To find the equation for circle B, we analyze the translation of the center of the circle.

1. Identify the center of Circle A:
The standard form of a circle equation is \( (x – h)^2 + (y – k)^2 = r^2 \), where \( (h, k) \) is the center.
For Circle A: \( x^2 + (y – 1)^2 = 49 \), the center is \( (0, 1) \).

2. Apply the shift:
Shifting the circle “down 2 units” means subtracting 2 from the y-coordinate of the center.
New y-coordinate \( = 1 – 2 = -1 \).
The x-coordinate remains the same (\( 0 \)).
The center of Circle B is \( (0, -1) \).

3. Construct the new equation:
The radius remains the same (\( r^2 = 49 \)).
Using the center \( (0, -1) \):
\( (x – 0)^2 + (y – (-1))^2 = 49 \)
\( x^2 + (y + 1)^2 = 49 \)

Therefore, the equation that represents circle B is \( x^2 + (y + 1)^2 = 49 \).

Choice C is correct. The median of a data set with an odd number of values, in
ascending or descending order, is the middle value of the data set, and the range
of a data set is the positive difference between the maximum and minimum values in the data set. Since the dot plot shown gives the values in data set A in
ascending order and there are 15 values in the data set, the eighth value in data
set A, 23, is the median. The maximum value in data set A is 26 and the minimum
value is 22, so the range of data set A is 26 22 – , or 4. It’s given that data set B is
created by adding 56 to each of the values in data set A. Increasing each of the
15 values in data set A by 56 will also increase its median value by 56 making
the median of data set B 79. Increasing each value of data set A by 56 does not
change the range, since the maximum value of data set B is 26 56 + , or 82, and
the minimum value is 22 56 + , or 78, making the range of data set B 82 78 – , or 4.
Therefore, the median of data set B is greater than the median of data set A, and
the range of data set B is equal to the range of data set A.

The correct answer is 51. A quadratic equation of the form 2 ax bx c + +=0, where
a, b, and c are constants, has no real solution if and only if its discriminant, 2 – + 4ac b , is negative. In the given equation, a =-1 and c =-676. Substituting
-1 for a and -676 for c in this expression yields a discriminant of
( )( ) 2 b — 4 1 676 , or 2 b -2,704. Since this value must be negative, 2 b – < 2,704 0, or 2 b <2,704. Taking the positive square root of each side of this inequality yields b<52. Since b is a positive integer, and the greatest integer less than 52 is 51, the greatest possible value of b is 51.

Choice A is correct. A solution to a system of equations must satisfy each
equation in the system. It follows that if an ordered pair ( ) 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. The only point that lies on each graph of the system of two linear
equations shown is their intersection point ( ) 8, 2 . It follows that if a new graph of
three linear equations is created using the system of equations shown and the
graph of x y + =- 4 16, this system has either zero solutions or one solution, the
point ( ) 8, 2 . Substituting 8 for x and 2 for y in the equation x y + =- 4 16
yields 8 4 2 16 + =- ( ) , or 16 16 =- . Since this equation is not true, the point ( ) 8, 2
does not lie on the graph of x y + =- 4 16. Therefore, ( ) 8, 2 is not a solution to the
system of three equations. It follows that there are zero solutions to this system.

In a right triangle \( JKL \) where \( J \) is the right angle, angles \( K \) and \( L \) are complementary, meaning \( K + L = 90^\circ \).

