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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

A total of

toothpicks of equal length were used to construct two types of figures: triangles and squares. The triangles and squares were constructed so that no two figures had a common side. The equation

represents this situation, where

is the number of triangles constructed and

is the number of squares constructed. What is the best interpretation of

in this context?

AIf 25 triangles were constructed, then 35 squares were constructed.BIf 25 triangles were constructed, then 35 toothpicks were used.CIf 35 triangles were constructed, then 25 squares were constructed.DIf 35 triangles were constructed, then 25 toothpicks were used.

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

Moving from left to right, the curve passes from quadrant to quadrant to quadrant to quadrant to quadrant .

The curve has 1 relative minimum and 1 relative maximum.

The curve crosses the axes at the following points: (negative comma ), approximately ( comma negative ), ( comma ), and (2 comma 0).

The graph of is shown, where the function is defined by and , , , and are constants. For how many values of does ?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

, what is the value of

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

The scatterplot has

data points. The data points are in a quadratic pattern opening downward. The data points have the following approximate coordinates:

. Which of the following equations is the most appropriate quadratic model for the data shown?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

A right circular cylinder has a volume of

cubic inches. The height of the cylinder is

times its radius. What is the radius of the cylinder, in inches?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

For a linear relationship between and the table gives three values of and their corresponding values of , where is a constant. Which equation represents this relationship?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

The solution to the given system of equations is . What is the value of ?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

For which of the following tables are all the values of and their corresponding values of solutions to the given inequality?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

In the given equation, and are constants. The equation has infinitely many solutions. What is the value of ?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

The given function models the balance of a bank account, in dollars, years after it is opened. Which statement is the best interpretation of ?

AEvery

months, the balance increases by about

.BEvery

years, the balance increases by about

.CAt the end of every

-month interval, the balance increases by about

of the balance at the beginning of the

-month interval.DAt the end of every

-year interval, the balance increases by about

of the balance at the beginning of the

-year interval.

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

At a hotel, guests used the pool for a total of

hours in March. At the same hotel, guests used the pool for

hours in April. What is the percent increase in the number of hours guests used the pool from March to April?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

In the given equation, , , and are positive numbers. Which expression is equivalent to ?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

The measure of angle

radians. If the measure of angle

degrees, where

is a constant, what is the value of

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

In triangle

, the measure of angle

. Point

lies on segment

, and segment

is perpendicular to segment

. The length of segment

, and the length of segment

. What is the value of

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

Which system of linear equations has no solution?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

The function g is defined by g(x)=16x+39. For what value of x does g(x)=43?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

In the xy-plane, an equation of circle R is ${(x+7)}^{2}+{(y+19)}^{2}=100$ . Circle S is obtained by shifting circle R to the right 2 units. An equation defining circle S is ${(x+h)}^{2}+{(y+k)}^{2}=100$ , where h and k are constants. What is the value of h?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

The function f is defined by the equation $f(x)={9}^{x}+b$ , where b is a constant. In the xy-plane, the graph of y=f(x) contains the points (0,27) and (3,p+16), where p is a constant. What is the value of p?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

The quadratic function g models the depth, in meters, below the surface of the water of a Weddell seal t minutes after the seal entered the water during a dive. The function estimates that the seal reached its maximum depth of 409.6 meters 8 minutes after it entered the water and then reached the surface of the water 16 minutes after it entered the water. Based on the function, what was the estimated depth, to the nearest meter, of the seal 11 minutes after it entered the water?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

${r}^{2}+qr=4r-55$

In the given equation, q is an integer constant. The given equation has no real solutions. What is the largest possible value of q?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

The function f is defined by f(x)=2x+b, where b is a constant and f(4)=1. What is the value of b?

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Chapter 21 · 2025.12 : B-A(analysis included) · MATH 2

A pharmacist mixes magnesium and choline. The mixture has a total mass of 120 grams. The mass of magnesium in the mixture is 50 grams. What is the mass, in grams, of choline in the mixture?

120

170