Mathematics 10

MTH 125 Final Exam for Week 10

Name___________________________________ Date: _________________________

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

Solve the system by graphing.

1) x + y = -8

8x - y = -64

1) _______

A) {(0, 8)} B) {( -8, 0)} C) {( -8, 8)} D) {(0, -8)}

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

2) x - y = -18

x + y = -9 2) _______

A) {(0, 12)} B) {(12, 0)} C) {(0, -12)} D) {(-12, 0)}

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

3) -7x + 9y = -42

-5x + 2y = -30 3) _______

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

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

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

4) 3x = y + 3

6x - 2y = 3 4) _______

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

Solve the problem.

5) Which of the ordered pairs listed is the only possible solution for the system whose graphs are shown in the viewing

window of a graphing calculator?

5) _______

A) (-16, -7) B) (-20, 12) or (16, 7)

C) (16, -7) D) None of the above

6) After retirement, Kelly's company offers her two options for receiving her retirement pension. According the the first

plan, she will receive monthly payments from a variable annuity that initially pays per month then decreases each

month at a rate of per month per year. Optionally, she may choose a plan that pays her a fixed amount of per

month for the rest of her life. The monthly payments for the two plans are illustrated in the graph below. After how many

years does the variable plan pay less per month than the fixed plan?

6) _______

A) Up to 8 years B) 9 years

C) 8 years D) The variable plan always pays less.

Provide an appropriate response.

7) Solving for which variable in which equation involves the least amount of work?

7x = 42

x - 8y = 78 7) _______

A) x in equation 2 B) x in equation 1 C) y in equation 2 D) y in equation 1

Solve the system of equations.

8) x + y - z = -4

- x - y - z = 2

x + y + z = 13 8) _______

A) B)

C) D)

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

9) 2x - 2y + 8z = 16

-5x + 5y - 20z = -40

x - y + 4z = 8 9) _______

A) ∅; inconsistent system

B) {(x, y, z)|x - y + 4z = 8}; dependent equations

C) {(7, 3, 1)}

D) {(0, 0, 2)}

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

Provide an appropriate response.

10) In solving a system of three equations in three variables, it is impossible to eliminate two variables. Thus, the the final

step yields the following equation:

z = x - 4.

How many solutions does this system have? Explain geometrically. 10) _____________

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

Solve the problem.

11) Bob fenced in a rectangular garden in his yard. The length of the rectangle is 8 feet longer than the width and the

perimeter is 116 feet. What is the width of the rectangle? 11) ______

A) 27 feet B) 50 feet C) 24 feet D) 25 feet

12) Don runs a charity fruit sale, selling boxes of oranges for $11 and boxes of grapefruit for $10. If he sold a total of 762

boxes and took in $8125 in all, then how many boxes of oranges did he sell? 12) ______

A) 458 boxes B) 505 boxes C) 383 boxes D) 257 boxes

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

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

14) x + y = 6

x - 24 = -4y 14) ______

A) {( 24, 0)} B) {( 4, 5)}

C) {(x, y) }; dependent equations D) ∅; inconsistent system

Multiply, then simplify the product. Assume that all variables represent positive real numbers.

15) ( + 5)( + 3) 15) ______

A) x + + 15 B) x + 15

C) x + 3 + 5 + 15 D) x + 15

Rationalize the denominator. Assume that all variables represent positive real numbers.

16) - 16) ______

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

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is

not zero.

17) 17) ______

A) B) 3 C) 3 D)

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

Provide an appropriate response.

18) Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way

to simplify the expression is to multiply both the numerator and denominator by

18) _____________

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

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables

represent positive real numbers.

19) log5 19) ______

A) 2 x - 7 y - 9 B) 2 x + 7 y + 9

C) ( 2 x)( 7 y) - 9 D) 2 x + 7 y - 9

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable

expressions are positive and bases are positive numbers not equal to 1.

20) 5 q - r 20) ______

A) ÷ r B) ( - r) C) D)

Decide whether the statement is true or false.

21) = 21) ______

A) False B) True

Provide an appropriate response.

22) Use a property of logarithms to evaluate . 22) ______

A) 6 B) 16 C) D)

Solve the equation. Give the solution to three decimal places.

23) 7x - 1 = 42 23) ______

A) { 2.921} B) { 3.921} C) { 1.921} D) { 6.273}

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise

indicated.

24) = 24) ______

A) B) { -4} C) { 4} D)

Solve the equation. Give the exact solution or solutions.

25) log (x - 9) = 1 - log x 25) ______

A) { -10, 1} B) { 10} C) { -10} D) { -1, 10}

Solve the problem.

26) Jorge invested $ 7500 at 8% compounded semiannually. In how many years will Jorge's investment have tripled?

Round your answer to the nearest tenth of a year. 26) ______

A) 14 years B) 1.5 years C) 13.7 years D) 6.2 years

27) The number of acres in a landfill is given by the function where t is measured in years. How many

acres will the landfill have after 3 years? (Round to the nearest acre.) 27) ______

A) 7206 B) 20,143 C) 8748 D) 8426

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

Provide an appropriate response.

28) Why can the equation log4(x - 6) = log4( 6 - x) be said to have no solution? 28) _____________

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

Solve the equation. Give the exact solution.

29) = 29) ______

A) B) C) D)

Choose the graph that matches the given function.

30) f(x) = - 2 30) ______

A)

B)

C)

D)