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Which statement best describes a system of linear equations that has no solution?

Select one option

The system is consistent and independent.

The system is consistent and dependent.

The system is inconsistent and independent.

The system is inconsistent and dependent.

What is the solution to the system of equations below?

$y = x - 1$ $y = -x + 5$

Select one option

$(1, 3)$

$(3, 2)$

$(2, 3)$

$(4, 1)$

Simplify the expression: $(2x^2 + 5x - 3) + (3x^2 - 3x + 2)$

Select one option

$5x^2 + 2x - 1$

$5x^2 + 8x - 5$

$x^2 + 8x - 5$

$x^2 + 2x - 1$

Subtract: $(7x^2 - 2x + 6) - (3x^2 + 3x - 4)$

Select one option

$4x^2 - 5x + 2$

$4x^2 + x + 2$

$4x^2 - 5x + 10$

$4x^2 + x + 10$

What is the product of $(x + 3)(x + 4)$ ?

Select one option

$x^2 + 7x + 7$

$x^2 + 12x + 7$

$x^2 + 7x + 12$

$x^2 + x + 12$

What is the greatest common factor (GCF) of $12x^2y$ and $20xy^2$ ?

Select one option

$4xy$

$2xy$

$4x^2y^2$

$60x^2y^2$

Which of the following is a factor of $x^2 - 6x + 9$ ?

Select one option

$(x + 3)$

$(x - 3)$

$(x + 9)$

$(x - 9)$

For the system $y = 3x - 5$ and $2x + y = 10$ , which method would be most efficient to solve it?

Select one option

Graphing

Substitution

Elimination

Matrix method

What does the solution to a system of two linear equations represent graphically?

Select one option

The slope of one of the lines.

The y-intercept of one of the lines.

The point where the two lines intersect.

The area between the two lines.

10.

What is the converse of the statement: "If a polygon is a quadrilateral, then it has four sides"?

Select one option

If a polygon is not a quadrilateral, then it does not have four sides.

If a polygon has four sides, then it is a quadrilateral.

If a polygon does not have four sides, then it is not a quadrilateral.

If a polygon is a quadrilateral, then it does not have four sides.

11.

What is the inverse of the statement: "If it is raining, then the ground is wet"?

Select one option

If it is not raining, then the ground is not wet.

If the ground is wet, then it is raining.

If the ground is not wet, then it is not raining.

If it is raining, then the ground is not wet.

12.

What is the contrapositive of the statement: "If a triangle is equilateral, then it has three equal sides"?

Select one option

If a triangle has three equal sides, then it is equilateral.

If a triangle is not equilateral, then it does not have three equal sides.

If a triangle does not have three equal sides, then it is not equilateral.

If a triangle is equilateral, then it does not have three equal sides.

13.

What is the sum of the measures of the interior angles of any triangle?

Select one option

$90^{\circ}$

$180^{\circ}$

$270^{\circ}$

$360^{\circ}$

14.

A triangle has angle measures of $60^{\circ}$ , $60^{\circ}$ , and $60^{\circ}$ . What type of triangle is it?

Select one option

Scalene

Isosceles

Right

Equilateral

15.

Which equation represents the Pythagorean theorem for a right triangle with legs $a$ and $b$ , and hypotenuse $c$ ?

Select one option

$a + b = c$

$a^2 - b^2 = c^2$

$a^2 + b^2 = c^2$

$(a+b)^2 = c^2$

16.

In the diagram above, angles $\angle1$ and $\angle3$ are what type of angles?

Select one option

Corresponding angles

Alternate interior angles

Vertical angles

Consecutive interior angles

1 2 4 3

5 6 8 7

l m

17.

In the diagram above, if lines $l$ and $m$ are parallel, angles $\angle3$ and $\angle6$ are what type of angles?

Select one option

Corresponding angles

Alternate interior angles

Alternate exterior angles

Consecutive interior angles

18.

A linear equation is given by $2x + y = 7$ . Which of the following equations represents the same line?

Select one option

$y = 2x + 7$

$y = -2x - 7$

$y = -2x + 7$

$y = 7x - 2$

19.

Solve the following system of equations using the substitution method.

$x + y = 5$ $2x - y = -2$

20.

Solve the following system of equations using the elimination method.

$3x + 2y = 7$ $5x - 2y = 17$

21.

Multiply the polynomials: $(2x - 1)(3x^2 - 4x + 3)$

22.

Factor the quadratic expression completely: $x^2 - 3x - 10$

23.

Using the Pythagorean theorem, find the length of the hypotenuse $c$ in the right triangle shown above, given legs $a = 5$ and $b = 12$ . Show your work.

24.

In a triangle, two of the angles measure $40^{\circ}$ and $65^{\circ}$ . What is the measure of the third angle?

1 2 4 3

5 6 8 7

p q t

25.

In the diagram above, if lines $p$ and $q$ are parallel and cut by transversal $t$ , and $\angle1 = 120^{\circ}$ , what is the measure of $\angle4$ ? Show your work.

26.

In the triangle above, $\angle A = 2x$ , $\angle B = x + 10^{\circ}$ , and $\angle C = x + 50^{\circ}$ . Find the value of $x$ . Show your work.

Proof Problem 1

27.

Complete the two-column proof using the diagram above.

Given: $\angle1$ and $\angle2$ are vertical angles. Prove: $\angle1 \cong \angle2$

Proof:

Statement	Reason
1. $\angle1$ and $\angle2$ are vertical angles	1. (27)

28.

Complete the two-column proof using the diagram above.

Proof (continued):

Statement	Reason
2. $\angle1$ and $\angle3$ form a linear pair. $\angle2$ and $\angle3$ form a linear pair.	2. (28)

29.

Complete the two-column proof using the diagram above.

Proof (continued):

Statement	Reason
3. $m\angle1 + m\angle3 = 180^{\circ}$
$m\angle2 + m\angle3 = 180^{\circ}$	3. (29)

30.

Complete the two-column proof using the diagram above.

Proof (continued):

Statement	Reason
4. $m\angle1 + m\angle3 = m\angle2 + m\angle3$	4. (30)

31.

Complete the two-column proof using the diagram above.

Proof (continued):

Statement	Reason
5. $m\angle1 = m\angle2$	5. (31)

32.

Complete the two-column proof using the diagram above.

Proof (continued):

Statement	Reason
6. $\angle1 \cong \angle2$	6. (32)

Proof Problem 2

1 2 4 3

5 6 8 7

l m t

33.

Complete the two-column proof using the diagram above.

Given: Line $l \parallel$ Line $m$ , and $t$ is a transversal. Prove: $\angle1 \cong \angle5$

Proof:

Statement	Reason
1. $l \parallel m$	1. (33)

34.

Complete the two-column proof using the diagram above.

Proof (continued):

Statement	Reason
2. $\angle1 \cong \angle3$	2. (34)

35.

Complete the two-column proof using the diagram above.

Proof (continued):

Statement	Reason
3. $\angle3 \cong \angle5$	3. (35)

36.

Complete the two-column proof using the diagram above.

Proof (continued):

Statement	Reason
4. $\angle1 \cong \angle5$	4. (36)