# Complex numbers Questions and Answers

Algebra

Complex numbersTime t Velocity a Find v 4 and explain what it means 02 4 6 8 0 32 48 61 73 b Find the average rate of change per second in the velocity from the time t 2 t the time t 4 Be sure to give the units

Algebra

Complex numbersFactor the polynomial f x Then solve the equation f x 0 f x x 6x 3x 10 The factored form is f x

Algebra

Complex numbersUse long division to find the quotient Q x and the remainder R x when P x is divided by d x and express P x in the form d x Q x R x 4 2 P x x 6x 28 d x x 3 P x x 3

Algebra

Complex numbersFactor the polynomial function f x Then solve the equation f x 0 3 f x x 12x 29x 42 The factored polynomial function is f x Factor completely

Algebra

Complex numbersg 1 j 2 8 4 7 9 8 n 1 n n 1 n n 1 n 2 n 1 n h i k n 2 n 1 n 2 n 1 n 1 n 2n 1 2n 2 2n 2n 1

Algebra

Complex numbersFind the equation of the line with same x intercepts and y intercepts x y 4x 4y 4 0 as the circle

Algebra

Complex numbersShow that the slope of the line passing through x x and x h x h can be expressed as

Algebra

Complex numbers2 Find the equation the line through the points 2 3 and 3 5 Write the answer in the form Ax By C 0

Algebra

Complex numbersGraph the following system of inequalities on your own graph paper Use your graph to answer the following questions x y 21 This line should be x 2y 4 This line should be The lines intersect at the point The solution region is the intersection point

Algebra

Complex numbersTools Write and solve a word problem that is modeled with the number line 0 77 78 10 20 30 40 50 28 35 SE YOU

Algebra

Complex numbersFind the equation of the line with the given properties Write the equation in slope intercept form Graph the line containing X Y 10 1 m 25 The equation of the line is y X 3 Type your answer in slope intercept form Use integers or fractions for any numbers in the equation Use the graphing tool to graph the line Click to enlarge graph 2 5 Points 0 5 of 1 10 10

Algebra

Complex numbers2 Graph the function f x x 8x 11 by starting with the graph of y x and using transformations shifting stretching compressing and or reflecting Select all the transformations needed to graph the given function using y x 2 A Compress the graph vertically by a factor of 5 B Shift the graph up 5 units C Reflect the graph about the y axis D Shift the graph down 5 units E Shift the graph to the right 4 units F Reflect the graph about the x axis G Stretch the graph vertically by a factor of 8

Algebra

Complex numbers2 4 pts Match the following correlation coefficients in the box to the right with their corresponding scatterplots below css linear r 0 6 r more linear r 0 8 r 0 8 0 6 r 0 r 0 9

Algebra

Complex numbers2 4 pts Match the following correlation coefficients in the box to the right with their corresponding scatterplots below r r r 0 8 r 0 6 r 0 r 0 9

Algebra

Complex numbersMake a scatter plot for the given data Use the scatter plot to describe whether or not the variables appear to be related 9 7 2 6 5 11 8 9 x y 12 4 0 3 6 12 O A 22 TTTTT 10 X TE 21 The variables appear to be related O B A 10 Ay 22 X 21 The variables do not appear to be related O C T 10 22 X 21 The variables appear to be related O D 10 Ay 22 9 21 The variables appear to be related

Algebra

Complex numbersThis question 1 point s possible First create a scatter plot for the data in the table Then use the shape of the scatter plot given to determine if the data are best modeled by a linear function an exponential function a logarithmic function or a quadratic function OA Ay 5 X T 6 0 logarithmic function OB Ay 5 X 6 quadratic function O C 0 6 exponential function O D Ay 5 linear function Q Q Submit quiz X y 0 05 4 1 0 4 3 12 2 1 3 5 0 2 4 0 15 5 0 1

Algebra

Complex numbersSolve f x g x What are the points of intersection of the graphs of the two functions g x 4 2 f x x 6x 4 The x values in the solution set of f x g x are 0 6 Use a comma to separate answers as needed What are the points of intersection of the graphs of the two functions Select the corre if necessary fill in the answer box within your choice O A The graphs of the two functions intersect at the point s Simplify your answer Type an ordered pair Use a comma to separate answer fractions for any numbers in the expression O B The graphs of the two functions do not intersect

Algebra

Complex numbersSuppose that f x x 5x 36 and g x x 3x 18 a Find the zeros of f g x b Find the zeros of f g x c Find the zeros of f g x a What are the zeros of f g x

