Complex numbers Questions and Answers

Write an equation for the line graphed below 7 6 5 4 3 2 1 7 6 5 4 3 2 1 1 2 3 4 5 6 7 1 2 3 4 5 6 7 q

9 7 7 9 A B 4n 2 C D A B C 2n 3n 6 21n 27n 10 5n 16 n 2 7 2n 3 5 5n 6 21n 22n 16 5n 6 n 2 20n 29n 10 5n 6 n 2 2 4n 20n 3 n 2 n 5 2n 2 17n 6 4n 4n 20n 3n 6 10 8 8 10 2 r 2 A B C D A B 4 3r 3 12 8r 3 2 1 2x 2 2r 2r 5 5r 14 3 3 r 2 r 1 2r 14 3 2 r 1 2x 18x 12x 48x 6 18x 12x 49x 2x 7 18x 12x 49x 9x 2x 6x 24r 3

1 Subtrating Rational Expressions Simplifych expression 1 n 5 6n 18n A C 5 6n 18n n 1 6n 18n n 8 3n 9n 6 B D 2 3n 9n n 5 6n 18n 2 2 b 5 6b 186 A B C 1 3b 96 6b 18b 1 6b 18b 3b 1 b b 3 6b 186 2

7 Graph the system of inequalities on the set of axes below y 3x 3 x 5 2y 4 X tom of inequalities Explain your answer

3 2022 Kuta Software LLC All rights Subtrating Rational Expressions Simplify each expression 1 2 6n A C A 4x 2 B n 5 C D 18n 5 6n 18n n 8 3n 9n 6 6n 18n n 1 4x 6x 3x 12x 6x 4 3 2x 1 37 x x 1 x 5 x 37 x 1 x 5 36 x 1 x 5 B D 2 3n 9n n 5 6n 18n 4 2 reserved 2 4 6b A B D A b 5 B 18b 1 96 36 6b 18b 1 6b 18b 4k 3 3b 1 b 2 3 b 3 6b 186 k 6 6k 15 C D 0 3k 7 6 3 k 30 k 4k 3 k 6 8k 21k 6 3 2k 5

4 Find a un vector in the O 13 13 O VIS VTS V13 O VTVT 13 13 13 8 13 13 13 26 12 13 13 Ion o1

0 State the domain of the relation or function 10 8 A The relation is not a function B The relation is a function

Researchers are conducting a study to test the effectiveness of a new medication Subjects are randomly divided into two groups the first group is given the medication and the second group is given s placebe herove the s two months after which subjects are asked to answer a questionnaire about their response to the drug and any potential side effects that they may have had This is an example of an experiment A B O D a sample survey an observational study a random phenomenon

7 Sketch the solution to each system of inequalities 17 x 3y 9 x 3y 3 A B 6 D 1 y x X x

Given 2 64 Which of the following expressions is the value of x log264 log64 O OC A C B U 64 64

Solve for x logg4 x O A B C 312 213 32

66 It takes DeShawn 9 5 hours to mop a warehouse Perry can mop the same warehouse in 8 4 hours Find how long it would take them if they worked together 3 Solve each question Round your answer to two digits 7 0 1 9 9 x x Find f 1 4 Evaluate each function Round to the nearest HUNDREDTH if necessary TWO DIGITS 8 h a 2 1a 1 3a Find h 1 9 Evaluate each function ANSWER SHOULD BE A FRACTION OR MIXED NUMBER ANSWERS GIVEN AS A DECIMAL WILL BE COUNTED AS INCORRECT State the domain of the relation or function 10 7 An aircraft carrier left Port 51 and traveled east A submarine left two hours later traveling 10 km h faster in an effort to catch up to it After four hours the submarine finally caught up Find the aircraft carrier s average speed Ay A The relation is not a function B The relation is a function 11 Determine the slope of the line represented by the equation 16 4 y x

2 Solve for 0 where 0 0 360 in the following equations Round to the nearest tenth of a degree if necessary Drawing an appropriate triangle finding a reference angle general solutions and applying restrictions are suggestions for full credit a sec 0 3 0 QII

