Parallel lines are defined as lines that lie in the same plane and do not intersect. This definition is fundamental in geometry because it captures the essence of what makes two lines parallel — their consistent distance apart and lack of intersection regardless of how far they are extended. The requirement that they lie in the same plane means that both lines exist in a two-dimensional space, allowing for a face-to-face comparison of their behavior regarding intersection. In contrast, other definitions do not accurately represent parallel lines. Lines that intersect at a right angle describe perpendicular lines, which meet at a 90-degree angle. Lines that connect at a point indicate convergence rather than parallelism, as they come together instead of maintaining a uniform distance apart. Finally, stating that lines are always horizontal does not encompass all parallel lines, as parallel lines can run in any direction as long as they never meet. Thus, the correct understanding of parallel lines is based on their inherent property of non-intersection within the same plane.

A variable in mathematical terms is defined as a symbol that represents a missing or unknown value. This representation allows for the formulation of equations and expressions that can model real-world situations and solve problems. Variables are typically denoted by letters, such as x, y, or z, and they can take on different values depending on the context of the problem. In mathematical equations, using variables gives flexibility and the ability to describe relationships between quantities that may change. For example, in the equation y = 2x + 5, both y and x are variables; y changes as x changes, reflecting that they are not fixed. The other options do not accurately describe a variable. A fixed number that does not change represents a constant, while a letter or symbol that represents a known value is more akin to a constant than a variable. Lastly, the term used for whole numbers only is incorrect, as variables can represent any type of number, including integers, fractions, and decimals. Therefore, the definition of a variable as a symbol for a missing or unknown value encompasses its essential role in mathematics.

An acute angle is defined as an angle that measures less than 90 degrees. This means that acute angles are sharp and smaller than a right angle, which measures exactly 90 degrees. Understanding acute angles is fundamental in geometry, as they are commonly encountered in various shapes and designs. This definition also highlights the contrast with other types of angles: right angles (90 degrees, which is not acute) and obtuse angles (greater than 90 degrees but less than 180 degrees). Therefore, the correct choice reflects the precise definition of acute angles in geometric terms.

A right angle is defined as an angle that measures exactly 90 degrees. This is a fundamental concept in geometry, representing a quarter of a full rotation. When two lines or line segments intersect at a right angle, they form a square corner, which is visually recognizable in everyday objects and structures. In the context of angles, 45 degrees represents an acute angle, which is less than 90 degrees, while 180 degrees corresponds to a straight angle, illustrating a half rotation. A full rotation is measured at 360 degrees. Therefore, understanding that a right angle specifically measures 90 degrees is crucial for geometry and is foundational for creating perpendicular lines and understanding more complex geometric concepts.

To solve the equation 2x + 6 = 18, the first step is to isolate the term with the variable. This is done by subtracting 6 from both sides of the equation, which simplifies it to 2x = 12. Next, to solve for x, you need to divide both sides of the equation by 2. Performing this division gives you x = 6. This solution is correct because substituting x back into the original equation (2(6) + 6 = 18) confirms that both sides are equal. Hence, the correct value for x that satisfies the equation is 6.