Choice C is correct. The solution to the system of two equations corresponds to
the point where the graphs of the equations intersect. The graphs of the linear
equation and the nonlinear equation shown intersect at the point (4, 5). Thus, the
solution to the system is (4, 5) .
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.

Choice D is correct. The y-intercept of a graph is the point where the graph
intersects the y-axis. The graph of function f shown intersects the y-axis at the
point (0, 8). Therefore, the y-intercept of the graph of f is (0, 8).
Choice A is incorrect. This is the point where the x-axis, not the graph of f,
intersects the y-axis. Choice B is incorrect and may result from conceptual or
calculation errors. Choice C is incorrect and may result from conceptual or
calculation errors.

The correct answer is 29. The range of a data set is the difference between its
maximum value and its minimum value. For the data set shown, the maximum
score is 52 and the minimum score is 23. The difference between those scores is
52-23, or 29. Therefore, the range of the 7 scores shown is 29.

The correct answer is 4. A solution to a system of equations must satisfy each
equation in the system. It follows that if (x, y), is a solution to the system, the point
(x, y) lies on the graph in the xy-plane of each equation in the system. According
to the graph, the point (x, y) that lies on the graph of each equation in the system
is (4, 1). Therefore, the solution to the system is (4, 1). It follows that the value of
x is 4.

Choice \( B \) is correct. The given values show that as \( x \) increases, \( f(x) \) also increases, which means that \( f \) is an increasing function. Furthermore, \( f(x) \) increases at a constant rate of \( 1 \) for each increase of \( x \) by \( 1 \). A function with a constant rate of change is linear. Thus, the function \( f \) can be described as an increasing linear function.

Choice \( A \) is incorrect. For a decreasing linear function, as \( x \) increases, \( f(x) \) decreases rather than increases.
Choice \( C \) is incorrect. For a decreasing exponential function, for each increase of \( x \) by \( 1 \), \( f(x) \) decreases by a fixed percentage rather than increases at a constant rate.
Choice \( D \) is incorrect. For an increasing exponential function, for each increase of \( x \) by \( 1 \), \( f(x) \) increases by a fixed percentage rather than at a constant rate.

Choice \( B \) is correct. The second equation in the given system is \( r = 3 \). Substituting \( 3 \) for \( r \) in the first equation in the given system yields \( s + 7(3) = 27 \), or \( s + 21 = 27 \). Subtracting \( 21 \) from both sides of this equation yields \( s = 6 \). Therefore, the solution \( (r, s) \) to the given system of equations is \( (3, 6) \).

Choice \( A \) is incorrect. This is the solution \( (s, r) \), not \( (r, s) \), to the given system of equations.
Choice \( C \) is incorrect and may result from conceptual or calculation errors.
Choice \( D \) is incorrect and may result from conceptual or calculation errors.

Choice \( B \) is correct. It’s given that the film club has \( 90 \) members on the first day of a semester, and \( 10 \) new members join the film club each day after the first day of the semester. This means that after \( 4 \) days, \( 4 \times 10 \), or \( 40 \), new members will have joined the club. Adding \( 40 \) members to the original \( 90 \) club members yields \( 130 \) members. Thus, the film club will have \( 130 \) total members \( 4 \) days after the first day of the semester.

Choice \( A \) is incorrect. This is the number of members that will have joined the film club \( 4 \) days after the first day of the semester if \( 100 \) new members, not \( 10 \), join the film club each day.
Choice \( C \) is incorrect. This is the number of members the film club will have \( 4 \) days after the first day of the semester if \( 1 \) new member, not \( 10 \), joins the club each day.
Choice \( D \) is incorrect. This is the number of members the film club has on the first day of the semester.

The correct answer is \( 6 \). It’s given that \( y = 4x \) and \( y = x^2 - 12 \). Since \( y = 4x \), substituting \( 4x \) for \( y \) in the second equation of the given system yields \( 4x = x^2 - 12 \). Subtracting \( 4x \) from both sides of this equation yields \( 0 = x^2 - 4x - 12 \). This equation can be rewritten as \( 0 = (x - 6)(x + 2) \). By the zero product property, \( x - 6 = 0 \) or \( x + 2 = 0 \). Adding \( 6 \) to both sides of the equation \( x - 6 = 0 \) yields \( x = 6 \). Subtracting \( 2 \) from both sides of the equation \( x + 2 = 0 \) yields \( x = -2 \). Therefore, solutions to the given system of equations occur when \( x = 6 \) and when \( x = -2 \). It’s given that a solution to the given system of equations is \( (x, y) \), where \( x > 0 \). Since \( 6 \) is greater than \( 0 \), it follows that the value of \( x \) is \( 6 \).