3tan x sec x 5 0

2 tan 0 3

A TI 84 calculator costs 79 99 What is the total cost of the graphing calculator if sales tax is 7 Round to the nearest cent 135 98 74 39 55 99 O 85 59

Write an equation in the form y mx b for the average cost y of a textbook x years after 1990 Use the data points 0 38 and 8 86 to find the equation Then use the equation to predict the average cost in 2012 1 y 38x 6 the cost in 2012 is 842 2 y 6x 38 the cost in 2012 is 86 3 y 6x 38 the cost in 2012 is 170 O 4 y y 38x 6 the cost in 2012 is 234

3 ft 13 ft 6 ft 3 ft Determine the area of the given polygon 66 ft 25 ft 50 ft

Position Administrative Assistant Sales CEO Project Management IT Human Resources Rounded to the nearest dollar what is the mean salary of these employees O a 55 650 b 29 500 c 43 500 Salary 31 400 29 500 109 000 49 500 77 000 37 500 d 31 436

Find the volume of the solid below 5 cm 6 cm 14 8 cm 4 cm 6 cm 8 cm

Evaluate the expression using the graphs of y f x and y g x Evaluate fog 2 99 g x 4 f x 8 x O A O B O C O D

Multiple Cholce Identify the choice that best completes the statement or answers the question 9 Which function has a translation of 3 units to the left a f x 3x 1 b f x x 3 1 c f x x 3 1 10 Which function has a translation a f x 5 x 2 b f x 5 x 2 of 2 units right and a vertical stretch by a factor of 57 c f x x 2 5 d f x 27 5 1 Which function has a translation of 7 units down and reflects over the x axis a f x x 7 1 b f x x 7 1 d f x x 1 3 f x x 7 1 c f x x 17 7 f x x 1 7 Which function describes a parabola that opens downward and has a vertex of 2 312 a f x x 2 3 b f x x 2 3 c f x x 29 3 alt

5 f x 2 x 3 X Y 7 f x x 1 4 X y B 1 R 0 4 2 2 8 0 4 2 y Y 6 f x x 1 2 X Y 8 f x 2 x 5 3 X 0 4 21 2

entify the vertex and find at least two other peints Graph each quadratic function x 3 2 F X X 6 XV 3 f x x 2 X y 11 A 4 y

B 15 4x 14x 6 17 Identify the zeros of each quadratic function ef V Method 18 12 40 6 16 x 4x 16 0 19 Metho

Date Name Find the solutions for each quadratic equation AND state the factoring method s 2x 7x 0 1 5x 10x 0 3 x 64 0 Method Method 2 12x 3x 0 Method Method

R 3 It RT 36 find the value of x r 1 19 Use the diagram below to answer questions 1 and 2 V S M 5 If UW 6x 35 find UW 4x 20 x 7 T This is a 2 page document W N 1 If LM 22 and MN 15 find LN 2 If LN 54 and LM 31 find MN 4 If DF 9x 39 find EF 3x 10 D 47 E F 6 If HJ 7x 27 find the value of s 3r 5

5 3 6 a 5 a 2 28 a a 6 a 5 7a 36 a A B C D a 5 a 2 28 5a a 6 a 5 9a 36 a 5 a 2 K 6 6 4 5 2b 6 b 1 A B C D 216 25 26 2 b 3 b 1 10 b 3 b 1 15b 25 2 b 3 b 1 7b 13 b 3 b 1

8 Graph y sin2x 3 15 1 0 1 3 2 X sinx Sin2x 4 04 it 2 3 f R TC 5m 34 5x 4 7 8 2 3r 2 7 4 21

Do Now 12 5 1 How are you today Is there anything you want your teacher to know 2 If 4 x 8 what is the value of x 2 3 if 3x 5 4x 6 what is the value of 3x 2 4 If Glenn is ffeet and 3 inches tall what is the value of fif Glenn is 51 inches tall 5 A pound of cement costs 75 If a construction company has a bill of 5 250 for cement

