Complex numbers Questions and Answers

5 m Which number line can be used to show that the sum of a number and its opposite is 0 3 2 3 2 1 4 3 2 1 3 2 1 0 0 0 0 1 2 M 3 23 L 23 0 2 2 Not equal to o NOT OPPOS f2 2 0 O opposites O Not Opposites 2 0 2 Not Opposites

Consider a tank containing at time t 0 20 pounds of salt dissolved into 1000 gallons of water Assume that water that contains 1 4 pound of salt per gallon is entering the tank at a rate of 30 gallons per minute and that the well stirred solution is leaving the tank at the same rate How much salt in pounds will be in the tank after 60 minutes

Find the exact value of the function 5 2 tan given tan tan B with 270 B 360

Use the graph paper provided and graph the following systems of inequalities Determine all the possible solutions Select all that apply y 4x 3 y 2x 3 1 1 1 2 1 5 3 4

The graph of g x 2 1 can be obtained from the graph of f x 2 by which actions a Reflecting the graph of f X across the x axis b Reflecting the graph of f x across the y axis Then a Shifting the resulting graph right 1 unit b Shifitng the resulting graph left 1 unit c Shifting the resulting graph up 1 unit d Shifting the resulting graph down 1 unit

A very special base e Euler s number P 22

Graph f x 30 20 10 20 10 0 10 10 20

The graph of inverse functions will show that the two functions are symmetrical across

Determine if f x 2x 9 and g x 9 are inverses

You deposit 3000 in an account earning 6 interest compounded monthly How much will you have in the account in 5 years

You are paying off a student loan in monthly installments After your 5th payment your remaining balance on the loan is 17 500 After your 16th payment your remaining balance is 12 000 What is the nth term rule for the sequence represented by this situation Fill in the formula a a d n 1 below an n 1

Is the following sequence arithmetic If so enter the common difference If not enter th word no 5 0 5 10 arithmetic

An ant colony invades the caramels in a candy store The 1st day they eat 1 4 of a caramel the 2nd day 1 2 of a caramel and the 3rd day 3 4 How many will they eat on the 4th 5th and 6th days 1 4 1 2 3 4 Enter any fractional answers like the fractions shown in the question numerator denominator with no additional characters or spaces

Find the next two terms 25 25 25 25 The next term in the sequence a5 is Select The next term in the sequence a6 is Select Select 25 25

Find the next three terms in the sequence 4 12 36 108

Find the next two terms 10 12 14 16 The next term in the sequence 95 is The next term in the sequence a6 is Select Select 18 45

Find the sixth term of the following sequence 2 10 2 O a6 096 O a6 a6 4 125 1 625 2 625 1 625

Use the compound interest formula to find the account balance A where P is principal r is interest rate n is number of compounding periods per year t is time in years and A is account balance P 1 57 609 6 2 r compounded Quarterly t 1 The account balance is approximately Simplify your answer Type an integer or decimal round to two decimal places as needed

Interest is compounded semianually Find the amount in the account after the given time Principal Rate of Interest 5000 4 Time 3 years The amount in the account is

function and check the graph with a graphing calculator Before doing so describe how the graph of the function can be obtained from the graph of a basic exponential function 5X 2 f x 2 Select the correct choice below and fill in the answer box to complete your choice OA Start with the graph of y Shift the graph 2 units to the left B Start with the X graph of y Shift the graph 2 units to the right OC Start with the

Solve the linear programming problem Maximize P 7x 7y Subject to 2x y 20 X 2y 16 X y 20

The monthly demand function for C 3 040 2x dollars Production Find the revenue function R x in dollars R x units of a product sold by a monopoly is p 6 100 is limited to 100 units Find the cost function C x in dollars C x Find the profit function P x in dollars P x Find P x P x Find the number of units that maximizes profits Round your answer to the nearest whole number units Find the maximum profit Round your answer to the nearest cent dollars and its average cost is Does the maximum profit result in a profit or loss profit

Find all the complex cube roots of w 125 cos 240 i sin 240 Write the roots in polar form with 8 in degrees Zo cos isin Type answers in degrees Simplify your answer

ivide Check your answer by showing that the product of the divisor and the ividend x 3 4x 2 8x 3 x 1

Finding Points of Inflection In Exercises 15 36 find the points of inflection and discuss the concavity of the graph of the function 15 f x x 9x 24x18 16 f x x 6x 5 17 f x 2 7 x 18 f x 4x 3x 19 f x x x 4 20 f x x 2 x 1 21 f x x x 3 22 f x x 9 x 6 x 23 x 25 f x sin 0 47 2 24 f x 33 y x ln x 35 f x arcsin 4 5 27 f x sec x 0 47 28 f x sin x cos x 0 2 29 f x 2 sin x sin 2x 0 27 30 f x x 2 cos x 0 2n 31 y e 3 x x 3 x 26 f x 2 csc 3x 21 32 y e ex 34 y In x 9 36 f x arctan x2 0 2

Expand the expression using the binomial theorem x 3 6

Solve the quadratic inequality Writ x 8 x 1 0

Write the statement as a biconditional Points in Quadrant III have two negative co Choose the correct answer below OA A point is in Quadrant III if and onl OB If a point is in Quadrant III then th OC If a point has two negative coordin OD A point is in Quadrant III if and onl

45 48 Evaluating Logarithms Use a calculator to evaluate the expression correct to four decimal places 45 a log 2 b log 35 2 46 a log 50 b log V2 47 a In 5 b In 25 3 e log 3 c log 3 2 c In 1 3

