Complex numbers Questions and Answers

Graph the function f x domain and range 3 Click to enlarge graph Use the graphing tool to graph the function 6 Give the The domain of the function f x The range of the function f x 9 2 is Type your answer in interval notation 9 2 6 6 is 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10

Use the properties of inverses to determine whether f and g are inverses f x 4 g x log 4x Are the functions f and g inverses OA Yes because fog x gof x x OB No because at least one of f o g x or go f x is not equal to x OC Yes because at least one of f o g x or g of x is not equal to x OD No because fog x gof x x

Use the definition of inverses to determine whether f and g are inverses 5X 4 x 3 f x g x 3x 4 5 x Are the f and g inverses of each other O Yes No

A t shirt company has overhead costs of 1250 per day and it costs the company 2 25 to produce each t shirt The company sells each t shirt for 18 50 The daily profit loss for this company can be modeled by the equation y 16 25x1250 The boss of the company has a goal to sell a minimum of 250 t shirts per day Use the model to predict the daily profit if the company sells exactly 250 t shirts per day Provide your answer below

Douglas is saving up money for a down payment on a condominium He currently has 3156 but knows he can get a loan at a lower interest rate if he can put down 3931 If he invests the 3156 in an account that earns 5 annually compounded quarterly how long will it take Douglas to accumulate the 3931 Round your answer to two decimal places if necessary Answer Keypac

Find parametric equations for the line that passes through the points P and Q Enter your answers as a comma separated list Let x y and z be in terms of 2 P 3 2 3 Q 0 2 8

Andrei deposits 25 400 into a pension fund that invests in stocks After a successful year of investing in the stock market the fund agrees to pay a simple interest rate of 12 What will the balance be after one year Round your answer to the nearest dollar Do NOT round until you have calculated your final answer Provide your answer below

Let f x 3 2 Evaluate f 4 Provide your answer below

4 45 Ghulam Syed Attempt 1 30 45 x x 6 x 3 8 27 3x 2x 8 3x 4 12 60 3x 4 3x 2x 8 x 3 x x 6 I x 5 x 2 3 x 2 4 x 2 1 5 2 6 5 7 1 1 20 8 2 30

Solve the following equation using the quadratic formula 3x 6x 1 Directions for entering your answers Give your answers as decimal approximations rounded to the nearest 2 decimal places separated by a comma with no space in between Do not place an x in your answer only a list of numbers Example 7 89 0 34

The radioactive isotope Molybdenum 99 is produced at Chalk River Laboratories Molybdenum 99 has a half life of 66 h The exponential function that would describe the relationship between the percent P of Molybdenum 99 remaining after t hours using the general function P a c bt Write your answers in decimal form The a value is The b value is The c value is

answer choices gives an equation of the graph given below 34 2 TT how Transcribed Text Select the correct answer below 7 3 TT 2 Select the correct answer below Oy 2 cos 2x 1 Oy 2 cos 2x x 1 y 2 cos x 4 1 C 0 723 5 56 0 TT 2 3

A party mix is made by adding nuts that sell for 2 50 per kg to a cereal mixture that sells for 1 per kg How much of each should be added to obtain 20 kg of a mix that will sell for 1 30 per kg

e pH of a fruit juice is 5 7 Find the hydronium ion concentration H3O of the juice se the formula pH log H30 he hydronium ion concentration H3O is approximately moles per liter Use scientific notation Use the multiplication symbol in the math palette as needed Pound to the nearest tenth as needed

Solve the given logarithmic equation log 1 4 x 5 3 The solution set is

Solve the equation for x log 4 2 The solution set is Simplify your answer Type integer or a fraction

Write the given statement in an equivalent exponential form 6 36 4 log The equivalent exponential form of the given statement is Type your answer using exponential notation Do not simplify

Which graph is an exponential function a Exponential Function A B O C d b e c

f x y 2 3y y x x 3y and h x y 3x y c 10pts Do the graphs of the functions f and h have any common points Explain If yes find the set of the common points

Approximate with a polynomial in P using the inner product p g f p t q t de 70 Let po P1 P2 be the orthogonal basis for P2 where Po x P x 1

Determine if the given function is linear quadratic exponential logarithmic or other g x ex O logarithmic O exponential O quadratic

in A questionnaire was given to students in an introductory statistics class during the first week of the course One question asked How stressed have you been in the last 2 weeks on a scale of 0 to 10 with 0 boing not at all stressed and 10 being as stressed as possible The students responses are shown in the frequency distribution below How many students were involved in the study Click the icon to view the frequency distribution students Get more Frequency Distribution Stress Rating 0 1 2 3 4 5 6 7 8 9 10 Frequency 5 2 1 15 11 14 11 35 31 4 14 11

The current climate of topic and how popular it is in the public consciousness reason O controversy trust refers to the way many people feel about the

9 A football is punted into the air and lands 25 yards away letermine what parent function best describes the situation 10 You start with 100 in an account and add 5 each week 11 The graph of y x is transformed by a vertical translation of 5 units down a horizontal translation of 2 u the right and a reflection over the x axis Which of the following points is NOT on the graph of the transfo function a 3 6 b 2 5 C 0 9 d 2 5

13 The graph of f x x 41 2 is shown below Which transformations will affect the x intercepts for this graph CHOOSE ALL THAT APPLY a y f x 5 b y f x 3 c y f x d y 2f x 10 10 10 5 y X 5 10 SE

4 The function f x is shown in a table below If the function is transformed to f x 1 3 what will the resu table be anoisemiotensiT weiven 4 1 2 6 X f x 1 6 3 4 y f x 1 3 X y enoitonul tesq how muoy to the worke

A certain strain of bacteria divides every three hours If a colony is started with 90 bacteria then the timer in hours required for the colony to grow to N bacteria is given by N log 90 log2 t 3 Find the time required for the colony to grow to a million bacteria Please round your answer to the nearest hundredth

Find the roots of the equation 5 1 z4 160 and 2 64 0 5 2 Additional Exercises for practice are given below Find the roots of a z8 16i 0 b z8 16 0 c z4 16 0 d z4 16 0 e z4 16 0

Recall that the rocket is fired at an angle of 0 9 radians and has traveled 200 yards a Relative to the diagram above which variables values are given Select all that apply 0 y z d b In this scenario which of the following is true relative to cos 0 O cos 0 cos 0 O cos 0 O cos 0 2 AH HA 754403 I d c Using your answer to part b determine the value of a in yards Portion 126 754103 126 754102

At a sports event a fair coin is flipped to determine which team has possession of the ball to start The coin has two sides heads H and tails T Identify the correct experiment trial and outcome below Select all that apply The experiment is identifying whether a heads or tails is flipped The experiment is flipping the coin A trial is flipping a heads A trial is one flip of the coin An outcome is flipping a tails An outcome is flipping a coin once

e the graphs of f and g to evaluate the composite function fog 2 Ima fog

translate the English phrase into an algebraic expression the sum of 8x and 3x

ERROR ANALYSIS Describe and correct the error in graphing f x x 2 2 X 2 y 2 2 4 x

Given f x 9x and g x 9x 7 find the following expressions a fog 4 b gof 2 c fof 1 d gog 0 a fog 4 1359 Simplify your answer b gof 2 Simplify your answer

Find the average rate of change for the function between the given values f x x3 x 8x 7 from 0 to 2 28 1

the The length of a vegetable garden is 8 feet longer than its width If the area of the garden is 65 square feet find its dimensions 4 ft by 12 ft 4 ft by 14 ft 5 ft by 13 ft 6 ft by 14 ft Page 4 of 1

Graph the line through the given point with the given slope 6 0 m 1

24x32 4 5x 2 6 00 4 0 6 4 6 4 6 00 5 5 5 94 96 7 7 7 8 8 8

1 Suppose SE L V is an injective operator on V Define by u v 1 Su Sv for u v E V Show that is an inner product on V

Find the values x1 x2 and x3 that maximize f x1 x2 x3 3x 4x2 2x3 subject to the following constraints Write the exact answer Do not round If the function has no maximum value write None If infinitely many values maximize the function write Inf Answer x 4x1 5x 2x3 2 2x1 2x2 4x3 2 Keypad Keyboard Shortce Tables

3 Show that 8Z 56Z Z7

Find the maximum value of f x1 x2 7x1 9x2 subject to the following constraints Write the exact answer Do not round If the function has no maximum value write None Answer 23 x 3x 12 2x x 14 Tables Keypad Keyboard Shortcu

the characteristic function of a random variable X is yct exp 1 what s the value of ECxial a 1 b 0 c blo

Evaluate e 1 6 1 6 Round your answer to five decimal places Sorry that s incorrect Try again e 16

If f x 2e find f 2 Round your answer to the nearest hundredth and if necessary include a leading 0 with any decimals less than 1 For example 0 5 instead of 5 Provide your answer below

2 In 50 words or less explain the difference if any between the solution s to sin 0 and 6 sin 10pts

The population of a certain inner city area is estimated to be declining according to the model P t 161 000e 0 021 where is the number of years from the present What does this model predict the population will be in 6 years Round to the nearest person Answer How to enter your answer opens in new window Keypad Keyboard Shortcuts

Jaquan hopes to earn 1000 in interest in 4 5 years time from 10 000 that he has available to invest To decide if it s feasible to do this by investing in an account that compounds annually he needs to determine the annual interest rate such an account would have to offer for him to meet his goal What would the annual rate of interest have to be Round to two decimal places Interest formulas Keypad

Hattie has recently inherited 6700 which she wants to deposit into a CD account She has determined that her two best bets are an account that compounds ann at an annual rate of 3 1 Account 1 and an account that compounds daily at an annual rate of 3 5 Account 2 Step 2 of 2 How much would Hattie s balance be from Account 2 over 6 3 years Round to two decimal places Answer your answer fopens in new window Keypa Keyboard Shortc

3 Consider the set of mutually orthogonal functions 1 cosa cos 2r sin 2r on 7 A trigono metric polynomial approximation of degree 2 S2 a can be defined as a linear combination of the functions in P Determine the discrete least squares trigonometric polynomial S r for 0 with z 0 1 and y exp x