Participation Exercise for Week 6

Name___________________________________

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

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

1) x + y = 6

x – y = 4 ; ( 5, 1) 1) _______

A) No B) Yes

Solve the system by graphing.

2) 4x + y = -17

x + 6y = -10

2) _______

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

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

3) y = – x

5x – 6y = -4 3) _______

A) B)

C) D) ∅; inconsistent system

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

4) -x + 6y = 9

8x – 6y = 54 4) _______

A) {( 10, 2)} B) {( 9, 3)}

C) {( -3, 9)} D) ∅; inconsistent system

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

5) 2x + 5y = -1

4x + 10y = -2 5) _______

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

Solve the problem.

6) The table shown was generated by a graphing calculator. The functions defined by and are linear. Based on the

table, find the coordinates of the point of intersection of the graphs.

6) _______

A) (7, 7) B) (7, 2) C) (2, 7) D) (3, 9)

7) Betsy doesn’t trust banks, so her savings are hidden under her mattress. Alla has her savings in an investment at

simple interest. During which years would Betsy’s savings be more than Alla’s?

7) _______

A) 1986 – 1988 B) 1989 C) 1989 – 1996 D) 1986 – 1989

Solve by any method. Assume a and b represent nonzero constants.

8) 4ax + 3y = 1

y = 2ax 8) _______

A) B) C) D)

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

Provide an appropriate response.

9) Give the definition or an example of the word or phrase.

Dependent system 9) _____________

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

Solve the system of equations.

10) x + y + z = 7

x – y + 2z = 7

5x + y + z = 11 10) ______

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

Solve the problem.

11) 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? 11) ______

A) Length: 15 cm; width: 7 cm B) Length: 11 cm; width: 3 cm

C) Length: 14 cm; width: 6 cm D) Length: 8 cm; width: 3 cm

12) 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? 12) ______

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

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

13) 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? 13) ______

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

14) A company manufactures three products. The graph shows the production from 1986 to 1996. Which of the companies

experience production growth over the period shown in the graph?

14) ______

A) Company B and Company C B) Company A

C) Company A and Company C D) Company A and Company B

Use a graph to solve the system.

15) x – y = 4

x + y = 12

15) ______

A) {( 16, 8)} B) {( 4, 8)} C) {( 8, 4)} D) {( 8, 16)}

MTH 125 Homework Ex for Week 6

Name___________________________________

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

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

1) x + y = 7

x – y = 3 ; ( -5, 2) 1) _______

A) Yes B) No

Solve the system by graphing.

2) -2x + 3y = -1

3x + 2y = 21

2) _______

A) {( 3, 5)} B) {( -2, 27)}

C) {( 5, 3)} D) ∅; inconsistent system

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

3) x = 22 – 4y

5x + 3y = 8 3) _______

A) {( 2, 7)} B) ∅; inconsistent system

C) {( -2, 6)} D) {( -3, 7)}

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

4) x + 4y = 13

2x + 3y = 6 4) _______

A) {(3, 5)} B) {(-3, 4)}

C) {(-4, 5)} D) ∅; inconsistent system

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

5) 4x – 16y = 12

y = x – 5) _______

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

Solve the problem.

6) Emilia doesn’t trust banks, so her savings are hidden under her mattress. Deepak has his savings in an investment

at simple interest. During which year did they have the same amount?

6) _______

A) 1996 B) 1988 C) 1989 D) 1986

Solve the system of equations.

7)

– = 7) _______

A) B) {( -5, 8}) C) {( 5, 8}) D) ∅

Solve by any method. Assume a and b represent nonzero constants.

8) 7ax – 2y = 2

y = 5ax 8) _______

A) B) C) D)

Solve the system of equations.

9) x – y + z = 8

x + y + z = 6

x + y – z = -12 9) _______

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

Solve the problem.

10) 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? 10) ______

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

C) Length: 9 m; width: 21 m D) Length: 15 m; width: 10 m

11) Andy has 27 coins made up of quarters and half dollars, and their total value is $ 9.25. How many quarters does he

have? 11) ______

A) 12 quarters B) 17 quarters C) 10 quarters D) 22 quarters

12) The speed of a stream is 6 mph. If a boat travels downstream in the same time that it takes to travel

upstream, what is the speed of the boat in still water? 12) ______

A) 18 mph B) 20 mph C) 12 mph D) 21 mph

13) A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels 5 mph slower

than the power boat. Find the speed of each boat. 13) ______

A) Power boat: 15 mph; cabin cruiser: 10 mph

B) Power boat: 10 mph; cabin cruiser: 5 mph

C) Power boat: 20 mph; cabin cruiser: 15 mph

D) Cannot be determined without more information

14) A company manufactures three products. The graph shows the production from 1986 to 1996. Which of the companies

experience production decline over the period shown in the graph?

14) ______

A) Company A B) Company A and Company C

C) Company C D) Company B and Company C

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

15) y = – x

-5x + 4y = 7 15) ______

A) B)

C) D) ∅; inconsistent system

MTH 125 MIDTERM EXAM WEEK 6

Name___________________________________

Solve the inequality. Give the solution set in both interval and graph forms.

1) -10 y + 6 > -11 y – 2

1) _______

A) ( 4, ∞)

B) (-∞, 4)

C) (-∞, -8)

D) ( -8, ∞)

2) < –

2) _______

A)

B)

–

C)

–

D)

Solve the problem.

