Complex numbers Questions and Answers

2 3x 10 X

3 Simplify each expression None of the answers have an exponent 1 5 Ln The imaginary unit i 1 bi is a pure imaginary number a bi is a complex number with real part a and b the imaginary part a bi anda bi are complex conjugates a bi a bi will always result in a real number Check alse Choose Choose Choose Choose Choose

Short Answer Please answer all questions and show your work on all problems Write your answers on the answer sheet at the last page of this packet per 1 A remote control car claims that it can travel at a rate of 132 feet per minute What is this rate in miles hour

Winter coat 13 Which item from the table below has the lowest cost per days worn Y 3 1 a Work shoes b Winter coat c Polo shirt d Gown Clothing item Work shoes Polo shirt 636 Gown Original cost Days worn 60 250 155 25 178 620 26 L 2

22 If a 3 pound pizza is sliced in half and each half is sliced into thirds what is the weight in ounces of each of the slices 1 pound 16 ounces e 4 f 6 g 8 h 16

3 A model for a company s revenue from selling a software package is R 2 5p 500p where p is the price in dollars of the software a What price will maximize the revenue Give a reason for your answer b What is the maximum revenue Give a reason for your answer

21 The monthly membership fee for an online television and movie service is 9 80 The cost of viewing television shows online is included in the membership fee but there is an additional fee of 1 50 to rent each movie online For one month Jill s membership and movie rental fees were 12 80 How many movies did Jill rent online that month e 1 f 2 g 3 h 4

lowest price per ounce The table at left gives the number of ounces and prices of different bottles of body wash Which has the a Bottle A b Bottle B c Bottle C d Pack D Bottle A Bottle B Bottle C Pack D with 6 bottles Ounces 12 21 32 24 each Price 0 99 2 97 3 97 34 50 ber

18 The monthly membership fee for an online television and movie service is 9 80 The cost of viewing television shows online is included in the membership fee but there is an additional fee of 1 50 to rent each movie online For one month Jill s membership and movie rental fees were 12 80 How many movies did Jill rent online that month a 1 b 2 3

17 Nate walks 25 meters in 13 7 seconds If he walks at this same rate which of the following is closest to the distance he will walk in 4 minutes a 150 meters b 450 meters c 700 meters d 1 4000 meters

peas Faba beans Field peas Lupins 240 70 225 150 a 3 00 b 5 50 c 6 67 d 7 34 of plants pl Area m 2 5 3 3 50 He spent the rest of the money on bowling a number of games If it took Zhang Lei 45 minutes to bowl each 16 Zhang Lei spent 20 00 during his last outing at the bowling alley This included a one time shoe rental fee of game and he spent 2 hours and 15 minutes bowling how much did it cost per game

the greatest planting density in plans per square meter PL 15 The table at left gives the numbers and planting area of several plants in a garden Which plant variety has m2 a Chickpeas b Faba beans c Field peas d Lupins Plant variety Chickpeas Faba beans Field peas Lupins Number of plants pl Area m 240 6 70 225 1 50 2 5 3

12 A line in the xy plane has a slope of and passes through the origin Which of the following points lies on the line a 0 b 2 3 c 6 4 d 9 4

11 In the xy plane the line determined by the points 2 k and k 32 passes through the origin Which of th following could be the value of k a 0 b 4 c 8 d 16

10 Graphene which is used in the manufacture of integrated circuits is so thin that a sheet weighing one ounce can cover up to 7 football fields If a football field has an area of approximately 1 acre about how many acres could 48 ounces of graphene cover a 250 b 350 c 450 d 1 350 009 5

Bonus Lett 2 that H X exph show Fast enten 1 X 4 O is a constant

For all positive integer numbers n the statement Sn 2 6 12 n n 1 n 3 n n 1 n 2

5 Elena is conducting a study about the effects of toxins in the water on the hormones of fish Elena surveys 350 male fish in a river and finds that 150 of the male fish have egg cells growing inside them According to Elena s survey what is the ratio of male fish with egg cells to male fish without egg cells in the river

If y kx where k is a constant and y 24 when x 6 what is the value of y when x 5

13 Simplify 5 x 5y 10 Type a response

briel s Expression 1 1 Gabriel and Kayla each received the same set of tiles They arranged them differently and they also wrote different expressions to represent their tiles What expression do you think Gabriel might have written

Josh is printing extra flyers to distribute The flyers are printed at a constant rate The table below shows the number flyers he has after different amounts of time Time minutes 10 15 Flyers 98 Answer the following questions 20 25 123 148 173 a Choose the statement that best describes how the time and the number of flyers Josh has are related Then give the value requested As time increases the number of flyers Josh has decreases At what rate is the number of flyers Josh has decreasing flyers per minute O As time increases the number of flyers Josh has increases At what rate is the number of flyers Josh has increasing flyers per minute b How many flyers did Josh already have when he started printing Quero 8 08 X 5