1. Use the definition of cosine:
\( \cos(K) = \frac{\text{adjacent leg to } K}{\text{hypotenuse}} = \frac{JK}{KL} = \frac{24}{51} \)

2. Identify the sides:
– Adjacent to \( K \): \( JK = 24 \)
– Hypotenuse: \( KL = 51 \)

3. Find the missing leg \( JL \) using the Pythagorean theorem:
\( JL^2 + JK^2 = KL^2 \)
\( JL^2 + 24^2 = 51^2 \)
\( JL^2 + 576 = 2601 \)
\( JL^2 = 2025 \)
\( JL = \sqrt{2025} = 45 \)

4. Calculate \( \cos(L) \):
The leg adjacent to angle \( L \) is \( JL \).
\( \cos(L) = \frac{\text{adjacent leg to } L}{\text{hypotenuse}} = \frac{JL}{KL} \)
\( \cos(L) = \frac{45}{51} \)

Alternatively, using trigonometric identities for complementary angles:
\( \cos(L) = \sin(K) \)
Since \( \cos(K) = \frac{24}{51} \), then \( \sin(K) = \frac{\sqrt{51^2 – 24^2}}{51} = \frac{45}{51} \).

Therefore, the value of \( \cos(L) \) is \( \frac{45}{51} \).

Choice C is correct. Vertical angles, which are angles that are opposite each
other when two lines intersect, are congruent. The figure shows that lines t and
m intersect. It follows that the angle with measure o x and the angle with
measure o y are vertical angles, so x y = . It’s given that x k = + 6 13 and
y k = – 8 29. Substituting 6 13 k + for x and 8 29 k – for y in the equation x y =
yields 6 13 8 29 k k +=- . Subtracting 6k from both sides of this equation yields
13 2 29 = -k . Adding 29 to both sides of this equation yields 42 2 = k, or 2 42 k = .
Dividing both sides of this equation by 2 yields k =21. It’s given that lines m and
n are parallel, and the figure shows that lines m and n are intersected by a
transversal, line t. If two parallel lines are intersected by a transversal, then the
same-side interior angles are supplementary. It follows that the same-side interior

Choice B is correct. A linear equation in one variable has no solution if and only
if the equation is false; that is, when there is no value of x that produces a true
statement. It’s given that in the equation -+ = 3 21 84 x px , p is a constant and
the equation has no solution for x . Therefore, the value of the constant p is one
that results in a false equation. Factoring out the common factor of -3x on the
left-hand side of the given equation yields – -= 3 1 7 84 x p ( ) . Dividing both sides
of this equation by -3 yields x p ( ) 1 7 28 – =- . Dividing both sides of this equation
by ( ) 1 7 – p yields 28
1 7p
x –
– = . This equation is false if and only if 17 0 – =p . Adding
7p to both sides of 17 0 – =p yields 1 7 = p. Dividing both sides of this equation
by 7 yields 1
7 = p. It follows that the equation 28
1 7p
x –
– = is false if and only if 1
7 p = .
Therefore, the given equation has no solution if and only if the value of p is 1
7
.

Choice A is correct. It’s given that a radio show stated that 3 times as many
people voted in favor of the proposal as people who voted against it. Let x
represent the number of people who voted against the proposal. It follows that
3x is the number of people who voted in favor of the proposal and 3x x – , or 2x,
is how many more people voted in favor of the proposal than voted against it. It’s
also given that a social media post reported that 15,000 more people voted in
favor of the proposal than voted against it. Thus, 2 15,000 x = . Since 2 15,000 x = ,
the value of x must be half of 15,000, or 7,500. Therefore, 7,500 people voted
against the proposal.

Choice C is correct. For the given line graph, the percent of cars for sale at a used
car lot on a given day is represented on the vertical axis. The percent of cars for
sale is the smallest when the height of the line graph is the lowest. The lowest
height of the line graph occurs for cars with a model year of 2014.

The correct answer is 3
10 . It’s given that there are a total of 100 tiles of equal
area, which is the total number of possible outcomes. According to the table,
there are a total of 30 red tiles. The probability of an event occurring is the ratio
of the number of favorable outcomes to the total number of possible outcomes.
By definition, the probability of selecting a red tile is given by 30
1