3) A car rental company has two rental rates. Rate 1 is per day plus per mile. Rate 2 is per day plus

per mile. If you plan to rent for one day, how many miles would you need to drive to pay less by taking Rate 2?

3) _______

A) more than 1800 miles B) more than 1000 miles

C) more than 900 miles D) more than 450 miles

4) Behemoth Back Packs, Inc. finds that the cost to make x back packs is while the revenue produced from

them is (C and R are in dollars). What is the smallest whole number of back packs, x, that must be sold for the

company to show a profit? 4) _______

A) 533,115 B) 36 C) 55 D) 823,905

For the compound inequality, give the solution set in both interval and graph forms.

5) -11 < 4x + 9 and 2x – 5 < -7

5) _______

A) ( -5, -1]

B) [ -5, -1]

C) [ -5, -1)

D) ( -5, -1)

Name the quadrant, if any, in which the point is located.

6) ( -11, -5) 6) _______

A) IV B) None C) III D) II

Complete the table for the equation.

7) y = -9x – 65

7) _______

A) 7; -79; 1 B) 7; -65; 1 C) 7; 0; 1 D) -8; -65; 1

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

8) x – 2y = -8; (0, ), ( , 0), ( 3, ), ( , 3)

8) _______

A)

B)

C)

D)

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

9) -6x – 12y = 24

9) _______

A) ( -2, 0); (0, -4)

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

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

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

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.

10) P( 4, 8) and M 10) ______

A) Q B) Q C) Q( -3, -3) D) Q

Provide an appropriate response.

11) Determine the quadrants in which the given point (x, y) may lie when xy > 0. 11) ______

A) II or III B) I or II C) II or IV D) I or III

Find the slope of the line.

12)

12) ______

A) -5 B) 5 C) 1 D) -1

Graph the line described.

13) Through (0, 5); m = – 4

13) ______

A)

B)

C)

D)

Solve the problem.

14) A motorcycle daredevil is planning a stunt to perform at a county fair. A ramp must be built to give him a 20% grade,

or slope. If the vertical height at the end of the ramp must be 15 ft to assure that the stunt is a success, what must be the

length of the horizontal run?

14) ______

A) 15 ft B) 2.7 ft C) 270 ft D) 75 ft

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

15) 4x – 5y = 5 15) ______

A) Slope 1; y-intercept (0, 1) B) Slope – ; y-intercept (0, 1)

C) Slope -1; y-intercept (0, -1) D) Slope ; y-intercept (0, -1)

Decide whether the relation is a function.

16)

16) ______

A) Function B) Not a function

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

Provide an appropriate response.

17) The equation y = x2 is satisfied by the points (2, 4) and (-2, 4). A horizontal line may be drawn between these two

points. Is y = x2 a function? Explain. 17) _____________

Determine whether or not the function is one-to-one.

18) f(x) = 3×2 – 5 18) ______

A) No B) Yes

Find the indicated value.

19) Let f(x) = . ( 8) 19) ______

A) 2 B) C) D) 3

Find the slope of the line.

20)

20) ______

A) 0 B) 2 C) -2 D) Undefined

Solve the problem.

21) A motorcycle daredevil is planning a stunt to perform at a county fair. A ramp must be built to give him a 20% grade,

or slope. If the vertical height at the end of the ramp must be 13 ft to assure that the stunt is a success, what must be the

length of the horizontal run?

21) ______

A) 234 ft B) 65 ft C) 13 ft D) 2.34 ft

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

22) 3x – 4y = 4 22) ______

A) Slope ; y-intercept (0, -1) B) Slope ; y-intercept (0, 1)

C) Slope – ; y-intercept (0, 1) D) Slope – ; y-intercept (0, -1)

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

23) 8y – 8 = -x

2x – 5y = -5 23) ______

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

24) x + y = 4

x – 2y = 21 24) ______

A) {(6, -8)} B) {(-6, 8)} C) {(6, 8)} D) {(-6, -8)}

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

25) x – 4y = -4

-4x – 3y = -3 25) ______

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

C) {(0, 1)} D) ∅; inconsistent system

26) -7x + 9y = -42

-5x + 2y = -30 26) ______

A) {( 6, 1)} B) {( 6, 0)}

C) {( 5, 1)} D) ∅; inconsistent system

Apply the product rule for exponents, if possible.

27) (-3 y)(-4 ) 27) ______

A) -12 B) 12 C) 12 D) 12

Evaluate the expression.

28) 28) ______

A) 1 B) 0 C) -1 D) -7

29) 29) ______

A) 64 B) 512 C) 24 D) 4096

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all

variables represent nonzero numbers.

30) 30) ______

A) – B) C) D)

31) 31) ______

A) 1 B) – C) D)

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero

real numbers.

32) 32) ______

A) B) C) D)

Determine whether or not the function is one-to-one.

33) f(x) = 5×2 + 5 33) ______

A) No B) Yes

If the following defines a one-to-one function, find its inverse. If not, write “Not one-to-one.”

34) f(x) = 8 – 4 34) ______

A) Not one-to-one B) (x) =

C) (x) = ± D) (x) =

Find the indicated value.

35) Let f(x) = . ( 243) 35) ______

A) B) 5 C) D) 3

Graph the line described.

36) Through (0, 3); m = –

36) ______

A)

B)

C)

D)