Choice \( C \) is correct. Dividing all terms in the given equation by \( 4 \) yields \( \frac{4x}{4} - \frac{28}{4} = -\frac{24}{4} \), or \( x - 7 = -6 \). Therefore, the value of \( x - 7 \) is \( -6 \).

Choice \( A \) is incorrect. This is the value of \( 4x - 28 \), not \( x - 7 \). Choice \( B \) is incorrect and may result from conceptual or calculation errors.
Choice \( D \) is incorrect and may result from conceptual or calculation errors.

Choice \( B \) is correct. It’s given that from the sample of \( 20 \) employees at the company, \( 16 \) of the employees are enrolled in exactly three professional development courses this year. Since \( \frac{16}{20} \) is equal to \( 0.80 \), or \( \frac{80}{100} \), it follows that \( 80\% \) of the employees in the sample are enrolled in exactly three professional development courses this year. Therefore, the best estimate for the percentage of employees at the company who are enrolled in exactly three professional development courses this year is \( 80\% \). It’s given that there are a total of \( 400 \) employees at the company. Therefore, the best estimate of the number of employees at the company who are enrolled in exactly three professional development courses this year is \( \left(\frac{80}{100}\right)(400) \), or \( 320 \).

Choice \( A \) is incorrect. This is the number of employees from the sample who aren’t enrolled in exactly three professional development courses this year. Choice \( C \) is incorrect. This is the number of employees who weren’t selected for the sample. Choice \( D \) is incorrect and may result from conceptual or calculation errors.

Choice \( B \) is correct. It’s given that the equation \( x + y = 1{,}440 \) represents the number of minutes of daylight, \( x \), and the number of minutes of non-daylight, \( y \), on a particular day in Oak Park, Illinois. It’s also given that this day has \( 670 \) minutes of daylight. Substituting \( 670 \) for \( x \) in the equation \( x + y = 1{,}440 \) yields \( 670 + y = 1{,}440 \). Subtracting \( 670 \) from both sides of this equation yields \( y = 770 \). Therefore, this day has \( 770 \) minutes of non-daylight.

Choice \( A \) is incorrect. This is the number of minutes of daylight, not non-daylight, on this day. Choice \( C \) is incorrect and may result from conceptual or calculation errors. Choice \( D \) is incorrect. This is the total number of minutes of daylight and non-daylight.

Choice C is correct. Vertical angles, or angles that are opposite each other when
two lines intersect, are congruent. It’s given that line k intersects line n. Based on
the figure, the angle with measure x° and the angle with measure 145° are vertical
angles. Therefore, the value of x is equal to 145.
Choice A is incorrect and may result from conceptual or calculation errors.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.

Choice \( B \) is correct. It’s given that at a particular track meet, the ratio of coaches to athletes is \( 1 \) to \( 26 \). If one number in a ratio is multiplied by a value, the other number must be multiplied by the same value in order to maintain the same ratio. If there are \( x \) coaches at the track meet, multiplying both numbers in the ratio by \( x \) yields \( 1(x) \) to \( 26(x) \), or \( x \) to \( 26x \). Therefore, the expression \( 26x \) represents the number of athletes at the track meet.

Choice \( A \) is incorrect and may result from conceptual or calculation errors.

Choice \( C \) is incorrect and may result from conceptual or calculation errors.

Choice \( D \) is incorrect and may result from conceptual or calculation errors.

Choice \( D \) is correct. It’s given that the graph of the rational function \( f \) is shown, where \( y = f(x) \) and \( x \ge 0 \). The graph shown passes through the point \( (3, 3) \). It follows that when the value of \( x \) is \( 3 \), the value of \( f(x) \) is \( 3 \). When the value of \( x \) is \( 3 \), the value of \( f(x) + 5 \) is \( 3 + 5 \), or \( 8 \). Therefore, the graph of \( y = f(x) + 5 \) passes through the point \( (3, 8) \). Of the given choices, choice \( D \) is the only graph that passes through the point \( (3, 8) \) and is therefore the graph of \( y = f(x) + 5 \).

