Quiz about 2025 Part 1

Question 1

Which expression is equivalent to $$4x^2 + 9x - (x - 3)^2 + 11$$ ?

Accepted Answer

$$3x^2 + 15x + 2$$

Answer

$$3x^2 + 3x + 20$$

Answer

$$5x^2 + 3x + 20$$

Answer

$$3x^2 + 3x - 2$$

Question 2

Which expression is equivalent to $$6x^2 + 2(x - 10) - (x - 4)^2$$ ?

Accepted Answer

$$5x^2 + 10x - 36$$

Answer

$$5x^2 - 6x - 4$$

Answer

$$5x^2 + 10x - 4$$

Answer

$$5x^2 - 10x - 28$$

Question 3

Which expressions are equivalent to $$2x^8 - 512$$ ? Select two answers.

Accepted Answer

$$2(x^4)^2$$ - 2(256)

Accepted Answer

$$2(x - 2)(x + 2)(x^2 + 4)(x^2 + 16)$$

Answer

$$2(x - 4)(x + 4)(x^2 + 16)$$

Answer

$$2(x^4 + 256)(x^4 - 256)$$

Answer

$$2(x - 4)(x + 4)(x^2 + 8)(x^4 + 16)$$

Question 4

Which expression is equivalent to $$3x^2 + 7x - (x + 4)^2 - 9$$ ?

Accepted Answer

$$2x^2 - x - 25$$

Answer

$$2x^2 + 7x - 25$$

Answer

$$2x^2 + 7x + 7$$

Answer

$$2x^2 + 6x + 7$$

Question 5

Consider the equation. 4 - 2(x + 3) = 6 - 3(x - 1). What is the value of x in the equation?

Accepted Answer

11

Answer

18

Answer

-11

Answer

-18

Question 6

Select the correctly identifies the only solution or the best description of how many solutions there are for the equation. $$\frac{1}{5}-\left(\frac{1}{3}x+3\right)=\frac{4}{5}(x+3)-2-\frac{1}{3}x$$

Accepted Answer

x = -4

Answer

x = 4

Answer

No solution

Answer

Infinite solutions

Question 7

Select the correctly identifies the only solution or the best description of how many solutions there are for the equation. $$3\left(x-4\right)-3=2x-\left(3x-1\right)$$

Accepted Answer

x = 4

Answer

No solution

Answer

x = -4

Answer

Infinite solutions

Question 8

Select the correctly identifies the only solution or the best description of how many solutions there are for the equation. $$6\left(x-7\right)+10=\frac{3}{2}\left(4x-8\right)-20$$

Accepted Answer

Infinite solutions

Answer

x = 4

Answer

No solution

Answer

x = -4

Question 9

Select the correctly identifies the only solution or the best description of how many solutions there are for the equation. $$5x+8-6x=\frac{1}{2}\left(4-2x\right)-10$$

Accepted Answer

No solution

Answer

x = 4

Answer

x = -4

Answer

Infinite solutions

Question 10

Select the correctly identifies the only solution or the best description of how many solutions there are for the equation. $$\left(x+7\right)\left(x-9\right)$$

Accepted Answer

$$\left(x-1\right)^2-64$$

Accepted Answer

$$x^2-2x-63$$

Answer

$$-\left(x-8\right)^2+1$$

Answer

$$x^2+16x+63$$

Answer

$$\left(x+7\right)\left(x+9\right)$$

Question 11

Select the answer that shows which expressions are equivalent. . $$\left(x+8\right)^2-1$$

Accepted Answer

$$x^2+16x+63$$

Accepted Answer

$$\left(x+7\right)\left(x+9\right)$$

Answer

$$-\left(x-8\right)^2+1$$

Answer

$$\left(x-1\right)^2-64$$

Answer

$$x^2-2x-63$$

Question 12

Select the answer that shows which expressions are equivalent. $$-x^2+16x-63$$

Accepted Answer

$$-\left(x-8\right)^2+1$$

Answer

$$\left(x-1\right)^2-64$$

Answer

$$x^2-2x-63$$

Answer

$$x^2+16x+63$$

Answer

$$\left(x+7\right)\left(x+9\right)$$

Question 13

Select the answer the correct solution or the best description of how many solutions there are for the equation. $$-7x-12=-7x+3\left(-4-x\right)$$

Accepted Answer

x = 0

Answer

x = -4

Answer

Infinite Solution

Answer

No Solution

Question 14

Select the answer the correct solution or the best description of how many solutions there are for the equation. $$4\left(2x+3\right)=5x+3x-6$$

Accepted Answer

No Solution

Answer

x = -4

Answer

x = 0

Answer

Infinite Solution

Question 15

Select the answer the correct solution or the best description of how many solutions there are for the equation. $$-3+\frac{1}{2}\left(-6x-4\right)=-\frac{1}{4}\left(8x+4\right)$$

Accepted Answer

x = -4

Answer

x = 0

Answer

Infinite Solution

Answer

No Solution

Question 16

Select the answer the correct solution or the best description of how many solutions there are for the equation. $$3\left(x-7\right)+12=\frac{1}{4}\left(12x-8\right)-7$$

Accepted Answer

Infinite Solution

Answer

x = -4

Answer

x = 0

Answer

No Solution

Question 17

A student is solving the equation $$6(2x + 1) = 5x + 3 + 2x$$ . Which describes a first step the student could use to solve the equation correctly?

