Complex numbers Questions and Answers

1 Which of the following is the value of sin 60 3 2 1 2 2 1 1 2 2 Written in exact form cos 135 3 1 1 2 2 2 2 2 3 4 3 3 4 2

oint Solve the following differential equation wer y x C y 4y sin C

2 5x 20 x 16 x 4 www Select the correct choice below and if necessary fill in th answer box to complete your choice OA The solution s is are Type an integer or a simplified fraction Use a comma to separate answers as needed OB The solution set is x x is a real number and x Type an integer or a simplified fraction Use a comma to separate answers as needed OC There is no solution

8 4 6y 2 y 2 y 2 4 Select the correct choice below and if necessary fill in th answer box to complete your choice OA The solution set is yly is a real number and y Type an integer or a simplified fraction Use a comma to separate answers as needed OB The solution s is are Type an integer or a simplified fraction Use a comma to separate answers as needed OC There is no solution

10 10 8 6 4 2 Ay 6 O C 1 6 B 10 2 x 3 x 5 y U Write the equation in factored form for the quadratic function shown OA 2 x 3 x 5 y OB 1 2 x 3 x 5 y OD x 3 x 5 y 8 10 N

Find an equation for the quadratic function whose graph contains the given vertex and point Vertex 3 1 Point 2 3 y 0

Exercise 7 An angle drawn in standard position whose radian measure is 2 radians would terminate in which of the following quadrants 1 I 2 II 3 III 4 IV bands

Find the value of the determinant 2 7 8 3 The value of the determinant is

Wite the augmented matrix of the given system of equations x y z 10 Ax 4y 5 2 x y 2z 0000

Complete the sentence below If a system of equations has one solution the system is If a system of equations has one solution the system is and the equations are and the equations are

Select all the relations which are not functions x y is the color of a traffic light and y is the lawful response of an approaching motorist to that light x y is a randomly selected person and y is that person s birthday x y is the suggested retail price of particular car and y is price paid by a random car buyer for that car x y is the date and y is the value of a stock at the close of the stock market that day D x y a is an amount of alcohol consumed and y is the blood alchohol concentration for a person consuming that amount of alcohol

Graph t x 2x 3 on the Cartesian plane to the right t x is increasing on the interval s t x is decreasing on the interval s t x has a maximum of t x has a minimum of The domain of t x is The range of t e is at x at x 10 9 8 7 6 5 4 Clear All Draw 327 10 9 8 7 6 5 4 3 2 1 4 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 AVO

Plot the inverse of the function shown on the grid below 8 7 6 5 4 3 2 8 7 6 54 3 2 1 Y 1 2 3 6 a 2 4 2 3 4 Warning It is very hard to get a perfect score on this problem If you have over 90 of the points you have done it very well 5 6 7 4 5 6 7 8

Use the straight line method to complete the first row of the depreciation table for an SUV that costs 38 000 has a residual value of 8 000 and an estimated life of six years Year 1 Annual Accumulated depreciation depreciation Complete the table below Annual depreciation S Year End of year book value Accumulated End of year depreciation book value S

Consider the following function A X 18 3x Find the derivative of the function 3 A x XM 3 x Find the values of x such that A x 0 Enter your answers as a comma separated list If an answer does not exist enter DNE if x Xw Find the values of x in the domain of A such that A x does not exist Enter your answers as a comma separated list If an answer does not exist en Find the critical numbers of the function Enter your answers as a comma separated list If an answer does not exist enter DNE

Complete the following probability distribution table and then calculate the stated probabili Outcome Probability a P a c e P a c e 0 77 X a 0 3 b 0 03 0 4 C c P E where E is as in part b P E 0 03 X b P EUF where E a c e and F b c e P EU F 0 8 x d 0 07 d P En F where E and F are as in part b P EF 0 47 e

O TB TF Qu 04 210 9 Sales discounts affect net

Find the global maximum for linear optimization f x y x y subject to 0 x 5 0 y 2 and 2x y 8

S Give the excluded values for 8m O 1 0 16 O 4 0 16 O 4 0 4 O 4 1 0 16 m 4 m 1 m 16 Do not solv

Question 46 of 60 Consider the equation below What is the value of z O 12 5 O 3 15 O 225 O 22 O 15 3

