Complex numbers Questions and Answers

Rationalize the denominator 4 5 5 2

1 1 Exercises 1 The height above ground h of a bailt seconds after being dropped given by the equation h t 4 91 60 and shown on the graph below MO a How high is the ball at f 2 seconds b How long does it take the ball to hit the ground c When is the ball at a height of 10 meters d When will the height of the ball be greater than 10 meters e Using the graph estimate the height of the ball at t 1 second then use the equation fo above to find the exact value f Using the graph estimate at what time the ball will be a height of 20 meters then u formula for h above to find the exact value

3 3 5 5 8x 3 Type an exact answer using radicals as needed

14 F 5 rature to its equivalent temperature on the Celsius scale Use C F 32 or F C 32 where F is the degrees in Fahrenheit and C is the degrees in Celsi 14 F C Round to the nearest tenth as needed

5 9 Convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale Use C F 32 or F C 32 where F is the degrees in Fahrenheit and C is the degrees in Celsius 43 F 43 F C nd to the nearest tenth as needed

Use the given equivalents along with dimensional analysis to convert the given unit to the unit indicated 45 lb to g 45 lb g 16 oz 1 lb 2000 lb 1T 1 oz 28 g 1 lb 0 45 kg 1T 0 91

two of the world s wettest places are given Determine which location has the greater average rainfall and by how many inches Round to the nearest in Bowden Pen Jamaica 7 821 millimeters and Henderson Lake Canada 262 inches Click the icon to view a table of English and Metric Equivalents The average rainfall is greater in The average rainfall is greater by approximately Data table English and Metric Equivalents 1 in 1 ft 1 yd 1 mi 2 54 cm 30 48 cm 0 9 m 1 6 km inches X

4 Graph the following inequality 20x 30y 420

Classify the number as one or more of the following natural number integer rational number or real number 7 9 Percent of students who graduate with honours from a university Of which of the following sets is 7 9 a member Select all that apply rational real natural integer

solve the initial value problem y 4 3x 2 3y 2 12y y 0 2 and determine the interval in which the solution is valid

Write the following as a unit rate Express the answer as a fraction with a denominator of 1 Then express the answer in words using the word per 234 roses for every 9 vases Express the answer as a fraction Select the correct choice below and fill in the answer boxes to complete your choice Simplify your answers OA The unit rate is 26 rose s 1 vase s Express the answer in words using the word per B The unit rate is vase s rose s The unit rate is

Which of the following statements are correct Select all that apply 1 xb a xa b Oxab x x a 0 2 2 bx x b None of the Above

se the graph to answer these questions a Find lim f x and lim f x X 4 X 47 b Find lim f x X 4 c Find f 4 d Is f x continuous at x 4 Why or why not a Select the correct choice below and if necessary fill in the answer box to complete your choice OA lim f x X 4 OB The limit does not exist Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer OA lim X 4 OB The limit does not exist f x Simplify your answer b Select the correct choice below and if necessary fill in the answer box to complete your choice OA lim f x Simplify your answer X 4 OB The limit does not exist c Select the correct choice below and if necessary fill in the answer box to complete your choice OA 1 4 Simplify your answer OB The function is undefined at x 4 d Is f x continuous at x 4 Why or why not OA Yes f x is continuous at x 4 because f 4 exists OB Yes f x is continuous at x 4 because lim f x f 4 X 4 OC No f x is not continuous at x 4 because f 4 is undefined OD No f x is not continuous at x 4 because lim f x does not exist

Fill in the blanks The function gof x is found by replacing each occurrence of x in the equation for with

olve the following system of linear equations using the substitution method 4x3 x 5x1 49 10x2 13x 30x3 10x 4x 5 4x

Compute the determinant of the following 3x3 matrix 4 1 51 8 8 7 10 7 5

Write the rate as a fraction in simplest form 370 robberies per 100 000 residents Select the correct answer below and fill in the answer boxes to complete your choice Simplify your answers OA The rate written as a fraction in simplest form is OB The rate written as a fraction in simplest form is residents robberies robberies residents

Multiply 4 5 0 1 4 5x0 1 Type a whole number or a decimal

Square function Constant function Absolute value function Identity function

Find the average rate of change of f x x 9x 3 over the following intervals a From 5 to 4 b From 3 to 5 c From 5 to 6 a The average rate of change from 5 to 4 is 52 b The average rate of change from 3 to 5 is

Given the function f x 2 x calculate the following values f x 1 f x f 3

Which one of the library of functions discussed has no intercepts Choose the correct answer below O A The square root function O B The reciprocal function O C The constant function D All of them had an intercent

There used to be a program in the Salt Lake valley where the electric company would pay customers who installed solar panels and contributed electricity to the grid A homeowner installed a solar panel system and made a contract with Rocky Mountain Power to sell them electricity Create a model which shows the cost of the system to the homeowner over time Here is information to use in this model This Salt Lake area gets an average of 8 hours of sunlight each day The system consists of 29 panels that each produce 380 Watts of power for each hour of sunlight 380 Watts 0 38 kilowatts The cost of the system was 21 200 Y The homeowner uses an average of 20 kWh each day for their home The rest they sell to Rocky Mountain Power at a rate of 0 13 for each kWh kilowatt hour a Find a linear equation that gives the total cost y of the panels after x days of use Enter the equation in slope intercept form y mx b You may write the slope as a decimal OR an unsimplified expression Recommendation Use the given information to determine how much the homeowner receives from Rocky Mountain Power each day Negating this will give you the slope b In how many days will the payments from Rocky Mountain Power pay for the system Round UP to the nearest day c In how many years will the payments from Rocky Mountain Power pay for the system Round UP to the nearest year Use 365 days 1 year

Solve each question Round your answer to the nearest hundredth 6 Asanji can wax a floor in 9 minutes One day his friend Maria helped him and it only took 5 63 minutes How long would it take Maria to do it alone A 10 91 minutes C 12 82 minutes By 15 04 minutes Dy 12 18 minutes 7 7 Working alone it takes Julio 12 hours to pick forty bushels of apples Molly can pick the same amount in 9 hours Find how long it would take them if they worked together A 6 29 hours C 4 23 hours zoom i B 6 51 hours D 5 14 hours

1 Graph on graph paper or a coordinate plane lined paper will not earn credit List the domain and range in interval notation a 1 if x 0 f x 2x if 0 x 3 6 if x 3 b f x x 51 c f x 2x 41 6

company is ordering booklets to promote their business The manufacturer charges 0 50 for each booklet when 50 or fewer are ordered 0 45 for each booklet when 51 to 100 booklets are ordered 0 40 for each booklet when 101 to 250 booklets are ordered and 0 35 for each booklet when 251 or more booklets are ordered Each order consists of a 10 shipping charge no matter the size of the order a What is the cost of purchasing 50 booklets b What is the cost of purchasing 252 books Check PARKING The rates at a short term parking garage are 5 00 for 2 hours or less 10 00 for 4 hours or less 15 00 for 6 hours or less and 20 00 for 8 hours or less Draw a graph that represents the charges State the domain and range Domain Range Check

x Function A 0 1 10 20 700 750 1200 1700 e the sentences to compare the two functions A appears to grow exponentially es the quantities for Function A Function B 600 624 888 1315 rounded value Function B appears to grow exponentially As will eventually exceed the quantities for Function B

1 2 10 4d 22 a Show algebraic steps to solve the inequality b Draw the number line graph c Write the solution in interval notation 2 Write the domain and range in interval notation 8 40 d 4 2 N 24 2 M to 00 10 3 Assume the graph continues in the same pattern beyond the scope of the the domain in interval notation

0 9 hours se in 8 3 hem if S S 12 Elisa can mop a warehouse in 10 4 hours One day her friend Pranav helped her and it only took 4 52 hours How long would it take Pranav to do it alone A 9 23 hours C 7 99 hours B 5 76 hours D 7 44 hours

10 H 4 721 12 8 6 4 2 8 6 4 8 10 10 8 6 12 8 6 4 2 4 21 6 8 10 2 4 6 8 X 10 X 24 6 8 10 O 10 8 6 4 27 10 8 6 4 2 To 8 8 6 4 10 10 8 6 4 4 6 8 10 2 4 6 8 10 X 24 6 8 10

point s possible A family has a monthly income of 3986 Their monthly expenditures are as shown in the graph below Rent 24 Food 22 Transportation 15 Other Expenses 19 Savings 20 How much money does the family save in a month Write your answer to the nearest dollar

stion Use the tree diagram below to predict the probability of flipping 3 coins and getting all heads or all tails www H T Ar Payor 2 H F TE H H H HI H T T T T 774 O A 1 2 OB 1 OC 2 O D 1 4

ultiply or divide the following rational expressions as indicated and simplify your answer 5z 14z 3 z 15z 56 2 8 z 3

Jim and Jack were curious about the number of red cars they saw each day One Saturday they decided to keep track of the red cars that passed their house each hour They recorded their findings in the table below Hour 1 2 4 5 Number of Red Cars 5 6 10 7 7 What was the average number of red cars that they saw each hour Round your answer to the nearest tenth

Suppose you are given a square with an inscribed circle as shown below If the area of the square is 36 m what is the area of the circle Use 3 14159 for T m Write your answer to two decimal places

Give the numerical coefficient of the term XW

Use the distributive property to remove the parentheses 8 K 6 8 K 6

Factor out the greatest common factor Simplify the factors if possible x 3 x 7 x 3 x 9 OA 2 x 3 x 8 O B x 3 x 16 O C 16 x 3 O D x 3 x 16

Factor by grouping 2 24x 18x 20x 15 O A 24x 1 x 15 O B 6x 5 4x 3 O C 24x 1 x 15 O D 6x 5 4x 3

The equation y 10 2x 13 2 estimates the amount that businesses will spend in billions of dollars on a certain business technology where x is the number of years after 2001 For what years will the spending be more than 105 billion Spending will be more than 105 billion more than years after 2001

Find the domain of the following function g x 8 4 x The domain is Type your answer in interval notation

Solve and graph the solution set 8 8y 17y 6 The solution set is y y Simplify your answer U fractions for any numbers in the expr

Write in interval notation 3 x 3 A T Ff BI

What polynomial should be added to 3x 6 so that the sum is zero The polynomial is Simplify your answer

Find the sum of 3x 9 and 6x 8 Sim

Perform the indicated operations 2p 26 4p 3p 6 2p 6p 20 2p 26 4p 3p 6 2p 6p 20 Simplify your answer Type your answer in standard form

Evaluate the polynomial 3x y 8xy 2 for x 4 and y 1 The polynomial 3x y 8xy 2 is Simplify your answer for x 4and y 1

Subtract the polynomials 5 X 3 3 x 6 12 12 3 4

Subtract the polynomials 6x 2 13x 7 6x 2 13x 7 Simplify your answer Type your answer in stand

Subtract the polynomials 4a b 4ab 3 4a b 3ab 9 4a b 4ab 3 4a b 3ab 9 Simplify your answer Type your answer in standard form