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Week 2 Homework for MTH 125

Name___________________________________ Date: ___July 20, 2021______________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Graph the equation by determining the missing values needed to plot the ordered pairs.

1) y + x = 3; ( 1, ), ( 3, ), ( 2, )

1) _______

Find the x- and y-intercepts. Then graph the equation.

2) 10y - 2x = -4

2) _______

A) ( -2, 0);

B) ; (0, -2)

C) ( 2, 0);

D) ; (0, 2)

Find the midpoint of the segment with the given endpoints.

3) ( 8, 4) and ( 7, 9) 3) _______

A) B) C) D)

Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates

of the other endpoint Q.

4) P( 5, 5) and M 4) _______

A) Q( 4, 4) B) Q C) Q D) Q

Solve the problem.

5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?

5) _______

A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3

Find the slope.

6) m = 6) _______

A) -5 B) 5 C) 12 D) 8

Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line

through the points rises from left to right, falls from left to right, is horizontal, or is vertical.

7) ( -3, -5) and ( 4, -4) 7) _______

A) - ; falls B) - 7; falls C) 7; rises D) ; rises

Find the slope of the line.

8) _______

A) B) C) - D) -

Find the slope of the line and sketch the graph.

9) 2x + 3y = 10

9) _______

A) Slope:

B) Slope: -

C) Slope: -

D) Slope:

Decide whether the pair of lines is parallel, perpendicular, or neither.

10) 3x - 4y = 12 and 8x + 6y = -9 10) ______

A) Parallel B) Perpendicular C) Neither

Choose the graph that matches the equation.

11) y = 2x + 4 11) ______

Find the equation in slope-intercept form of the line satisfying the conditions.

12) m = 2, passes through ( 6, -3) 12) ______

A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14

Write the equation in slope-intercept form.

13) 17x + 5y = 7 13) ______

A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -

Find the slope and the y-intercept of the line.

14) 7x + 5y = 48 14) ______

A) Slope - ; y-intercept B) Slope ; y-intercept

C) Slope ; y-intercept D) Slope - ; y-intercept

Find an equation of the line that satisfies the conditions. Write the equation in standard form.

15) Through ( 5, 4); m = - 15) ______

A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56

The boundary of the graph of the linear inequality will be a _____ line, and the shading will be _____ the line. Fill in

the first blank with either solid or dashed. Fill in the second blank with above or below.

16) y < x - 16) ______

A) solid; above B) solid; below C) dashed; above D) dashed; below

Graph the linear inequality in two variables.

17) 4x + y ≤ -6

17) ______

Graph the compound inequality.

18) x + y ≥ 2 and y ≤ 2

18) ______

19) 3x + 2y > 4 or x > 2

19) ______

Choose the inequality that best matches the given calculator graph.

20)

20) ______

A) y ≤ 2x + 2 B) y ≤ -2x - 2 C) y ≥ -2x - 2 D) y ≥ 2x + 2

Decide whether the relation is a function.

21) {( -2, -9), ( 2, 8), ( 6, -2), ( 9, -2), ( 11, -8)} 21) ______

A) Function B) Not a function

22) 22) ______

A) Function B) Not a function

Decide whether the relation is a function, and give the domain and range.

23)

23) ______

A) Not a function; domain: {-3, 0, 6}; range: { -4, -9}

B) Function; domain: { -4, -9}; range: {-3, 0, 6}

C) Function; domain: {-3, 0, 6}; range: { -4, -9}

D) Not a function; domain: { -4, -9}; range: {-3, 0, 6}

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

24) The table shows the percentage of seniors at a certain 4-year college who believed that after graduating they would be

able to find a job related to their field of study.

(a) Does the table define a function?

(b) What are the domain and range?

Provide an appropriate response.

25) Give a definition of Range. 25) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

26) Find f( -3) when f(x) = x2 + 3x - 4. 26) ______

A) 22 B) -4 C) 14 D) 4

Evaluate the function.

27) Find f( 0) if f = {(-2, 3), (3, 0), (0, 5), (5, -2)} 27) ______

A) ( 5, 3) B) 5 C) None of these D) 3

Graph the linear function. Give the domain and range.

28) f(x) = 2x + 3

28) ______

A) Domain: (-∞, ∞) Range: (-∞, ∞)

B) Domain: (-∞, ∞) Range: (-∞, ∞)

Solve the problem.

29) Crafty Bill's Cool Car Sales opened as a used car sales lot in 1991. The graph shows the number of cars sold as a

function of time. Is this the graph of a function? What is the domain?

29) ______

A) Function; Domain: [2005, 2011] B) Function; Domain: [2007, 2011]

C) Not a function; Domain: [2007, 2011] D) Not a function; Domain: [2005, 2011]

Provide an appropriate response.

30) If the ordered pair ( 6, 8) belongs to function g, then g( ) = . 30) ______

A) 6; 8 B) x; 8 C) 8; 6 D) y; 6

Complete the table of ordered pairs for the equation.