Choice \( A \) is incorrect. This is the graph of \( y = f(x) - 5 \), rather than \( y = f(x) + 5 \).
Choice \( B \) is incorrect. This is the graph of \( y = \frac{f(x)}{5} \), rather than \( y = f(x) + 5 \).
Choice \( C \) is incorrect and may result from conceptual or calculation errors.

Choice \( C \) is correct. The volume, \( V \), of a right circular cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius of the base of the cylinder and \( h \) is the height of the cylinder. It’s given that a right circular cylinder has a height of \( 6 \) centimeters. Therefore, \( h = 6 \). It’s also given that the cylinder has a base diameter of \( 22 \) centimeters. The radius of a circle is half the diameter of the circle. Since the base of a right circular cylinder is a circle, it follows that the radius of the base of the right circular cylinder is \( \frac{22}{2} \), or \( 11 \), centimeters. Therefore, \( r = 11 \). Substituting \( 11 \) for \( r \) and \( 6 \) for \( h \) into the formula yields \( V = \pi (11)^2 (6) \), which is equivalent to \( V = \pi (121)(6) \), or \( V = 726\pi \). Therefore, the volume, in cubic centimeters, of the cylinder is \( 726\pi \).

Choice \( A \) is incorrect. This is the volume of a right circular cylinder that has a base diameter of \( 2\sqrt{22} \), not \( 22 \), centimeters and a height of \( 6 \) centimeters. Choice \( B \) is incorrect. This is the volume of a right circular cylinder that has a base diameter of \( 4\sqrt{11} \), not \( 22 \), centimeters and a height of \( 6 \) centimeters. Choice \( D \) is incorrect. This is the volume of a right circular cylinder that has a base diameter of \( 44 \), not \( 22 \), centimeters and a height of \( 6 \) centimeters.

The correct answer is \( 4.51 \). It’s given that the equation \( 4.51x + 6.07y = 896.86 \) represents this situation, where \( x \) is the number of smaller containers sold, \( y \) is the number of larger containers sold, and \( 896.86 \) is the store’s total sales, in dollars, of blueberries last month. Therefore, \( 4.51x \) represents the store’s sales, in dollars, of smaller containers, and \( 6.07y \) represents the store’s sales, in dollars, of larger containers. Since \( x \) is the number of smaller containers sold, the price, in dollars, of each smaller container is \( 4.51 \).

The correct answer is \( 6 \). It’s given that \( y = 4x \) and \( y = x^2 - 12 \). Since \( y = 4x \), substituting \( 4x \) for \( y \) in the second equation of the given system yields \( 4x = x^2 - 12 \). Subtracting \( 4x \) from both sides of this equation yields \( 0 = x^2 - 4x - 12 \). This equation can be rewritten as \( 0 = (x - 6)(x + 2) \). By the zero product property, \( x - 6 = 0 \) or \( x + 2 = 0 \). Adding \( 6 \) to both sides of the equation \( x - 6 = 0 \) yields \( x = 6 \). Subtracting \( 2 \) from both sides of the equation \( x + 2 = 0 \) yields \( x = -2 \). Therefore, solutions to the given system of equations occur when \( x = 6 \) and when \( x = -2 \). It’s given that a solution to the given system of equations is \( (x, y) \), where \( x > 0 \). Since \( 6 \) is greater than \( 0 \), it follows that the value of \( x \) is \( 6 \).

Choice \( B \) is correct. An equation of the form \( (x - h)^2 + (y - k)^2 = r^2 \), where \( h, k, \) and \( r \) are constants, represents a circle in the xy-plane with center \( (h, k) \) and radius \( r \). Therefore, the circle represented by the given equation has center \( (-4, 19) \) and radius \( 11 \). Since the center of the circle has an x-coordinate of \( -4 \) and the radius of the circle is \( 11 \), the least possible x-coordinate for any point on the circle is \( -4 - 11 \), or \( -15 \). Similarly, the greatest possible x-coordinate for any point on the circle is \( -4 + 11 \), or \( 7 \). Therefore, if the point \( (a, b) \) lies on the circle, it must be true that \( -15 \le a \le 7 \). Of the given choices, only \( -14 \) satisfies this inequality.
Choice A is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors

The correct answer is \( 336 \). By the zero product property, if \( (x + 14)(t - x) = 0 \), then \( x + 14 = 0 \), which gives \( x = -14 \), or \( (t - x) = 0 \), which gives \( x = t \). Therefore, \( g(x) = 0 \) when \( x = -14 \) and when \( x = t \). Since the graph of \( y = g(x) \) passes through the point \( (24, 0) \), it follows that \( g(24) = 0 \), so \( t = 24 \). Substituting \( 24 \) for \( t \) in the equation \( g(x) = (x + 14)(t - x) \) yields \( g(x) = (x + 14)(24 - x) \). The value of \( g(0) \) can be calculated by substituting \( 0 \) for \( x \) in this equation, which yields \( g(0) = (0 + 14)(24 - 0) \), or \( g(0) = 336 \).