Algebra

Complex numbersUse the graphs below to choose the correct symbol from each dropdown menu h x 5 g x 4 5 4 3 2 10 1 3 2 1 b h 0 1 2 3 4 5 4 3 2 1 3 2 1 O 1 2 3 A g 0 1 10 3 4 5 2 X F3 4 X a The number of values for x where h x 0 The number of values for x where g x 0 75

Algebra

Complex numbersSolve f x g x What are the points of intersection of the graphs of the two functions 2 f x x x 1 g x 2x 3x 62 f f x g x then x

Algebra

Complex numbersAnnual high temperatures in a certain location have been tracked for several years Let X represent the year and Y the high temperature Based on the data shown below calculate the regression line each value to two decimal places y 03 X y 5 17 78 6 18 86 7 16 44 8 17 32 9 18 4 10 17 08 11 16 26 12 16 94 13 16 92 Xx 20 25 X

Algebra

Complex numbersA 10 5 m fire truck ladder is leaning against a wall Find the distance d the ladder goes up the wall above the fire truck if the ladder makes an angle of 41 24 with the horizontal 10 5 m d 4 41 24 d 6 92 m Simplify your answer Type an integer or a decimal Round to the nearest hundredth

Algebra

Complex numbersUse the following graph to choose the correct responses from each dropdown menu below a f 2 f x c For LO 4 3 2 1 4 3 2 1 0 1 2 1 2 b When f x 0 the value of x is values of x f x 1 3 4

Algebra

Complex numbersWhat are the roots of the polynomial equation 0 x 26x 48 Select each correct answer 0 24 0 0 0 0 2 02

Algebra

Complex numbersWhat are the solutions to the equation 4x X 36x Enter your answers in the boxes or x or x

Algebra

Complex numbersA 10 5 m fire truck ladder is leaning against a wall Find the distance d the ladder goes up the wall above the fire truck if the ladder makes an angle of 41 24 with the horizontal 10 5 m 41 24 Points 0 of 1 Save dem Simplify your answer Type an integer or a decimal Round to the nearest hundredth

Algebra

Complex numbersWat is the meaning of the term angle of elevation OA If B is a point above point A as shown in the figure then the angle of elevation from A to B is the obtuse angle formed by the horizontal line through A and the line of sight from A to B Angle of elevation Horizontal A B O C If B is a point above point A as shown in the figure then the angle of elevation from A to B is the acute angle formed by the vertical line through A and the line of sight from A to B Vertical Angle of elevation Q Q G M B If B is a point above point A as shown in the fig then the angle of elevation from A to B is the acu angle formed by the horizontal line through A and line of sight from A to B B Angle of elevation Horizontal D If B is a point above point A as shown in the figure then the angle of elevation from A to B is the acute angle formed by the horizontal line through B and the line of sight from A to B Horizontal Angle of elevation B

Algebra

Complex numbersSolve the right triangle ABC with C 90 A 35 6 b 34 7 cm B a C www Simplify your answer Type an integer or a decimal Round to the nearest tenth as needed cm Simplify your answer Type an integer or a decimal Round to the nearest tenth as needed cm Simplify your answer Type an integer or a decimal Round to the nearest tenth as needed

Algebra

Complex numbersEvaluating and Solving an Equation Application Identify the information given to you in the application problem below Use that information to answer the questions that follow Round your answers to two decimal places as needed Hampton is a door to door vacuum salesman His weekly salary S v is given by the linear function S v 400 120v where v is the number of vacuums sold Identify the slope and complete the following sentence to explain the meaning of the slope Hampton earns 120 Find the Vertical Intercept Complete the following sentence to explain the meaning of the Vertical Intercept If Hampton sells 400 per vacuum sold x vacuums he will still earns a base salary of

Algebra

Complex numbersFind the equation of the line with the given properties Write the equation in slope intercept form Graph the line m 2 containing x x 4 5 The equation of the line is Type your answer in slope intercept form Use integers or fractions for any numbers in the equation

Algebra

Complex numbersThe point slope form of a nonvertical line that has a slope of m and contains the point X is y y m x x x x m y Y

Algebra

Complex numbersIn the figure shows the relationship between the percentage of married females of child bearing age using contraceptives and births per female in selected countries Use the sca plot to determine whether there is a strong negative correlation between contraceptive use and births per female Click the icon to view a scatter plot of contraceptive prevalence and average births per female There is a strong negative correlation between contraceptive use and births per female O False O True Scatter Plot of Contraceptive Prevalence vs Births per Female Births per Female 5987654321 10 0 0 Contraceptive Prevalence and Average Number of Births per Female Selected Countries Kenya Syria Jordan Botswana Zimbabwe Lesotho 10 Vietnam Honduras Fiji Chile CLUB M Costa Rica Spain Denmark 20 30 40 50 60 Percentage of Married Females of Child Bearing Age Using Contraceptives 70 80 X