31) 4x + 6y = 24

31) ______

A) 4; 0; ; B) 0; ; 1 C) 4; ; 0 D) 0; ;

Find the x- and y-intercepts, and graph the equation.

32) 2x - 4y = -8

32) ______

A) (0, 2), ( 4, 0)

B) (0, -4), ( 2, 0)

C) (0, -2), ( -4, 0)

D) (0, 2), ( -4, 0)

33) x = 4

33) ______

A) None; (0, 4)

B) ( 4, 0); none

C) ( 4, 0); none

D) None; (0, 4)

Find an equation of the line, and write it in (a) slope-intercept form if possible and (b) standard form.

34) Through ( -4, -6) and perpendicular to y = x + 13 34) ______

A) (a) y = -2x – 14 (b) 2x + y = -14

B) (a) y = x – 4 (b) x - 2y = 8

C) (a) y = 2x – 14 (b) 2x - y = -14

D) (a) y =- x – 8 (b) x + 2y = -16

Graph the inequality or compound inequality.

35) 2x + 3y > -5

35) ______

Decide whether the ordered pair is a solution of the given system.

36) x + y = 6 x - y = 4 ; ( 5, 1) 36) ______

A) Yes B) No

Solve the system by graphing.

37) 4x + y = -17 x + 6y = -10

37) ______

A) {( 4, -1)} B) {( -4, -1)} C) {( -5, 3)} D) {( -4, -5)}

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

38) y = - x 5x - 6y = -4 38) ______

A) B) ∅; inconsistent system

C) D)

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

39) -x + 6y = 9 8x - 6y = 54 39) ______

A) {( 10, 2)} B) {( -3, 9)} C) {( 9, 3)} D) ∅; inconsistent system

Tell how many solutions the system has. Do not actually solve.

40) 2x + 5y = -1 4x + 10y = -2 40) ______

A) No solution B) Infinitely many C) One solution

Solve the system of equations.

41) x + y + z = 7

x - y + 2z = 7

5x + y + z = 11 41) ______

A) {(1, 4, 2)} B) {(4, 1, 2)} C) {(4, 2, 1)} D) {(1, 2, 4)}

42) x - y + z = 8

x + y + z = 6

x + y - z = -12 42) ______

A) {(2, -1, 9)} B) {(2, -1, -9)} C) {(-2, -1, 9)} D) {(-2, -1, -9)}

43) 5x + 2y + z = -11

2x - 3y - z = 17

7x + y + 2z = -4 43) ______

A) {(3, 0, -4)} B) {(-3, 0, 4)} C) {(0, 6, -1)} D) {(0, -6, 1)}

44) 7x + 7y + z = 1

x + 8y + 8z = 8

9x + y + 9z = 9 44) ______

A) {(-1, 1, 1)} B) {(1, -1, 1)} C) {(0, 0, 1)} D) {(0, 1, 0)}

45)

45) ______

A) {( 2, -1, 4)} B) {( -1, 4, 2)} C) {( -1, 2, 4)} D) {( 4, 2, -1)}

46)

46) ______

A) {( 1, 3, -3)} B) {( -3, 3, 1)} C) {( -3, 1, 3)} D) {( 3, -3, 1)}

47) x + y - z = -4

- x - y - z = 2

x + y + z = 13 47) ______

A) B)

C) D)

48) 48) ______

A) {( 2.0, 3.7, 4.1)} B) {( 4, 3.7, -12.3)}

C) {( 2.0, 3.7, -4.1)} D) {( 2.0, -3.7, -4.1)}

49)

49) ______

A) {( 0, -5, 0)} B) {( 0, -5, 5)} C) {( -5, 0, -5)} D) {( 0, 0, -5)}

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.

50)

50) ______

A) ∅; inconsistent system

B) {( -3, 2, 1)}

C) {( 2, 1, -3)}

D) {(x, y, z) }; dependent equations

Solve the problem.

51) During the 1998-1999 Little League season, the Tigers played 47 games. They won 25 more games than they lost.

How many games did they win that season? 51) ______

A) 36 games B) 33 games C) 11 games D) 38 games

52) During the 1998-1999 Little League season, the Tigers played 50 games. They won 6 more games than they lost.

How many games did they lose that season? 52) ______

A) 28 games B) 22 games C) 20 games D) 25 games

53) The perimeter of a rectangle is 28 cm. The length is 8 cm longer than the width. What are the length and width of

the rectangle? 53) ______

A) Length: 15 cm; width: 7 cm B) Length: 8 cm; width: 3 cm

C) Length: 11 cm; width: 3 cm D) Length: 14 cm; width: 6 cm

54) The perimeter of a rectangle is 60 m. If the width were doubled and the length were increased by 15 m, the

perimeter would be 108 m. What are the length and width of the rectangle? 54) ______

A) Length: 9 m; width: 21 m B) Length: 15 m; width: 10 m

C) Length: 15 m; width: 15 m D) Length: 21 m; width: 9 m

55) Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 23 coins with a total face value of $ 4.55 ,

how many of the coins are nickels? 55) ______

A) 8 nickels B) 6 nickels C) 17 nickels D) 22 nickels