The correct answer is \( \frac{11}{28} \). The cosine of an acute angle in a right triangle is defined as the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse. In the triangle shown, the length of the leg adjacent to the angle with measure \( x^\circ \) is \( 11 \) units and the length of the hypotenuse is \( 28 \) units. Therefore, the value of \( \cos x \) is \( \frac{11}{28} \). Note that \( \frac{11}{28} \), \( .3928 \), \( .3929 \), \( 0.392 \), and \( 0.393 \) are examples of ways to enter a correct answer.

Choice A is correct. A trigonometric ratio can be found using the unit circle, that
is, a circle with radius 1 unit. If a central angle of a unit circle in the xy-plane
centered at the origin has its starting side on the positive x-axis and its terminal
side intersects the circle at a point ^ h x y, , then the value of the tangent of the There are \( 2\pi \) radians in a circle. Dividing \( \frac{92\pi}{3} \) by \( 2\pi \) yields \( \frac{92}{6} \), which is equivalent to \( 15 + \frac{2}{3} \). It follows that on the unit circle centered at the origin in the xy-plane, the angle \( \frac{92\pi}{3} \) is the result of 15 revolutions from its starting side on the positive x-axis followed by a rotation through \( \frac{2\pi}{3} \) radians. Therefore, the angles \( \frac{92\pi}{3} \) and \( \frac{2\pi}{3} \) are coterminal angles and \( \tan\left(\frac{92\pi}{3}\right) \) is equal to \( \tan\left(\frac{2\pi}{3}\right) \). Since \( \frac{2\pi}{3} \) is greater than \( \frac{\pi}{2} \) and less than \( \pi \), it follows that the terminal side of the angle is in quadrant II and forms an angle of \( \frac{\pi}{3} \), or \( 60^\circ \), with the negative x-axis. The terminal side of the angle intersects the unit circle at the point \( \left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \). It follows that the value of \( \tan\left(\frac{2\pi}{3}\right) \) is \( \frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}} \), which is equivalent to \( -\sqrt{3} \). Therefore, the value of \( \tan\left(\frac{92\pi}{3}\right) \) is \( -\sqrt{3} \).

Choice \( B \) is incorrect. This is the value of \( \frac{1}{\tan\left(\frac{92\pi}{3}\right)} \), not \( \tan\left(\frac{92\pi}{3}\right) \). Choice \( C \) is incorrect. This is the value of \( \tan\left(\frac{\pi}{3}\right) \), not \( \tan\left(\frac{92\pi}{3}\right) \). Choice \( D \) is incorrect. This is the value of \( \tan\left(\frac{\pi}{3}\right) \), not \( \tan\left(\frac{92\pi}{3}\right) \).

Choice \( D \) is correct. It’s given that the equation \( y - 5x = 6 \) represents the relationship between the number of suits that Kaylani made, \( x \), and the total length of fabric she purchased, \( y \), in yards. Adding \( 5x \) to both sides of the given equation yields \( y = 5x + 6 \). Since Kaylani made \( x \) suits and used \( 5 \) yards of fabric to make each suit, the expression \( 5x \) represents the total amount of fabric she used to make the suits. Since \( y \) represents the total length of fabric Kaylani purchased, in yards, it follows from the equation \( y = 5x + 6 \) that Kaylani purchased \( 5x \) yards of fabric to make the suits, plus an additional \( 6 \) yards of fabric. Therefore, the best interpretation of \( 6 \) in this context is that Kaylani purchased \( 6 \) yards more fabric than she used to make the suits.

Choice \( A \) is incorrect. Kaylani made a total of \( x \) suits, not \( 6 \) suits. Choice \( B \) is incorrect. Kaylani purchased a total of \( y \) yards of fabric, not a total of \( 6 \) yards of fabric. Choice \( C \) is incorrect. Kaylani used a total of \( 5x \) yards of fabric to make the suits, not a total of \( 6 \) yards of fabric.