The first question asks us to identify which of the given numbers is not a rational number. The options are 14, 0, 5/2, and $\sqrt{7}$. The second question asks for the domain of the expression $\frac{x}{x+7}$.

1. Problem Description

The first question asks us to identify which of the given numbers is not a rational number. The options are 14, 0, 5/2, and $\sqrt{7}$.

The second question asks for the domain of the expression $\frac{x}{x+7}$.

2. Solution Steps

For the first question:

A rational number is a number that can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

* 14 can be written as $\frac{14}{1}$, so it is a rational number.

* 0 can be written as $\frac{0}{1}$, so it is a rational number.

* $\frac{5}{2}$ is already in the form of a fraction with integers, so it is a rational number.

* $\sqrt{7}$ is an irrational number because 7 is not a perfect square. Its decimal representation is non-terminating and non-repeating.

Therefore, $\sqrt{7}$ is not a rational number.

For the second question:

To find the domain of the expression $\frac{x}{x+7}$, we need to determine the values of $x$ for which the expression is defined. A rational expression is undefined when the denominator is equal to zero. Thus, we need to find the values of $x$ such that $x+7 \neq 0$.

$x+7 \neq 0$

$x \neq -7$

The domain is the set of all real numbers except $x = -7$. This can be written as $\{x | x \neq -7\}$.

3. Final Answer

For the first question, the number that is not a rational number is $\sqrt{7}$, which is option (4).

For the second question, the domain of the expression is $\{x | x \neq -7\}$, which is option (3).