

is true?

\newline

Choices:

\newline

(A)

7 + r

is rational.

\newline

(B)

7 + r

is irrational.

\newline

(C)

7 + r

can be rational or irrational, depending on the value of

r

Evaluate Number Types: Evaluate the nature of the sum of a rational number and an irrational number. $\newline$ $7$ is a rational number because it can be expressed as a fraction $\frac{7}{1}$ . $\newline$ $r$ is given as an irrational number, which means it cannot be expressed as a fraction of two integers. $\newline$ The sum of a rational number and an irrational number is always irrational.
Identify Rational and Irrational Numbers: Conclude the nature of $7 + r$ based on the evaluation. $\newline$ Since adding a rational number to an irrational number results in an irrational number, $7 + r$ is irrational.