In the xy-plane, the graph of y = x + b, where b is a constant, intersects the x-axis at (-6, 0). What is the value of b ?

y = 2x + 5
y=kx+3
In the given system of equations, k is a constant. The system has exactly one solution. Which of the following could be the value of k ?
I. 2
II. 5

A system of equations in algebra is made up of two or more equations that seek common solutions. A group of equations that all depend on the same variables is known as a "linear equation system." A system of equations is a group of equations that work together to provide a solution for all variables. Example:
• 2x - y = 12
• x - 2y = 48
Any system of equations can be solved using different methods. For example, we need at least two equations in a system of equations in two variables to solve. Similarly, we'll need at least three equations to solve a three-variable system of equations. So let us look at three different approaches to solving equations with two variables.
1. Substitution Method
2. Elimination Method
3. Graphical Method

8x - 4y = 7
3x + 6y = 12
If (x, y) is the solution to the given system of equations, what is the value of x ?

For a certain group of fish, the graph models the relationship between body length L, in centimeters (cm), and tail area A, in square centimeters (cm²), where . Which equation represents the relationship between body length and tail area?

The given equation relates the variables c, x, and y, where c > 0, x > 0, and y > 0. Which equation correctly expresses y in terms of c and x ?

In the xy-plane, line l has a slope of 2. Line k is perpendicular to line l and contains the point (4, 2). Which of the following is an equation of line k?

In right triangle ABC, the length of side is 12, the measure of A is 40°, and B is a right angle. Which of the following can be determined using the information given?
I. The measure of C
II The length of side

If 2n + 12 = 26n, what is the value of 6n?

I2x - 4 I = 8
What is the positive solution to the given equation?

Two lines intersect as shown. What is the value of x ?

y = 2x + 4
y = (x − 3)(x + 2)
The system of equations above is graphed in the xy-plane. At which of the following  points do the graphs of the equations intersect?

During mineral formation, the same chemical compound can beco me different  minerals depending on the temperature and pressure at the time of formation. A  phase diagram is a graph that shows the conditions that are needed to form each  mineral. The graph above is a portion of the phase diagram for aluminosilicates,  with the temperature T, in degrees Celsius (°C), on the horizontal axis, and the  pressure P, in gigapascals (GPa), on the vertical axis.
Which of the following systems of inequalities best describes the region where sillimanite can form?

The budget for a school band was $8,000 in 2010. The budget decreased by 15%  from 2010 to 2011 and then increased by 22% from 2011 to 2012. Which of the  following expressions represents the budget, in dollars, for the school band in 2012?

The circumference of Earth is estimated to be 40,030 kilometers at the equator.  Which of the following best approximates the diameter, in miles, of Earth’s  equator?  (1 kilometer ≈ 0.62137 miles)

The bar graph above shows the total number of scheduled flights and the number of delayed flights for five airlines in a one-month period. Values have been rounded to the nearest 1000 flights.
According to the graph, for the airline with the greatest number of delayed flights, what fraction of the total number of scheduled flights for the airline were delayed?

Two numbers, a and b, are each greater than zero, and the square root of a is equal to the cube root of b. For what value of x is a^2x-1 equal to b?

• To calculate the square root
To find the square root of the numbers, first find a number that, when multiplied twice by itself, yields the original number, and we must first determine which number was squared to obtain the original number. So, for example, if we need to find the square root of 4, we know that multiplying '2' by '2' yields 4. Hence, √4 = 2.
• To calculate the cube root
We must first find a number that, when multiplied three times by itself, yields the original number, and to find the cube root of a number, say 64, it is simple to see that the cube of 4 equals 64. As a result, the cube root of 64 is 4.