Accepted Answer

The student can distribute 6 on the left side of the equation, resulting in $$12x + 6 = 5x + 3 + 2x$$ .

Answer

The student can combine like terms on the right side of the equation, resulting in $$6(2x + 1) = 3x + 3$$ .

Answer

The student can combine like terms on the right side of the equation, resulting in $$6(2x + 1) = 10x$$ .

Answer

The student can distribute 6 on the left side of the equation, resulting in $$12x + 1 = 5x + 3 + 2x$$ .

Question 18

Which numerical expression would provide the solutions to the equation $$3x^2 - 5x + 1 = 5$$ ?

Accepted Answer

$$\frac{5 \pm \sqrt{73}}{6}$$

Answer

$$\frac{-5 \pm \sqrt{73}}{6}$$

Answer

$$\frac{-5 \pm \sqrt{75}}{3}$$

Answer

$$\frac{5 \pm \sqrt{75}}{3}$$

Question 19

Which numerical expression would provide the solutions to the equation $$2x^2 - 7x = 3 - x^2$$ ?

Accepted Answer

$$\frac{7 \pm \sqrt{85}}{6}$$

Answer

$$\frac{7 \pm \sqrt{37}}{2}$$

Answer

$$\frac{-7 \pm \sqrt{37}}{2}$$

Answer

$$\frac{-7 \pm \sqrt{85}}{6}$$

Question 20

What is the solution to 12m - 7(4m - 7) > 5(1 - m)?

Accepted Answer

m < 4

Answer

m > 4

Answer

m > -52

Answer

m < 52

Question 21

What is the solution to the inequality 4(3x + 2) - 6 > 8 + 2(x - 8)?

Accepted Answer

x > -1

Answer

x < -1

Answer

x < 1

Answer

x > 1

Question 22

$$\frac{\left(4+x\right)}{2}<\frac{\left(x+1\right)}{3}$$ Consider the inequality.

What is the solution to the inequality?

Accepted Answer

B. x < -10

Answer

A. x > -10

Answer

C. x > -1/10

Answer

D. x < -1/10

Question 23

$$\frac{\left(x+5\right)}{4}>\frac{\left(x+6\right)}{3}$$ Consider the inequality.

What is the solution to the inequality?

Accepted Answer

A. x < -9

Answer

B. x > -9

Answer

C. x < 9

Answer

D. x > 9

Question 24

Which number could be placed in the empty cell so that the table of values satisfies the definition of a function?

Accepted Answer

3

Answer

-16

Answer

-8

Answer

20

Question 25

A relation is defined by the coordinates shown.

{(-5,-5), (-3,-7), (-1,-2), (-1,0), (1,0), (3,7), (5,7)}

Removing which coordinates will make the relation a function?

Accepted Answer

(-1, -2)

Answer

(-5, -5)

Answer

(1, 0)

Answer

(3, 7)

Question 26

Which graphs show functions?

Accepted Answer

I and III

Answer

I and II

Answer

II and III

Answer

I, II, and III

Question 27

Which statements are true about the line shown on the graph?

Select two answer choices.

Accepted Answer

B. The point (0, -4) is on the line.

Accepted Answer

E. The graph represents the equation 2x + 3y = -12.

Answer

A. The point (-4, 0) is on the line.

Answer

C. The point (36, 28) is on the line.

Answer

D. The graph represents the equation 2x - 3y = -12.

Question 28

Consider the graph of the linear equation.

Which statement is true?

Accepted Answer

The point (0, 3) is on the line.

Answer

The point (0, -6) is on the line.

Answer

The graph represents the equation 3x + 6y = 18.

Answer

The graph represents the equation 3x - 6y = 18.

Question 29

Which statements are true about the line, f, shown on the graph?

Select three answers.

Accepted Answer

The point (-16, -28) is on line f.

Accepted Answer

The point (-4, -4) is on line f.

Accepted Answer

The graph of line f represents the equation 2x - y = -4.

Answer

The graph of line f represents the equation 2x + y = 4.

Answer

The point (16, 38) is on line f.

Question 30

Which points are on the graph of the equation -3x + 6y + 5 = -7?

Select all that apply.

Accepted Answer

(0, -2)

Accepted Answer

(8, 2)

Answer

(-3, 6)

Answer

(-2, 0)

Answer

(6, -3)

Question 31

The manager of a school store orders 250 pencils at the beginning of the school year to sell to students. The functiion f(x) =250 -7x represents the number of pencils remaining after x days of school.

Which statement about f(14) is true?

Accepted Answer

The value of f(14) is 152, and it represents 152 remaining pencils after 14 school days.

