Our answer choices consist of two types of numbers: rational numbers and irrational numbers. In order to correctly answer this question, we need to know the difference between the two types of numbers. 

Rational numbers are numbers that we use most often, and can be written as a simple fraction. 

Irrational numbers cannot be written as fractions, and are numbers that have decimal places that never repeat or end. 

In this case,  is our only rational number because it can be written as a simple fraction: 

In order to solve this problem, we need to recall our exponent rules:

When our base numbers are equal to each other, like in this problem, we can add our exponents together using the following formula:

Let's apply this rule to our problem

Solve for the exponents

We cannot leave this problem in this format because we cannot have a negative exponent. Instead, we can move the base and the exponent to the denominator of a fraction:

Solve the problem

Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values. 

In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:

Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function: 

In order to determine if an equation defines a linear function, we want to make sure that the equation of the line is in slope-intercept form:

If we are unable to put an equation in this form, then the equation is not linear. 

Let's take a look at our answer choices:

Notice that in this equation our  value is to the third power, which does not match our slope-intercept form. 

Though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power. 

Again, though this equation is not written in  form, we can tell straight away that this does not define a linear function because the  value is to the second power. 

For this equation, we can solve for  to make sure this equation can be written is slope-intercept form. From first glance it looks to be correct because none of our variables are written to a power. In order to tell for certain, we need to isolate the y variable on the left side of the equation.

First, we can subtract  from both sides:

Next, we can divide each side by 

This equation is in slope-intercept form; thus,  is the correct answer. 

There are a couple of ways to solve a system of linear equations: graphically and algebraically. In this lesson, we will review the two ways to solve a system of linear equations algebraically: substitution and elimination. 

Substitution can be used by solving one of the equations for either  or , and then substituting that expression in for the respective variable in the second equation. You could also solve both equations so that they are in the  form, and then set both equations equal to each other. 

Elimination is best used when one of the variables has the same coefficient in both equations, because you can then use addition or subtraction to cancel one of the variables out, and solve for the other variable. 

For this problem, substitution makes the most sense because the first equation is already solved for a variable. We can substitute the expression that is equal to , into the  of our second equation:

Next, we need to distribute and combine like terms:

We are solving for the value of , which means we need to isolate the  to one side of the equation. We can subtract  from both sides:

Then divide both sides by  to solve for 

Remember, when we are solving a system of linear equations, we are looking for the point of intersection; thus, our answer should have both  and  values. 

Now that we have the value of , we can plug that value into the  variable in one of our given equations and solve for 

Our point of intersection, and the solution to the system of linear equations is .

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other. 

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

• Vertical angles are congruent
• Corresponding angles are congruent
• Alternate interior angles are congruent
• Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships. 

Angle  and  are vertical angles.

Angle  and  are corresponding angles. 

Angle  and  are exterior angles. 

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and . 

For this problem, we want to find the angle that is congruent to angle . Based on our answer choices, angle  and  are vertical angles; thus, both angle  and  are congruent and equal 

The provided triangle is a right triangle. We know this because the angle marker in the left corner of the triangle indicates that the triangle possesses a right or  angle. When a triangle includes a right angle, the triangle is said to be a "right triangle." 

We can use the Pythagorean Theorem to help us solve this problem.

The Pythagorean Theorem states that for right triangles, the square of the hypotenuse is equal to the sum of the square of the other two sides. In other terms:

We can use the formula and substitute the known side lengths from the problem to solve for the missing side length:

In order to solve this problem, we need to recall the formula used to calculate the volume of a cone:

Now that we have this formula, we can substitute in the given values and solve:

The data points in the scatter plot move up the y-axis as the x-axis decreases; thus the data points show a negative association. Also, the data points do not curve, or go up and down, but gradually decreased; thus the scatter plot shows a linear association. We could even draw a "best fit" line:

To help answer this question, we can construct a two-way table and fill in our known quantities from the question.

The columns of the table will represent the students who have a laptop or do not have a laptop and the rows will contain the students who have a car or do not have a car. The first bit of information that we were given from the question was that  students had a laptop; therefore,  needs to go in the "laptop" column as the row total. Next, we were told that of those students,  owned a car; therefore, we need to put  in the "laptop" column and in the "car" row. Then, we were told that  students do not own a laptop, but own a car, so we need to put  in the "no laptop" column and the "car" row. Finally, we were told that  students do not have a laptop or a car, so  needs to go in the "no laptop" column and "no car" row. If done correctly, you should create a table similar to the following: 

Our question asked how many students have a laptop, but do not own have a car. We can take the total number of students that own a lap top, , and subtract the number of students who have a car, 

This means that  students who have a laptop, don't have a car.