5 3 6 a 5 a 2 A B 7 C D A B C D 28 a a 6 a 5 7a 36 a x 5 5x x 4 x 2 a 5 a 2 28 5a a 6 a 5 9a 36 a 5 a 2 5x 17x 6 x 4 x 2 6x 2 x 2 6x 21x 6 x 4 x 2 6x 23x 10 x 4 x 2 6 8 6 4 5 2b 6 b 1 A B C D 8 5p A B C D 216 25 26 2 b 3 b 1 10 b 3 b 1 15b25 2 b 3 b 1 7b 13 b 3 b 1 P 4 18p 114p 120p 5p 3 4p 90p 570p 600p p 4 6p p 5 3p 4 2 4p 2p 5 10p p 3 p 2

Include a title and a short explanation of your data DO NOW 19 On the grid below solve the system of inequalities equations graphically for x and y 3x y 2 3 x 2y 4

Do the following for the points 5 2 3 1 1 1 3 1 If you are entering decimal approximations enter at least five decimal places a Find the equation for the best fitting parabola y ax bx c for these points y 7 176 x 2 7x 220 673 880 b Find the equation for the best fitting parabola with no constant term y ax bx for these points y c Find the equation for the best fitting parabola with no linear term y ax c for these points y

3 Determine the surface area of his can 7 inches height 10 inches Show your work here SA 2 TT r 2 rh

5 Determine the minimum amount of aluminum needed to make this can Deca radius 2 in height 5 inches Show your work here SA 2 TT r 2 rh 2 3 14 4 2 3 14 2 5 25 13

h eight radius A r A lw A 2 rh A r Circle examples of surface area below The amount of wrapping paper for a gift The amount of carpet for a room The amount of cereal in a box The amount of water in a fishtank The amount of paint on a wall

Problem 3 20 points In AABC let a 4 in b 5 in and angle C 101 32 13 the remaining side and angles of the triangle Round all answers to the neares

Area of Cylinders 4 Determine the surface area of the pot diameter 8 in 4 r 4 height 12 in Show your work here SA 2 TT r 2 rh SA 2 4 2 4 12 2 3 14116 2 3 14 48 6 28 16 2 3 14 48 100 48 2 3 14 48

Find the following power Write the answer in rectangular form 3 2 3 21 4 CIDE O Points 0 of 1 3 2 3 21 4 1296 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi

Given that z 5 cos 60 i sin 60 then the following is true 125 cos 180 isin 180 125 1 i 0 11 125 Oi or simply 125

Write the expression as a single logarithm 3 log3x 3 log3z 3 log3y log 7 3

Raise the number to the given power and write the answer in rectangular form 2 cis 55 6 GCEE 2 cis 55 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi

Find the power Write the answer in rectangular form 2 2 3 4 6 8 4 13 HW Score 0 0 of 9 poi O Points 0 of 1 2 2 3 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi

The one to one function fis defined below f x 5x 10 Find f the inverse of f Then give the domain of fusing interval notation Domain of 8 6 0 0 0 0 QUO 0 0 0 0 8

Do 5 In the movie Diehard the prop gold bars are 10 0 inches by 2 50 inches by 1 50 inches one inch 2 54 cm exactly If these were a real gold bar what would their mass be the density of gold Au is 19 3 g cm 12k9

2x 20 3x 15 20 15 3x 2x 5ax x 5 2x 15 3x 20 5x 20 15 5 5 x 1 Equation Checklist Note You will not have all of these steps in every problem Distribute the outside factor to all terms within parentheses Check the left side of the equation combine like terms Cancel out the constant term Check the right side of the equation combine like terms If there are variable terms on both sides of the equation cancel out the one with the lower coefficient

Write the complex number 5 cos 358 isin 358 in the form a bi 5 cos 358 isin 358 Type your answer in the form a bi Round to the nearest tenth as needed

Write the complex number in rectangular form 20 cos 300 i sin 300 The complex number is Simplify your answer including any radicals Type your answer in the form a bi Use integers or fractions for any numbers LOVER

Write the complex number in trigonometric form r cos 0 i sin 0 with 0 in the interval 0 360 4 4i 0 4 4i 0 cos isin Type the value for r as an exact answer using radicals as needed Type the value for 0 as an integer or decimal rounded t

Write the following complex number in the form a bi 14 cos 0 i sin 0 14 cos 0 i sin 0 Type an exact answer