Complex numbers Questions and Answers

3 x 5 2x 10 The solution using set builder notation is x Simplify your answer Use integers or fractions for any numbers in the inequality The solution using interval notation is Simplify your answer Use integers or fractions for any numbers in the expression Graph the inequality Choose the correct answer below OA 5 OB 1 45 OC OD 5 0 val notation Graph the solution set 0 0 10 10 10

Write the inequality that results from the following direction Then state which property of inequalities is being utilized Subtract 3 from each side of the inequality x 3 7 The resulting inequality is Which of the following properties is being utilized Choose the correct answer below O Addition Property of Inequalities O Multiplication Property of Inequalities

Solve the linear inequality Write the solution using set builder notation and interval notation Graph the solution set 1 5x52 The solution using set builder notation is x The solution using interval notation is Graph the inequality Choose the correct answer below OA 5 O B 5 OC 5 OI 5 H 20 20 20 20

Click here to watch the video Given 3 6 write the inequality obtained by adding 3 to each side of the given inequality What property of inequalities does this illustrate Add 3 to each side of the given inequality Type an inequality Simplify your answer What property of inequalities does this illustrate Choose the correct answer below O Multiplication Property O Addition Property

Write the interval as an inequality Graph the inequality 1 7 What is the inequality Type an inequality using x as the variable Choose the correct graph below O A O C 10 8 10 8 6 4 6 4 2 2 0 2 4 0 2 4 6 8 6 8 10 10 O B O D 10 8 10 8 6 6 4 4 2 2 0 2 to 0 2 4

Find all complex solutions of the equation 2 z 1 2 z 1 Which one is closest to the imaginary unit i

2 If the sum of the interior angles of a polygon is 2340 how many sides does the polygon have A 11 sides B 13 sides C15 sides D 16 sides 20

Solve the equation for y Then find the value of y for each value of x 3x 5y 17 x 2 0 2 Solve the equation for y y

2 Fortunately in a not too distant future Dorothy Gale arrives in her farmhouse and lands on the Wicked Witch and ends her reign of tyranny Munchkins from far and wide return to their homeland but are required to pursue employment in the Emerald City to pay for the damage inflicted by the Wicked Witch The population of Munchkin Land is now modelled via the equation dp dt a 2 t rp 1 rp 1 1 1 sin 172 N 2 2 Set r 0 056 N 10000 and p 0 10000 and p 0 3000 130 where 8 and 3 are the respective fifth and sixth digits of your student number i e if 8 1 and 3 then r 0 051 and p 0 3130 a Set a 200 and use ode45 to simulate the population over a period of ten years Plot and label the Munchkin population as a function of time b How large a value can a take while ensuring the population of Munchkin Land remains positive Support your answer with example simulations in ONE clearly labelled plot Use the legend command to distinguish different a cases 5 MARKS Please include the MATLAB code used in Question 2 and all labelled plots in your final

then that a well known result from geometry states sum of the lengths of the sides equal to the length of Proof the is greater than side or Z Z That is 1Z Z 12 1 12 1 which is known as Z and Z the third the triangle inequality

If the following statement is false choose False Statement Otherwise identify the property that justifies it If one of the properties is being used to transform the equation identify the quantity that is added to or multiplied by both sides Answer 8x x z False Statement z 8x 2y 0 Selecting an option will display any text boxes needed to complete your answer O Multiplicative Cancellation Property O Additive Cancellation Property O Zero Factor Property

plify the following union and or intersection er 2 3 U 3 00

Vrite the following set as an interval using interval notation Answer x 14 x 3

ver Natural Number Integer Irrational Number 10 3 Whole Number Rational Number Real Number

Assessment 36 A restaurant has 15 pounds of alligator meat to make tasty alligator dishes PART A PART B Each pot of alligator stew requires 23 pounds of alligator meat Which solution shows how many pots of alligator stew can be made The restaurant could make a stew that uses 13 pounds of a many more smaller pots of a made than the larger pots A 36 pots 15 1 233 pot 2 15 7 pots 15 23 6 pots 15 23

Consider this formula Z y X f z 4 0 and y 9 2 what is the value of x Express your answer to the tenths place i e one digit after the decimal poir

4 10 pts Answer the following questions about the graph Our World World population growth 1750 2100 in Data 296 1 8 1 6 1 4 1 2 196 0 8 0 6 0 4 0 2 0 A Annual growth rate of the world population World population 0 9 Buition 1760 1780 1800 1 65 JY 7 4 lion Data sources Up to 2015 OurWorldinData sories based on UN and HYDE Projections for 2015 to 2100 UN Population Division 2015 Medium Variant The data visualization is taken from OurWorldinData org There you find the raw data and more visualizations on this topic a When did we have an annual growth rate of 1 b When will we have an annual growth rate of 1 c When will we have the highest annual growth rate 02 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2020 2040 2060 2080 2100 Projection 2015 11 2 0 1 Licensed under CC BY SA by the author Max Roser What will be the rate of growth when the population is 10 2 billion

