Complex numbers Questions and Answers

Find the indicated complex roots Write the results in polar form using degree measure for the argument List the roots in increasing order of for 0 0 360 The fourth roots of 256 cos 228 i sin 228 are 0 0 0 0 Wo W W W3 h i 2 Give exect answers Use the degree symbol where necessary

Convert the complex number from polar form to rectangular form a bi Give an exact answe 3x i The rectangular form is D EC

7 To see Lindsey better Pete walks out into the street so he is 4 3 meters from the base of the building Find the angle of depression from Lindsey to Pete to the nearest tenth of a degree

For 6 11 fand g are defined for all real 6 f g x 8 f g 2 10 a f x 1 pt 2 pts 2 pts

An equation is shown 6 6 65 63 6b What is the value of a O A OB O C OD 0 430 0 775 0 786 1 000

automatically A formula for compound interest is shown below where A is the value of an account with a one time principal P growing at an annual interest rate r for t years with n compound periods per year A P 1 n ynt How many years will it take a 5 000 deposit into a savings account to grow to 7 500 with an interest rate of 2 5 compounded quarterly

Question 12 Which equation is equivalent to log 32 5 A 5 32 O B O C O D 325 x 32 5 x5 32 x

Question 5 Which of the following expressions are equivalent to 3 64 Select THREE that apply A 86x B 0 C D E 46x 22 18 4 3 x 82 3x

15 What percent of 90 is 43 Round answer to the nearest hundredth

10 What percent of 108 is 36 Round your answer to the nearest hundredth of percent of necessary

For the following function find the hole x intercept y intercept vertical asymptote horizontal asymptote and oblique asymptote If something doesn t exist enter NONE in all caps f x 6x x 3 hole x y No Response x intercept x y No Response y intercept x y No Response vertical asymptote No Response horizontal asymptote No Response

Name Date QC Substitut Solve each system of equations method No r 21 Ex 3x 4y 8 Step 3x 4y 8 3 2y 4y 8 6y 4y 8 2y 8 2 2 y 4 1 y 5 3x 4y 8 graphing Step 1 The variable x is already by itself Step 4 Step 3 x 2y x 2y x 2 4 8 2 4 x 8 8 8 8 4 3x 4y 8 3 8 4 4 8 24 16 8 8 8 1 Solve one This is a section 2 Substitute equation 3 Once you plug this equations 4 Check yo both equ 2 x y 4 2x 3y

Use a calculator with ay key or a key to solve the following The exponential function f x 565 1 026 models the population of a country f x in millions x years after 1968 Complete parts a e a Substitute 0 for x and without using a calculator find the country s population in 1968 The country s population in 1968 was 565 million b Substitute 27 for x and use your calculator to find the country s population to the nearest million in the year 1995 as modeled by this function The country s population in 1995 was 1130 million c Find the country s population to the nearest million in the year 2022 as predicted by this unction The country s population in 2022 will be 2259 million d Find the country s population to the nearest million in the year 2049 as predicted by this function The country s population in 2049 will be million

6y 4y 8 x 8 8 4 2y 8 2 2 8 8 3x 4y Name Lacesha Taylor Date A U2L5 Solving re is a system of linear equat 1 Which would be more helpfu equations or subtracting one Adding The two equ without

5 In 2002 the population of a certain city was 2 million If the city s population is declining at the rate of 1 8 per year when will it fall to 1 5 million

Expand the logarithmic expression log x 1

Homework aspx homeworkld 641589557 ques onential Functions Use the compound interest formulas A P1 n Find the accumulated value of an investment of 20 compounded continuously

PlayerHomework aspx homeworkld 641 Exponential Functions 12

Approximate the following number using a calculator 7 1 9 7 1 9 22 Round to three decimal places as needed

Check if the following series converge you might need to use Ratio Root tests c En 1 1 3 5 2n 1 2 5 8 2n

Determine the intervals of the domain over which the function is continuous Over what intervals of the domain is the function continuous O A The function is continuous over the interval 2 1 OB The function is continuous over the interval 0 0 O C The function is continuous over the interval 3 and over the interval 3 00 O D The function is continuous over the interval 31 and over the interval 3 00

Given f x 6x and g x 2x 6 find the following expressions a fog 4 b gof 2 c fof 1 d gog 0 a fog 4 Simplify your answer

2 The average price of a movie ticket in 1990 was 4 22 Since then the price has increased by approximately 3 1 each year Write an exponential function to model this situation then find the price of a ticket in 2016 3 A virus has infected 400 people in the town and is spreading to 25 more people each day Write an exponential function to model this situation then find the number of people that will be infected in 10 days

This is a 2 page document Exponential Growth Decay 1 Vanessa invested 2 500 into an account that will increase in value by 3 5 each year Write an exponential function to model this situation then find the value of the investment after 20 years

Consider the following polynomial Step 4 of 4 Find the zero s at w Answer Select the number of zero s at w Selecting an option will display ar

Given the parent function is f x which would be the function vertically compressed to the x axis by a factor of O A x

Stephanie Vega Martinez Attempt 1 Given the following graphs of the two function which statement is mote likely to be true A 80 0 4 8 x x 4 8 x 4 8 a 4 g x

pu Point A is plotted in the graph below 4 2 3 A 23 61 4 19 2 2 12 3 A A What would be the location of the image of A after it is reflected over the y axis 4 12 A

11 DETAILS a Use the properties of multiplication and opp 1 Ox 1 O x 1 O x Ox O 1 x LARMPMT1 8 3 012 Explain your process The product of x and Ox 3 is ed b Use the properties of multiplication and op x 3

All of these functions have a domain of all real numbers 00 Question 9 10 points What is the average rate of change of the function f x x 3 from x 0 to x 2 32 I Question 10 10 points A partial set of values for the function of g x is given

Write the speed at each velocity Remember in physics and engineering speed is the absolute value of velocity a 31 miles per hour mph b 67 miles per hour mph d 43 miles per hour mph 27 miles per hour mph

Complete each statement to illustrate the Additive Inverse Property a 10 0 b c d 11 1 0 4 0 0 Sm

tephanie Vega Martinez Attempt 1 identify the inequality that represents the grapn 54 3 2 N O A 2 12 Oy 2x 3 y 2x 2 y 2x 3 y 3x 2 2 B N Question 3 23 33 points x 37

Ellie left Riverside California driving her motorhome north on Interstate 15 towards Salt Lake City at a speed of 64 miles per hour Half an hour later Israel left Riverside in his car on the same route as Ellie driving 72 miles per hour Solve the system 64y 72x y x 1 A for x to find out how long it will take Israel to catch up to Ellie B What is the value of y the number of hours Ellie will have driven before Israel catches up to her

The measure of one of the small angles of a right triangle is 34 more than 6 times the measure of the other small angle Find the measure of both angles Smallest angle Other non right angle

Identify the key characteristics of the rational function 1 f x x 3 x 2 2 f x x 1 x 5 3 f x x 3 x 3 10 Zeros VA Domain HA Range Zeros VA Domain HA Range Zeros VA Domain HA Range

Given the polynomial function f x x4 5x3 7x 10x 14 A State the coordinates of the x intercepts B State the coordinates of the relative maximums C State the coordinates of the relative minimums D State the range of the function using interval notation

COM 9 12 15 18 Question 29 3 3 points What is the critical value associated with a 99 confidence interval 00 990 1 645 Moreno Miran Attempt 1 1 960 2 575 Question 30 3 3 points

Question 16 3 3 points Reading from the dot plot James says that there are 5 students who read 3 books What is James error 34567 9 10 11 12 13 14 1 Number of Books Read James read the dot plot incorrectly There are more than 5 students who read 3 books James read the dot plot incorrectly There are 3 students who read 5 books not 5 students who read 3 books James read the dot plot incorrectly There are twice as many students who read 3 books James read the dot plot incorrectly The dot plot does not show the number of students who read 3 books

00 2 Time Left 1 33 46 Neftall Moreno Miranda Attempt 1 There would be no effect on the range Question 12 3 3 points Consider the following dot plots Data Set A Data Set B 10 10 Which of the below statement is the only one that is TRUE Data set A has a larger Mean Absolute Deviation Data set B has a larger Mean Absolute Deviation Data set B has a larger Mean Question 13 3 3 points

For Exercises 1 4 what is the minimum additional information needed to prove each triangle pair is congruent using the given theorem 1 SAS 2 HL AA 3 ASA 77 For Exercises 5 and 6 for what values of a and b are the triangle pairs congruent by the HL Theorem Use 9 5 Notes Page 2 5 15 A Her 20 4 AAS 4 1 6 20 15 2 1 7 Understand Adam says AABC ADEF by the 11441 3 2

Condense to a single logarithm Simplify if possible 1 log 9 log 4 1097 36 4 3 log x 5log x loga 14 7 log4 x log x 4log x Expand each logarithm 8 logs x y 10 log x y Date 2 log 80 log 5 16 1092 5 7log x 3log x logs logsx 3 1093 13 1093 X 10 3 1 109 3 X 9 log 3 108 81 109 811 2 10939 11 log 6 2log 4log x log3x 10934 10931 log3

Find the area of a regular hexagon if a a side is 4 b the radius of the circumscribed circle is 6 c the diameter of the circumscribed circle is 20

17 For the imaginary number indicate whether its value is i 1 i or 1 93

Condense the logarithm and simplify if possible 2 In a 3 in 6 In a In 2a b In ab In 2ab In 2ab

Find the inverse of the following y log 3 x 8 O y 13 8 Y 13 8 y 13 8 y 13 8

2 Find A where A 3 5i 1 6i Ai 2 7i 2 1 3i

The inverse Laplace transform of F s A e 2xcosx e 2x sinx B e E 2x 2x e cosx 3e D 2x cosx e e 2x cosx 3e2Xsinx 2x cosx e sinx None of the above sinx s 1 S 4s 5 is equal

Exercise 8 Prove that the following is not an identity by finding a counterexample Verify that it is a counterexample tant sect 1 sect 1 tant a c csc 2x secx csc r 2 sin x 2 cos r

Exercise 9 If sec A 5 with A in QI and sec B 10 with B in QI find sec A B Draw a diagram