is the base of the natural logarithm. The number v is irrational. Which statement about - v is true? Choices: (A) - v is rational. (B) - v is irrational. (C) - v can be rational or irrational, depending on the value of v.

Identify e nature: Identify the nature of the number e. The base of the natural logarithm, e, is known to be an irrational number.Consider v nature: Consider the nature of the number v. The problem states that v is an irrational number.Analyze e - v: Analyze the expression e - v. Since both e and v are irrational, the difference between two irrational numbers can be either rational or irrational. It depends on the specific values of e and v. For example, if v were equal to e, then e - v would be 0, which is rational. However, if v were some other irrational number not related to e in a way that their difference produces a rational number, then e - v would remain irrational.Determine correct choice: Determine the correct choice based on the analysis. Since e - v can be rational or irrational depending on the specific value of v, the correct statement is that e - v can be rational or irrational, depending on the value of v.

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is the base of the natural logarithm. The number $v$ is irrational. Which statement about $- v$ is true? $\newline$ Choices: $\newline$ (A) $- v$ is rational. $\newline$ (B) $- v$ is irrational. $\newline$ (C) $- v$ can be rational or irrational, depending on the value of $v$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

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Q. is the base of the natural logarithm. The number

v

is irrational. Which statement about

- v

is true?

\newline

Choices:

\newline

(A)

- v

is rational.

\newline

(B)

- v

is irrational.

\newline

(C)

- v

can be rational or irrational, depending on the value of

v

Identify $e$ nature: Identify the nature of the number $e$ . The base of the natural logarithm, $e$ , is known to be an irrational number.
Consider $v$ nature: Consider the nature of the number $v$ . The problem states that $v$ is an irrational number.
Analyze $e - v$ : Analyze the expression $e - v$ . $\newline$ Since both $e$ and $v$ are irrational, the difference between two irrational numbers can be either rational or irrational. It depends on the specific values of $e$ and $v$ . $\newline$ For example, if $v$ were equal to $e$ , then $e - v$ would be $0$ , which is rational. $\newline$ However, if $v$ were some other irrational number not related to $e$ in a way that their difference produces a rational number, then $e - v$ would remain irrational.
Determine correct choice: Determine the correct choice based on the analysis. $\newline$ Since $e - v$ can be rational or irrational depending on the specific value of $v$ , the correct statement is that $e - v$ can be rational or irrational, depending on the value of $v$ .