Acme Movers charges 70 plus 20 per hour to move household goods across town Hank s Movers charges 55 per hour For what lengths of time does it cost less to hire Hank s Movers It costs less to hire Hank s Movers for times less than hours

9 1 point Solve the system of equations by substitution y 2 2 x y 12 O 14 12 5 3 0 1 7 5

3 1 point The table below shows the cost of riding in a taxi cab What is the rate of change Miles Taxi Cab Driven 10 15 20 25 10 mile 1 mile 5 mile 2 mile Cost 25 35 45 55

thes transactions 1 Stockholders invested 52 000 cash and inventory with a fair value of 28 000 2 Sales on account 17 000 What will Martex s total assets equal OA 97 000 OB 52 000 OC 69 000 OD 80 000

Form a polynomial f x with real coefficients having the given degree and zeros Degree 5 zeros 2 i 9 i Enter the polynomial f x a Type an expression using on the variable Line intenors or fractions for any numbers in the expression Simplify your

Vertical asymptotes at x 4 and x 2 x intercepts at x 6 and x 3 y intercept at 6 y 56 x 6 x 3 18 x 4 x Preview Show Transcribed Text Write an equation for a rational function with Vertical asymptotes at x 3 and x 2

Find LAVE S TBCI Lat x 1 satl 1 x 5

2 Factor completely 12p 21p 28p 49

Find the solutions for f x x 7x 10

Find the domain of the following function g x 7 6 x The domain is

Determine the domain of the following function y x 5 The domain is Type your answer in interval notation

Solve and graph the solution set 12x x 6 2 6x 1 x 7 x x The solution set is x x

Nick and his cousin Sara have the same birthday but Nick is four years older than Sara Let the variable x represent Nick s age and y represent Sara s age Which graph represents the relationship between Nick s age and Sara s age

In the 2009 2010 school year in country A there were 103 000 foreign students from country B This number is 23 more than the number of students from country C How many foreign students were from country C There were about students from country C Simplify your answer Round to the nearest thousands as needed

A boat moves at a rate of 13 mph in still water If the river s current flows at a rate of 2 mph how long does it take the boat to travel 26 miles upstream It takes hours Round to the nearest tenth

Money is borrowed at 10 simple interest After one year 996 60 pays off the loan How much was originally borrowed The amount of the original loan was

Find the zero of the linear function f x 2x 3 x Simplify your answer

1 05 03 05 04 HC Triangle AABC has side lengths of a 18 b 18 5 and c 36 inches Part A Determine the m2A 5 points Part B Show how to use the unit circle to find tan A 2 points Part C Calculate the area of AABC 3 points

For what values is the statement cos cos 0 0 true Explain your answe

Establish the identity csc u sinu sin u cos u Write the left side term csc u in term of sin u 2 sin oi

14 1 point Which of the following equations represent this line O X 1 y x 1 x 1 y 1

13 Calculate the slope of the line that contains the points 2 3 and 6 3 2 3 0 2 3 undefined Previous

11 1 point Calculate the slope of the line graphed below 2 3 2 3 3 2

Is the relation a function What is the domain and range 2345 24960 8 10 Yes the relation is a function D 1 2 3 4 5 R 4 No the relation is not a function D 1 2 3 4 5 R 2 4 6 8 10 No the relation is not a function D 1 2 3 4 5 R 4 Yes the relation is a function D 4 R 1 2 3 4 5

9 1 point The relation represents a function 3 2 1 3 5 1 1 2 True False

6 1 point Solve the inequality statement 2v 1 7 Ov 4 v 3 Ov 4 v 3

3 Let f XY be a function and C be a non empty family of subsets of Y Let f C f C CEC Show that of C f o C Here C r X f x C

The perimeter of a college athletic field is 100 meters and the length is 18 m more than the width Find the length and width What is the width 16 m What is the length m

A truck enters a highway driving 60 mph A car enters the highway at the same place 10 minutes later and drives 71 mph in the same direction From the time the car enters the highway how long will it take the car to pass the truck The car will pass the truck in Round to the nearest minute minutes

A trimaran boat with a top speed of 63 knots won the tournament cup in 2010 Its top speed is 7 knots more than 3 5 times the top speed of the winner monohull in the 2007 tournament Find the top speed of the monohull in the 2007 tournament The top speed of the monohull in the 2007 tournament was knots Type an integer or a decimal

10 Which of the following graphs could represent y x 2x 3 Justify your reasoning A C Explain 2 V 1 B T D

In the 2009 2010 school year in country A there were 125 000 foreign students from country B This number is 23 more than the number of students from country C How many foreign students were from country C There were about students from country C Simplify your answer Round to the nearest thousands as needed

Find the x intercepts for the function belo 2p 24p 40