Which expression produces an irrational number O 5 x 5 O 16 x 3 O 5 2 O 15 3 O 12 x 3

estion 34 of 60 on is the coach of a baseball team There are three innings left in the game and they are losing When losing by the same score in the past Ron has replaced the pitcher a total of 14 times and left the pitcher in a total of 10 times is table shows the results after nine innings when Ron replaces the current pitcher and when he leaves him in sed on the information above if the goal is to win the game in nine innings should Ron replace the pitcher O Ron should wait until the last inning and then replace the pitcher O Ron should not replace the pitcher Ron should replace the pitcher Ron replacing or not replacing the pitcher has no advantage There is not enough information to determine if Ron should replace the pitcher or not Replace Pitcher Leave Pitcher In Won Lost Tie 8 4 2 4 5 1

Question 33 of 60 CompPlus and TechStar are tablet computer manufacturers CompPlus claims their tablets have at minimum a seven hour battery life TechStar claims their tablet computers have at minimum a ten hour battery life A software company recently purchased 15 new fully charged tablet computers from each company Jonathan a software developer for the company decided to test the claims from the two manufacturers He had his employees run the same software on all of the fully ch After observing the battery life Stephen reported that the battery life of a CompPlus tablet computer is 7 25 hours and the battery life of a TechStar tablet computer is 10 5 hours What can be concluded from Stephen s report O CompPlus s claim and Tech Star s claim are both false but Tech Star s tablet computers are more effective in regards to battery life since the battery life is greater than that of CompPlus s tablet computers O Only Tech Star s claim is true therefore Tech Star is the more effective tablet computer in regards to battery life O CompPlus s claim and TechStar s claim are both true but TechStar s tablet computers are more effective in regards to battery life since the battery life is greater than that of CompPlus s tablet computers O CompPlus s claim and TechStar s claim are both true but CompPlus s tablet computers are more effective in regards to battery life since the battery life is greater than that of Tech Star s tablet computers O Only CompPlus s claim is true therefore CompPlus is the more effective tablet computer in regards to battery life

the given zero s and synthetic division to help y 3x 3 7x 2 50x 104 x 4 2

valuate J 20 here D is the tetrahedron with vertices 0 0 0 1 0 0 0 1 0 and 0 0 x y dx dy dz

mutual fund inflation bond prospectus OTC market securities perferred stock risk tolerance level of risk initial public offering IPO proxy Treasury bill investment portfolio Amount of uncertainty a person is willing to handle Financial assets issued by corporations governments and other organizations I Investment created by pooling the money of many people and investing it in a collection of securities Collection of the investments a person has made Overall rise in prices Company s first sale of stock to the public Certificate of debt issued by a corporation or government Short term debts with maturities ranging from a few days to

4 points 00 A stock trade is only the purchase of a stock and does not include the sale of stock after purchase O True O False

Use Descartes rules rule of signs to determine how many positive real zeros and negative real zeros there are for the function DO NOT ENTER IN ANSWERS IN ANY OTHER FORM THAT YOU WERE NOT INSTRUCTED BY THE PROFESSOR TO DO DOING SO CAN CAUSE YOUR ANSWER TO BE MARKED AS INCORRECT AND CAN RAISE SUSPICION OF YOUR ANSWER f x 2x5 7x 6x 8 Positive Negative

graph of a sin wave High Low 2 High value B Given the function y 3sin x 5pi 4 1 Origin horizontal vertical e g pi 2 3 Low value 4 Value of interval A 5 Value of interval B 6 Value of interval C 7 Value of interval D D 8 Value of interval E E

14 TB MC Qu 05 98 Algo Misty Mountain Outf Miety Mountain Outfittore le a morchardicor of specialized

ACT PREP MATH PART ACT Math Test Edition Question 8 of 60 Janie wants to sell homemade cookies at a chanty fundraiser The recipe she uses yields 12 cookies in a batch She knows that the actual number of cookies in a batch could differ from the desired number of cookies by a maximum of 2 cookies Sesed the correct inequality that model the situation above 0512 2 0 25 13 01 12 22 1 2 212 12 2 Net

would like to have a one course meal with a single entree chosen from following menu Entrees Devilled Fish with Scalding Sauce Served with Charred Tomatoes or Infernal Potatoes Alphabet Soup with a Dash of Digits Barbecued Lamb Chops with French Fries Apple Creme or Mint Jelly Grilled Wild Chicken with Tame Rice or Docile Corn The number of possible meals is reible meals that exclude potatoes and seafood is Check Clear Check Clear Help

ACT PREP MATH PART ACT Math Test 1 Edition 3 Question 9 of 60 What are the soluns for 0 3 and 2 and 0 and 23 11 04 and 4 Ned Reset 3z 5 3z 5 x 2 x 5