Consider the angle shown below with an initial ray pointing in the 3 o clock direction that measures radians where 0 0 27 The circle centered at the angle s vertex has a radius 3 units long h 2 d Therefore 0 2 2 1 a The terminal point is how many radius lengths to the right of the circle s center 2 1 41 2 65 b Then cos h c Does the number we get in part b give us the correct value of 0 radii Preview Preview Preview

What is the equation of the line with a slope of 2 and passes through the origin 0 0

Human blood can contain the A antigen the Ba the A and B antigens or neither antigen A third called the Rh antigen is important in human rep and again may or may not be present in an indiv is called type A positive if the individual has the but not the B antigen A person having only the antigens is said to have type AB negative blood having only the Rh antigen has type O positive blood types are defined in a similar manner Ide blood types of the individuals in regions a thro the right

percent Examples 1 2 1 Andy earned a score of 24 points out of a possible 25 points on a recent math test What percent is this 96 3 During a fundraiser 30 out of 50 orders included gift wrap What percent of the orders included gift wrap 60 5 A video game is on sale for 15 off the original price of 60 What percent of the original price is the discount 7 At the football team banquet 60 out of the 80 people attending had dessert with their dinner What percent of the attendees had dessert Find each percent 9 54 is what percent of 60 11 27 is what percent of 270 2 Stacia wants to but a new hoverboard that costs 125 She has already saved 50 What percent of the cost of the hoverboard has she saved 4 Last softball season Evelyn had 36 hits in 50 at bats What percent of her at bats did she get a hit 72 6 Mr Harris is buying a pair of headphones for 225 He plans to pay 45 in cash and put the rest on his credit card What percent of the total cost is he paying for in cash 8 During a recent tennis match 15 of Ariana s 50 serves were aces What percent of Ariana s serves were aces 30 10 16 is what percent of 64 12 24 is what percent of 30 bor

Find the domain and range of the relation 8 9 7 9 6 9 5 9 Then determine whether the relation is a function Separate your answers by commas Domain Range Separate your answers by commas Is the relation a function Yes O No

Use the change of base formula to approximate log 53 Round to 3 decimal places Provide

Use the set of ordered pairs to determine whether the relation is a function Then find the domain of the relation and the range of the relation 8 10 4 2 2 8 1 0 7 7 Is the relation a function O Yes No The domain of the relation is commas The range of the relation is commas Writte Enter the domain elements separated by Enter the range elements separated by

Find the slope of the following line If the slope is undefined enter DNE 2y 19 Slope

Use the power property to rewrite the following log 2

Write as a difference and simplify log 100 Provide your answer below

A line has a slope of 1 Plot the point on the graph 2 Use the slope to find two other points the one immediately to the left and one immediately to the right 3 Graph the line 4 Write the ordered pairs for each of your points on the right Note Plot the three points using the Point Tool Then draw the line using the Line Tool 10 and contains the point 2 2 for S 10 S TC Slope a Left Point Middle Point Right Point Given Point 2 2 32 W 2 2

Use the Quotient Property of Logarithms to write the logarithm as a difference of logarithms and simplify if possible 10 000 log Y Provide your answer below

A line has a slope of 0 and contains the point 1 6 1 Plot the point on the graph 2 Use the slope to find two other points one at x 0 and one at x 2 3 Graph the line 4 Write the ordered pairs for each of your points on the right Note Plot the three points using the Point Tool Then draw the line using the Line Tool 10 10 5 5 5 10 y 5 x 10 Slope 0 Given Point 1 6 First Point A Second Point Third Point 0 1 6 2

4000 3600 3200 2800 2400 2000 1600 1200 800 400 Determine the intercepts of the graph below 40 80 120 160 200 Q Vertical Intercept as an ordered pair Horizontal Intercept as an ordered pair

Convert 7 7 7 to logarithmic form Sorry that s incorrect Try again

Find the intercepts of 5x ly 5 0 x intercept y intercept Using the intercepts from above draw the graph of 5x ly 5 0 5 4 5 4 3 2 1 Clear All Draw 3 2 1 1 2 3 5 1 2 3 4 5 1

Maxwell is driving from San Diego to San Francisco a distance of 500 miles The x axis on the gr shows the time in hours since Maxwell left San Diego The y axis represents the distance he has drive 500 400 300 200 100 1 2 3 4 5 6 7 8 Use the graph to identify the x and y intercepts of the graph Note the scale on each axis since they may not be the same 2 1 a intercept y intercept 0 0 Explain what the x intercept means for Maxwell O The x intercept is the number of miles will have to drive total O The x intercept is the speed in miles per hour that drives

14 Alfredo Gutierrez bought 2 000 shares of a phone company s stock at 36 50 a share He sold his stock at 48 25 per share Each transaction paid a sales commission of 49 95 plus 0 02 per share a What was the net amount of the sale b What was the profit or loss from the sale

1 3 marks Evaluate JJ JSS x y 2 3 dv where E is the region satisfying the following inequalities 2 y 2 16 z 2

1 2 2 1 Write the matrix A 0 1 3 as a product of elementary matrices 2 4 5 3

I I Y Y Y Y y Y Y x I x x x 1 X x x 5 4 3 2 x Y X 4 3 2 1 1 1 2 3 4 5 4 3 2 1 5 A 3 2 1 2 3 5 4 3 2 1 2 3 1 2 3 4 4