Answer

The value of f(14) is 98, and it represents 98 remaining pencils after 14 school days.

Answer

The value of f(14) is 98, and it represents selling 98 pencils in 14 school days.

Answer

The value of f(14) is 152, and it represents selling 152 pencils in 14 school days.

Question 32

Which graph represents the system of equations? x + 3y = 12 5x + 3y = 24

Accepted Answer

Graph C

Answer

Graph A

Answer

Graph B

Answer

Graph D

Question 33

Which system of equations is represented by the graph?

Accepted Answer

3x + 3y = 6

2x + 5y = -2

Answer

x - 5y = 14

5x - 4y = 28

Answer

x + 5y = -6

5x + 4y = 12

Answer

3x - 3y = 6

2x - 5y = 18

Question 34

Two catering companies each charge a flat fee for delivery and charge a price per attendee. The graph shows the situation.

Which point represents the number of attendees, x, for which the total cost, y, is the same for each company?

Accepted Answer

(24, 150)

Answer

(0, 50)

Answer

(0, 100)

Answer

(150, 24)

Question 35

In order to solve the equation $$\frac{2}{3}x - 3 = -\frac{1}{3}x - 6$$ , a student graphs the equations $$y = \frac{2}{3}x - 3$$ and $$y = -\frac{1}{3}x - 6$$ correctly, as shown.

What is (are) the solution(s) to the equation $$\frac{2}{3}x - 3 = -\frac{1}{3}x - 6$$ ?

Accepted Answer

x = -3 only

Answer

x = -6 and x = -3

Answer

x = -5 and x = -3

Answer

x = -5 only

Question 36

Consider the system of equations.
$$3x-2y=-8$$

$$7x+4y=-10$$

Which system of equations is equivalent to the given system?

Accepted Answer

6x - 4y = -16

7x + 4y = -10

Answer

6x - 4y = -16

14x + 12y = -10

Answer

9x - 6y = -8

7x + 4y = -10

Answer

9x - 6y = -8

14x + 12y = -10

Question 37

What value of y makes the following system of equations true?

3x + 6y = 12

5x + 6y = 4

Accepted Answer

4

Answer

-4

Answer

-1

Answer

0

Question 38

Consider the system of equations. -2x + 6y = 24 x + y = 2 Which shows an equivalent system of equations?

Accepted Answer

-2x + 6y = 24

2x + 2y = 4

Answer

-2x + 6y = 24

2x - 2y = 4

Answer

-2x + 6y = 24

2x - 2y = 6

Answer

-2x + 6y = 24

2x + 2y = 6

Question 39

In order to solve the equation
$$-\left|x\right|+4=-\frac{1}{2}x+1$$ , a student graphs the equations $$y=-\left|x\right|+4$$ and $$y=-\frac{1}{2}x+1$$ correctly, as shown.

What are the solutions to the equation $$-\left|x\right|+4=-\frac{1}{2}x+1$$ ?

Accepted Answer

x = -2 and x = 6

Answer

x = -2 and x = 2

Answer

x = 1 and x = 4

Answer

x = 2 and x = 4

Question 40

Given g(x) = $$-(x - 1)^2 + 4$$ and f(x) = $$|x + 3| - 2$$ , which value of x is a solution to the equation f(x) = g(x)?

Accepted Answer

-1

Answer

3

Answer

0

Answer

-2

Question 41

Given a(x) = $$|x + 6|$$ and b(x) = $$-x^2 + 8$$ , which value of x is a solution to the equation a(x) = b(x)?

Accepted Answer

1

Answer

7

Answer

2

Answer

4

Question 42

What is the minimum value for the equation $$y = 2x^2 - 4x + 5$$ ?

Accepted Answer

(1,3)

Answer

(0,5)

Answer

(4,1)

Answer

(1,4)

Question 43

What is the maximum value for the quadratic equation y = $$-3x^2 + 12x - 13$$ ?

Accepted Answer

(2, -1)

Answer

(-2, -1)

Answer

(0, -13)

Answer

(-2, 1)

Question 44

Which statements are true for the function represented by the graph?

Select three answer choices.

Accepted Answer

The function is increasing on the interval 0.76 < t < 1.1.

Accepted Answer

The function is increasing on the interval 0 < t < 0.38.

Accepted Answer

The function is decreasing on the interval 0.39 < t < 0.76.

Answer

The function increases for all real numbers.

Answer

The function decreases for all real numbers.

Question 45

A roofer tosses a hammer off the roof of a house that is 12 feet above the surface of the ground. The graph shows the height above the surface of the ground, y, in feet, the hammer is x seconds after being thrown from the roof.

Which equation best represents the graph?

Accepted Answer

$$y = -3x^2 + 12$$

Answer

$$y = 3x^2 + 12$$

Answer

$$y = 3x^2 - 12$$

Answer

$$y = -3x^2 - 12$$

2025 Part 1

49 questions

Consider the equation. 4 - 2(x + 3) = 6 - 3(x - 1). What is the value of x in the equation?

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