Algebra

Complex numbersThe figure shows the graphs of the cost and revenue functions for a company that manufactures and sells external hard drives The solid line represents the revenue function R x 45x the dashed line represents the cost function C x 5000 20x Use the formulas to find R 350 C 350 Describe what this means for the company R 350 C 350 3750 Type an integer or a decimal Describe what this means for the company When the company produces and sells hard drives the for the company is Ints 0 25 of 1 OF LAMB 40 000 30 000 20 000 10 000 0 0 AY Rex x ext5000 20x 200 400 600 800 Hard Drives Produced and Sold Save Q G

Algebra

Complex numbersO Points 0 of 1 The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells external hard drives The solid line represents the revenue function R x 60x the dashed line represents the cost function C x 5000 35x Use the formulas to find R 150 C 150 Describe what this means for the company R 150 C 150 Type an integer or a decimal Part 1 of 2 40 000 30 000 20 000 10 000 of 0 0 AY RX 60x Cx 5000 5x 200 400 600 800 Hard Drives Produced and Sold Save O Gi

Algebra

Complex numbersF The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells external hard drives The solid line represents the revenue function R x 60x the dashed line represents the cost function C x 15 000 25x a Use the formulas to write the company s profit function P from producing and selling x hard drives b Find the company s profit if 21 000 hard drives are produced and sold a The company s profit function is P x Simplify your answer Score 43 75 3 5 of 8 points Points 0 5 of 1 40 000 30 000 20 000 Ay 10 000 0 0 5 Rpx 637 Cix 15 800 25 Save 200 400 600 800 Hard Drives Produced and Sold Q Q 15

Algebra

Complex numbers9 Fill in the integer values of each square root on the number line 0 VI 10 5 Between 13 Between r line above to 4 ann and 9 Use the number line above to help determine the two positive integers each square roc between and 5 What two integers is 15 between Which integer is it closer to aproximate 15 to the nearest tenth 16 25 36 and 49 13 26 Between 11 59 Between and 20 64 and

Algebra

Complex numbers10 8 6 4 2 10 8 6 4 2 Slope 2 4 6 8 10 2 4 What is the slope of the graph Leave your answer as a reduced fracti 6 8 10 Identify the y intercept Write as a coordinate

Algebra

Complex numbersFind an equation of the line that has a slope of 6 and a y intercept of 0 5 Write your answer in the form y mx b y

Algebra

Complex numbersFind the area of a triangle with sides of length 14 and 20 and included angle 27 degrees Round to the tenths

Algebra

Complex numbersUse the graphs of f x and g x below to fill in the blanks that follow f g 0 fg 2 f g 3 f g 4 G g 4 W 4 20 2 671 6 0 If 4 6 X

Algebra

Complex numbersUse a calculator to find a decimal approximation of cos 3 sin 3 Round to four decimal places as needed 22 cos 3 sin 3 Simplify the expression first

Algebra

Complex numbersQuestion Use a calculator to find a decimal approximation for each value cot 264 26 cot 264 26 Simplify your answer Round to seven decimal places as needed

Algebra

Complex numbersUse a calculator to evaluate the expression cos 35 sin2 35 cos 35 sin 35 Simplify your answer

Algebra

Complex numbersFind the exact values of the six trigonometric functions 690 1 Question 12 2 2 29 Part 3 of 6 the angle cos 690 Points 0 17 of 1 sin 690 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators 3 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators tan 690 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators

Algebra

Complex numbersAmount of Commission 5 0 Commission on Purchases 80 6 Amount of Purchase 5 1 What information do you see on the axes of the graph What relationship is being shown JF Y 2 Construct a table for the relationship 3 How do you know that the relationship in the graph above is proportional 4 What is the rate of change shown in the graph above 5 If a salesman wants to earn 90 in commission how many purchases would they have to oversee 6 If a salesman sells 800 worth of goods how much money would they earn in commission

Algebra

Complex numbersd e c 10 0 15 5 a b X y 5 ful for you An example of a table has been provided for line a Anch of the lines shown below You may make a table if that Y x 5 2 5 or 2 5 2 FIVE LINES GRAPH b a 10 0 0 15 2 5 20 4 10 6 15 equation y 2 5x or y 5 x 2

Algebra

Complex numbersEvaluate the expression 2 tan 2120 5 sin 150 cos 180 2 tan 2120 5 sin 2150 cos 2 180 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression