Let \( x \) represent the percentage of 300 that is 75. This can be written as \( \frac{x}{100}(300) = 75 \), or \( 3x = 75 \). Dividing both sides of this equation by 3 yields \( x = 25 \). Therefore, \( 25\% \) of 300 is 75.

Choice D is correct. The given phrase “8 times a number x ” can be represented
by the expression 8x . The given phrase “3 more than” indicates an increase of 3
to a quantity. Therefore “3 more than 8 times a number x ” can be represented
by the expression 8 3 x + . Since it’s given that 3 more than 8 times a number x
is equal to 83, it follows that 8 3 x + is equal to 83, or 8 3 83 x + = . Therefore, the
equation that represents this situation is 8 3 83 x + = .

Choice A is correct. It’s given that t represents the number of monthly deposits.
In the given function f(t )= 100 + 25t , the coefficient of t is 25. This means that
for every increase in the value of t by 1, the value of f t( ) increases by 25. It
follows that with each monthly deposit, the amount in Hana’s bank account
increased by $25.

The correct answer is 10. It’s given that the cost for the entire purchase was $27
after a coupon was used for $63 off the entire purchase. Adding the amount
of the coupon to the purchase price yields 27 + 63 = 90 . Thus, the cost for the
entire purchase before using the coupon was $90. It’s given that Nasir bought
9 storage bins. The original price for 1 storage bin can be found by dividing the
total cost by 9. Therefore, the original price, in dollars, for 1 storage bin is 90
9 ,
or 10.

Choice A is correct. An equation that defines a linear function f can be written
in the form f x mx b ( )= + , where m and b are constants. It’s given in the table
that when x =0, f x( )=29. Substituting 0 for x and 29 for f x( ) in the equation
f x mx b ( )= + yields 29 0 = + m b ( ) , or 29= b. Substituting 29 for b in the
equation f x mx b ( )= + yields f x mx ( )= +29. It’s also given in the table that f x mx ( )= +29 yields 32 1 29 = + m( ) , or 32 29 = + m . Subtracting 29 from
both sides of this equation yields 3= m. Substituting 3 for m in the equation
f x mx ( )= +29 yields fx x ( )= + 3 29.

Choice B is correct. In similar triangles, corresponding angles are congruent. It’s
given that right triangles PQR and STU are similar, where angle P corresponds
to angle S. It follows that angle P is congruent to angle S. In the triangles shown,
angle R and angle U are both marked as right angles, so angle R and angle U
are corresponding angles. It follows that angle Q and angle T are corresponding
angles, and thus, angle Q is congruent to angle T . It’s given that the measure of
angle Q is o 18 , so the measure of angle T is also o 18 . Angle U is a right angle,
so the measure of angle U is o 90 . The sum of the measures of the interior angles
of a triangle is o 180 . Thus, the sum of the measures of the interior angles of
triangle STU is 180 degrees. Let s represent the measure, in degrees, of angle
S. It follows that s++= 18 90 180, or s+ = 108 180. Subtracting 108 from both
sides of this equation yields s =72. Therefore, if the measure of angle Q is
18 degrees, then the measure of angle S is 72 degrees

Choice D is correct. The data points suggest that as the variable x increases, the
variable y decreases, which implies that an appropriate linear model for the data
has a negative slope. The data points also show that when x is close to 0, y is
greater than 9. Therefore, the y-intercept of the graph of an appropriate linear
model has a y-coordinate greater than 9. The graph of an equation of the form
y a bx = + , where a and b are constants, has a y-intercept with a y-coordinate
of a and has a slope of b. Of the given choices, only choice D represents a graph
that has a negative slope, -0.9, and a y-intercept with a y-coordinate greater than
9, 9.4.

Choice A is correct. The number of birds can be found by calculating the value of
b when r =16 in the given equation. Substituting 16 for r in the given equation
yields 2.5 5 16 80 b+ = ( ) , or 2.5 80 80 b+ = . Subtracting 80 from both sides of
this equation yields 2.5 0 b = . Dividing both sides of this equation by 2.5 yields
b =0. Therefore, if the business cares for 16 reptiles on a given day, it can care
for 0 birds on this day

An equation of a line can be written in the form \( y = mx + b \), where \( m \) is the slope of the line and \( (0, b) \) is the y-intercept of the line. The line shown passes through the point \( (0, -8) \), so \( b = -8 \). The line shown also passes through the point \( (-8, 0) \). The slope, \( m \), of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) can be calculated using the equation \( m = \frac{y_2 – y_1}{x_2 – x_1} \). For the points \( (0, -8) \) and \( (-8, 0) \), this gives \( m = \frac{(-8) – 0}{0 – (-8)} \), or \( m = -1 \). Substituting \( -8 \) for \( b \) and \( -1 \) for \( m \) in \( y = mx + b \) yields \( y = (-1)x + (-8) \), or \( y = -x – 8 \). Therefore, an equation of the graph shown is \( y = -x – 8 \).

The correct answer is \( \frac{1}{5} \). Since the number 5 can also be written as \( \frac{5}{1} \), the given equation can also be written as \( \frac{x}{8} = \frac{5}{1} \). This equation is equivalent to \( \frac{8}{x} = \frac{1}{5} \). Therefore, the value of \( \frac{8}{x} \) is \( \frac{1}{5} \). Note that 1/5 and .2 are examples of ways to enter a correct answer.

Alternate approach: Multiplying both sides of the equation \( \frac{x}{8} = 5 \) by 8 yields \( x = 40 \). Substituting 40 for \( x \) into the expression \( \frac{8}{x} \) yields \( \frac{8}{40} \), or \( \frac{1}{5} \).

The correct answer is 80. Subtracting the second equation in the given system
from the first equation yields ( ) ( ) 24 6 48 72 xy xy +- += – , which is equivalent
to 24 6 24 x xyy – + – =- , or 18 24 x =- . Dividing each side of this equation
by 3 yields 6 8 x =- . Substituting -8 for 6x in the second equation yields
-+ = 8 72 y . Adding 8 to both sides of this equation yields y =80.
Alternate approach: Multiplying each side of the second equation in the given
system by 4 yields 24 4 288 x y + = . Subtracting the first equation in the given
system from this equation yields ( ) ( ) 24 4 24 288 48 x y xy + – += – , which is The correct answer is 80. Subtracting the second equation in the given system
from the first equation yields ( ) ( ) 24 6 48 72 xy xy +- += – , which is equivalent
to 24 6 24 x xyy – + – =- , or 18 24 x =- . Dividing each side of this equation
by 3 yields 6 8 x =- . Substituting -8 for 6x in the second equation yields
-+ = 8 72 y . Adding 8 to both sides of this equation yields y =80.
Alternate approach: Multiplying each side of the second equation in the given
system by 4 yields 24 4 288 x y + = . Subtracting the first equation in the given
system from this equation yields ( ) ( ) 24 4 24 288 48 x y xy + – += – , which is

Choice D is correct. The equation that defines line \( t \) in the \( xy \)-plane can be written in slope-intercept form \( y = mx + b \), where \( m \) is the slope of line \( t \) and \( (0, b) \) is its y-intercept. It’s given that line \( t \) has a slope of \( -\frac{1}{3} \). Therefore, \( m = -\frac{1}{3} \). Substituting \( -\frac{1}{3} \) for \( m \) in the equation \( y = mx + b \) yields \( y = -\frac{1}{3}x + b \), or \( y = -\frac{x}{3} + b \). It’s also given that line \( t \) passes through the point \( (9, 10) \). Substituting 9 for \( x \) and 10 for \( y \) in the equation \( y = -\frac{x}{3} + b \) yields \( 10 = -\frac{9}{3} + b \), or \( 10 = -3 + b \). Adding 3 to both sides of this equation yields \( 13 = b \). Substituting 13 for \( b \) in the equation \( y = -\frac{x}{3} + b \) yields \( y = -\frac{x}{3} + 13 \).

Choice B is correct. It’s given that the function ( ) ( ) 206 1.034 x
f x = models the
value, in dollars, of a certain bank account by the end of each year from 1957
through 1972, where x is the number of years after 1957. It follows that f x( )
represents the estimated value, in dollars, of the bank account x years after
1957. Since the value of f( ) 5 is the value of f x( ) when x =5, it follows that “f( ) 5
is approximately equal to 243” means that f x( ) is approximately equal to 243
when x =5. In the given context, this means that the value of the bank account
is estimated to be approximately 243 dollars 5 years after 1957. Therefore, the
best interpretation of the statement “f( ) 5 is approximately equal to 243” in this
context is the value of the bank account is estimated to be approximately
243 dollars in 1962.

Choice B is correct. It’s given that the ratio of the rectangular region’s length to its
width is 35 to 10. This can be written as a proportion: length 35
width 10 = , or  35
w 10 = . This
proportion can be rewritten as 10 35 = w, or =3.5w . If the width of the
rectangular region increases by 7, then the length will increase by some number
x in order to maintain this ratio. The value of x can be found by replacing  with
+ x and w with w +7 in the equation, which gives += + x w 3.5 7 ( ). This
equation can be rewritten using the distributive property as += + x w 3.5 24.5Since =3.5w , the right-hand side of this equation can be rewritten by
substituting  for 3.5w, which gives   +=+ x 24.5, or x =24.5. Therefore, if the
width of the rectangular region increases by 7 units, the length must increase by
24.5 units in order to maintain the given ratio.

Choice B is correct. The area, \( A \), of a triangle can be found using the formula \( A = \frac{1}{2}bh \), where \( b \) is the length of the base of the triangle and \( h \) is the height of the triangle. It’s given that the triangle is a right triangle. Therefore, its base and height can be represented by the two legs. It’s also given that the triangle has sides of length \( 2\sqrt{2} \), \( 6\sqrt{2} \), and \( \sqrt{80} \) units. Since \( \sqrt{80} \) units is the greatest of these lengths, it’s the length of the hypotenuse. Therefore, the two legs have lengths \( 2\sqrt{2} \) and \( 6\sqrt{2} \) units. Substituting these values for \( b \) and \( h \) in the formula \( A = \frac{1}{2}bh \) gives \( A = \frac{1}{2}(2\sqrt{2})(6\sqrt{2}) \), which is equivalent to \( A = 6\sqrt{4} \) square units, or \( A = 12 \) square units.

Choice A is incorrect. This expression represents the perimeter, rather than the area, of the triangle. 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 A is correct. It’s given that points \( A \) and \( B \) lie on the circle with center \( C \). Therefore, \( \overline{AC} \) and \( \overline{BC} \) are both radii of the circle. Since all radii of a circle are congruent, \( \overline{AC} \) is congruent to \( \overline{BC} \). The length of \( \overline{AC} \), or the distance from point \( A \) to point \( C \), can be found using the distance formula, which gives the distance between two points, \( (x_{1}, y_{1}) \) and \( (x_{2}, y_{2}) \), as \( \sqrt{(x_{1} – x_{2})^{2} + (y_{1} – y_{2})^{2}} \). Substituting the given coordinates of point \( A \), \( (h + 1, k + \sqrt{102}) \), for \( (x_{1}, y_{1}) \) and the given coordinates of point \( C \), \( (h, k) \), for \( (x_{2}, y_{2}) \) in the distance formula yields \( \sqrt{(h + 1 – h)^{2} + (k + \sqrt{102} – k)^{2}} \), or \( \sqrt{1^{2} + (\sqrt{102})^{2}} \), which is equivalent to \( \sqrt{1 + 102} \), or \( \sqrt{103} \). Therefore, the length of \( \overline{AC} \) is \( \sqrt{103} \) and the length of \( \overline{BC} \) is \( \sqrt{103} \). It’s given that angle \( ACB \) is a right angle. Therefore, triangle \( ACB \) is a right triangle with legs \( \overline{AC} \) and \( \overline{BC} \) and hypotenuse \( \overline{AB} \). By the Pythagorean theorem, if a right triangle has a hypotenuse with length \( c \) and legs with lengths \( a \) and \( b \), then \( a^{2} + b^{2} = c^{2} \). Substituting \( \sqrt{103} \) for \( a \) and \( b \) in this equation yields \( (\sqrt{103})^{2} + (\sqrt{103})^{2} = c^{2} \), or \( 103 + 103 = c^{2} \), which is equivalent to \( 206 = c^{2} \). Taking the positive square root of both sides of this equation yields \( \sqrt{206} = c \). Therefore, the length of \( \overline{AB} \) is \( \sqrt{206} \).

Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect. This would be the length of \( \overline{AB} \) if the length of \( \overline{AC} \) were 103, not \( \sqrt{103} \). Choice D is incorrect and may result from conceptual or calculation errors.