Choice B is correct. Multiplying each side of the given equation by -16 yields 2 64 112 576 x x + = . To complete the square, adding 49 to each side of this
equation yields 2 64 112 49 576 49 x x + += + , or ( )2
8 7 625 x + = . Taking the
square root of each side of this equation yields two equations: 8 7 25 x + = and
8 7 25 x + =- . Subtracting 7 from each side of the equation 8 7 25 x + = yields
8 18 x = . Dividing each side of this equation by 8 yields 18
8
x = , or 9
4
x = .
Therefore, 9
4 is a solution to the given equation. Subtracting 7 from each side of
the equation 8 7 25 x + =- yields 8 32 x =- . Dividing each side of this equation
by 8 yields x =-4. Therefore, the given equation has two solutions, 9
4
and -4.
Since 9
4 is positive, it follows that 9
4 is the positive solution to the given equation.
Alternate approach: Adding 2 4x and 7x to each side of the given equation
yields 2 0 4 7 36 = +- x x . The right-hand side of this equation can be rewritten as 2 4 16 9 36 x xx + — . Factoring out the common factor of 4x from the first two
terms of this expression and the common factor of -9 from the second two
terms yields 4 49 4 xx x ( ) ( ) +- + . Factoring out the common factor of ( ) x +4
from these two terms yields the expression ( )( ) 49 4 x x – + . Since this expression
is equal to 0, it follows that either 4 90 x – = or x + =4 0. Adding 9 to each side
of the equation 4 90 x – = yields 4 9 x = . Dividing each side of this equation by 4
yields 9
4
x = . Therefore, 9
4 is a positive solution to the given equation. Subtracting
4 from each side of the equation x + =4 0 yields x =-4. Therefore, the given
equation has two solutions, 9
4
and -4. Since 9
4 is positive, it follows that 9
4
is the
positive solution to the given equation.

Choice A is correct. It’s given that the truck can tow a trailer if the combined
weight of the trailer and the boxes it contains is no more than 4,600 pounds. If
the trailer has a weight of 500 pounds and each box weighs 120 pounds, the expression 500 120 + b, where b is the number of boxes, gives the combined
weight of the trailer and the boxes. Since the combined weight must be no more
than 4,600 pounds, the possible numbers of boxes the truck can tow are given
by the inequality 500 120 4,600 + £b . Subtracting 500 from both sides of this
inequality yields 120 4,100 b£ . Dividing both sides of this inequality by 120 yields
205
6
b£ , or b is less than or equal to approximately 34.17. Since the number of
boxes, b, must be a whole number, the maximum number of boxes the truck can
tow is the greatest whole number less than 34.17, which is 34.

Choice A is correct. It’s given that the estimate for the proportion of the
population that has the characteristic is 0.49 with an associated margin of error
of 0.04. Subtracting the margin of error from the estimate and adding the margin
of error to the estimate gives an interval of plausible values for the true proportion
of the population that has the characteristic. Therefore, it’s plausible that the
proportion of the population that has this characteristic is between 0.45 and
0.53.

Choice A is correct. The given point, ( ) 8, 2 , is located in the first quadrant in the
xy-plane. The system of inequalities in choice A represents all the points in the
first quadrant in the xy-plane. Therefore, ( ) 8, 2 is a solution to the system of
inequalities in choice A.
Alternate approach: Substituting 8 for x in the first inequality in choice A, x >0,
yields 8 0 > , which is true. Substituting 2 for y in the second inequality in
choice A, y >0, yields 2 0 > , which is true. Since the coordinates of the
point ( ) 8, 2 make the inequalities x >0 and y >0 true, the point (

Choice A is correct. The second equation in the given system defines the value
of x as 5y . Substituting 5y for x into the first equation yields 5 18 y y + = or
6 18 y = . Dividing each side of this equation by 6 yields y =3. Substituting 3 for
y in the second equation yields 5 3( )= x or x =15. Therefore, the solution ( ) x y,
to the given system of equations is ( ) 15, 3 .

Choice B is correct. For the given line graph, the estimated number of chipmunks
is represented on the vertical axis. The greatest estimated number of chipmunks
in the state park is indicated by the greatest height in the line graph. This height is
achieved when the year is 1994.