2 Determine the sequence generated by each of the following exponential generating functions a f x 3e x b x 6e x 36 x c x e x d x e x 3x 5x 7x e f x 1 1 x f f x 3 1 2x e

The functions fand g are defined as follows f x g x X 2 x 81 x 1 x x 2 For each function find the domain Write each answer as an interval or union of intervals Domain off Domain of g 0

e Physics Club executive committee at ESU Enormous State U consists of four members of whom one is designated as chairperson and two as secretaries There are five people available to serve on the comm hich of the following are valid decision algorithms to count the number of possible committees that can be formed Step 1 Choose a person to exclude from the committee 1 choice O Valid Step 2 Choose a chairperson 1 choice Invalid Step 3 Choose an ordinary member 3 choices Step 1 Choose a person to exclude from the committee 5 choices Valid Step 2 Choose a chairperson 5 choices Invalid Step 3 Choose an ordinary member 4 choices Step 1 Choose an ordinary member 5 choices Step 2 Choose a chairperson 4 choices Step 3 Choose a person to exclude from the committee 3 choices Valid Invalid Step 1 Choose a person to exclude from the committee 5 choices Valid Step 2 Choose a chairperson 4 choices O Invalid Step 3 Choose an ordinary member 3 choices

The function fis defined by f x 2x 3 Find f x 4 f x 4 0

Find the average rate of change of g x 2x 5 from x 2 to x 4 Simplify your answer as much as possible 0 2 5

Solve the following system of equations 3x 4y 21 9x 2y 21 0 0 3 X

A line passes through the point 8 5 and has a slope of Write an equation in slope intercept form for this line 0 0 0 8 5

4 Deandre wants to save 600 to buy a TV He saves 19 each week The amount A in dollars that he still needs after w weeks is given by the follow function 4 w 600 19 Answer the following questions a How much money does Deandre still need after 5 weeks 0 b If Deandre still needs 258 how many weeks has he been saving weeks

that between 2007 and 2010 messaging became increasingly popular The number of me ds reported by a microblogging company can be modeled by T x 15 807x 118 226 wh of years after 2000 is the slope of the graph of this function ret the slope as a rate of change GELEN lope of the graph of this function is your answer ret the slope as a rate of change Choose the correct choice below From 2007 to 2010 the number of messages decreased by 15 807 thousand per year From 2007 to 2010 the number of messages increased by 15 807 thousand per year From 2007 to 2010 the number of messages increased by 118 226 thousand per year From 2007 to 2010 the number of messages decreased by 118 226 thousand per year

X 1 4 5 8 10 3 x 12 X 12 3 x 12 y 11 10 8 7 6

Find the zeros and state their multiplicity Enter your answer in as a whole number or as a fraction Use sqrt to represent a radical when necessary For Example 2 sqrt 2 f x x 2 x 7 with a multiplicity of with a multiplicity of with a multiplicity of

4 Betty attempted to prove that the diagonals of a parallelogram bisect each other using the image shown Statements 1 Diagonals PR and QS intersect at point Given T Reasons 2 PQ and RS are parallel PS and QR Given are parallel 3 PQRS Opposite sides of a parallelogram are congruent

De 18 Select one a 1 Exponential Functions and Equations Question 8 Which equation is equivalent to the following De log2 1 O 4 O 21 X O 1 X 3 2 x 6 O2 x

Exponential Functions and Equations Question 1 1 Which equation is equivalent to log v 2 Select one Oy 1 x Ox 1 2 y X Oy x2 2 Ox y 2 1

Use synthetic division to divide z 3x 9z 15 by 2 Give your answer in the form quotient remainder divisor if necessary 3 9 15

7 A hiker whose eyes are 5 5 feet above ground stands 25 feet from the base of a redwood tree She looks up at an angle of 71 to see the top of the tree To the nearest tenth of a foot what is the height of the tree 8 Error Analysis To find the distance XY across a large rock formation a student stands facing one endpoint of the formation backs away from it at a right angle for 20 meters and then turns 55 to look at the other endpoint of the formation The student s calculations are shown Critique the student s work 671 X 20 m Z 25 ft 55 5 5 ft tan 55 XY tan 55 20 XY 20 tan 55 14 0 m

20 What is the end behavior for the polynomial function f x x5 A O B O CO D O f x 0 X f x 00 x f x 0 X 18 f x 0 x118 f x 0 x 0 f x 00 x 00 f x x 0 f x 0 x