Vertex Form What is the vertex of f x 2 x 4 3 What is the vertex of g x x 5 2

Find the product of the polynomials x 2 x 5x 8 x 2 x x 8 Simplify your answor

Divide using any appropriate method 5 3y 12y 9y 3y 7 5 3y 12y 9y 3y UC COL 11

The function ha x 3 1 is graphed on 1 1 5 determine the following information from the graph provided 4 10 00 2 C 2 A 3 9 8 10 L

Solve r r 2 5 2r 11 7

Solve 3x 4 4x 8 3 8x 1 X

Solve 7x 3 2x 13 O x 55 or 5 16 O x 2 9 Ox 1 10 O x 2

Given P x 2x5 4x x 5 what is the exact number of real and complex zeros of P x respectively A 5 0 B 4 1 C 3 2 D 1 4

Divide and simplify 25b 5b 5b 2 25b 5h

Multiply vertically x 2x 9 2x 8x 3 x 2x 9 2x 8x 3 Simplify your answer

Find the quotient x 25x 5x x 25x 5x 4 5x 5 x 25x 5x 4 5x Simplify your answer Use positive exponent

37 Which point is located in the third quadrant on a coordinate grid A 5 6 B 1 5 C 3 4 D 7 2

ANALYZE A catalyst is used to increase the rate of a chemical reaction The reaction rate or the speed at which the reaction is where x is the concentration of 3 occurring is given by Rix the catalyst solution in milligrams of solute per liter What does the end behavior of the graph mean in the context of this experiment x 10 Reaction Rate 2222 8 0 2 1 40 120 160 Concentration mg L

100 Correct 100 Correct 100 Correct O Macmillan Learning A desalination process reduces the amount of salt in a container of salt then the amount of salt remaining after t hours is modeled by S 35 x 0 96 grams Make a graph of the amount of salt remaining after t hours Suggestion You may zoom in to the graph to manage points easier alogad

b The graph of y g x is shown Draw the graph of y g x kt 8 6 4 2 6 17 2 2 8 X X

The graph of a polynomial function is given to the right On the basis of the graph answer the following questions a Find as many factors of the polynomial as possible b Construct a polynomial function with the zeros shown in the graph c Is it possible to find any other polynomial functions with the given zeros d Is it possible to find any other polynomial functions with the given zeros and the same graph a The factor s is are Simplify your answer Use a comma to separate answers as needed b P x Type your answer in factored form c Is it possible to find any other polynomial functions with the given zeros Yes 400 400

b The graph of y g x is shown Draw the graph of y 2g x KH 8 6 4 2 19 2 T 6 8 2 6 8 x X

A member of your research team wants to compare the prevalence of liver cancer in Japan to the prevalence of liver cancer in the Philippines The only information you have with you is Surveillance data for the year 2015 shows there were 7 734 existing cases of liver cancer in the Philippines Among those cases 1 432 were new cases of liver cancer In the same year there were 36 147 existing cases of liver cancer in Japan During this time Japan s population was 127 600 000 people and 96 710 000 people were living in the Philippines What do you tell your team Which country has higher prevalence 4 points for calculating prevalence in each country 2 points for explaining your response

For certain decisions the time it takes to respond is a logarithmic function of the number of choices faced C R 0 17 0 44 log N where R is the reaction time in seconds and N is the number of choices Find a formula that gives the numb can be faced in terms of the reaction time Express numbers in exact form Use symbolic notation and fractions where needed eachillan Learning

In Venezuela the population on January 1 2000 was 24 8 million and the 2000 mid year population was 25 million people 125 000 deaths occurred during the year ending December 31 2000 These included 15 000 deaths from diabetes For the year 2000 80 000 new cases of diabetes were diagnosed As of the start of 2000 1 1 million residents of Venezuela had diabetes You may assume that no one immigrated into or emigrated from Venezuela in 2000 note this study would be difficult to conduct today in part because of problems counting the large number of emigrants 1 point each for the correct numerator denominator and answer 1 2 point will be deducted for missing UNITS cases deaths per population if applicable a What was the diabetes specific mortality rate in Venezuela in 2000 per 100 000 population b What was the prevalence of diabetes per 100 000 population at the end of the year on December 31 2000 assuming the population was the same as mid year

2 3x x 14x The solution set is Type your answer in interval notation

8 Let be an angle such that sin 9 Find the exact values of tan 0 and sec 0 tan 0 sece 0 0 and cot0 0 3 16 X S

Find two numbers that a multiply to 40 and add to 6

x 12 3 The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed

X b The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed

Solve x 4 x 5 2 X 5 x 7 The solution set is Type your answer in interval notation

and the exact value S T 6 COS Points 0 of 1 Type an integer or a fraction Type an ex

Write a polynomial f x in completely factored form with leading coefficient 1 that satisfies the conditions Then determine the graph of f x Degree 3 zeros 4 with multiplicity 2 and 3 with multiplicity 1 Type your answer in factored form Type exponential notation with positive exponents