Complex numbers Questions and Answers

determine the inverse z transform of the following sign z 2z 3 z 1 z 2

Determine the domain and range of the function 4 3 2 Part 1 of 2 3 Part 2 of 2 N 2 3 y 2 3 4 The domain of the function in interval notation is 0 0 0 0 0 X C

Match each system of equations to the corresponding graphical representation below A 2 19 x 2 2 0 6 3x 5 5 y 2 19 x 2 2 0 0 2x 5 5 y22 19x 8 76x 6 76 B C D E 10 8 6 10 8 6 4 D 6 0 1 10 8 6 10 2 10 10 A 6 10 A 2 10 20 2 2 10 8 86 8 10 68 10D X 8 10 X 8 10 X X B 6 12 mul 6 8 10 X

The graph shows the relationship between the number f minutes Maria spent jogging on a treadmill and the istance she jogged Distance in miles 87656 st 32 Miles on the Treadmill 5 10 15 20 25 30 35 40 45 x Number of Minutes What was her speed O 0 1 mile per minute O 0 5 mile per minute O 5 miles per minute O 10 miles per minute

10 10 33 X54 X 4 5 CH 10 3 10 10 LE 10 O 10 10 y 10 10

Using the given graph of the function f find whether the function is even odd or neither 4 3 2 Ay 09 10 3 2 Q Determine whether the function is even odd or neit O O O Even Odd Neither

Use the vertical line test to identify graphs in which y is a function of x CITS Which of the following statements is correct Oy is a function of x y is not a function of x

se transformations to graph y 10x se the graphing tool to graph the function Click to enlarge graph Cao um STE MET Vertical Stretch or Compression a LLLLL Del Cle Horizontal Stretch Compression ddddd

X X 22 Fill in each blank with the appropriate expression that is required to solve the equation 4 6 4 y 5 y 5 y 25 a The restricted values are Type your answer here in the first blank not enter none in the blank and Type your answer here b When you solve the equation are there any extraneous solutions If so enter the value of the extraneous solution in the blank If Write your response here Enter the smaller number c Enter the solution set of the equation Write your response here

5 Find an algebraic rule for the sinusoidal function f graphed below Calculator allowed The graph of y f

Solve the following inequality 8 5y 10 right side of the inequality 8 Subtract 8 from both sides of the inequality 8 5y 10 8 5y 8 2 10 8 5y 2 Simplify Type the terms of your expression in the same order as they appear in the original expression What is the next step to solve the inequality Divide both sides of the inequality by 5 Multiply both sides of the inequality by 5 Divide both sides of the inequality by the number expression found in the previous step www y 2 5 S Simplify Type the terms of your expression in the same order as they appear in the original expression

L f t P p 1 p 1 2p 1 then find L f 2t by applying change of scale property

Find an eigenvector of the matrix 92 44 24 5 48 corresponding to the eigenvalue A 1 0 0 5

Write the given trigonometric function as an algebraic expression in x and y 1 sin sin tan

Solve the inequality Graph the solution set and write it in interval notation 6 x 4 7 6 x 5 11 Choose the correct graph below O A O C 0 ACCED B O Points 0 of 1 0 0

Given z1 3 cos 43degree i sin 43degree z2 6 cos 17degree i sin 17degree find product z1 z2

Find the missing interest earned Principal Rate Compounded quarterly 1050 7 Time 10 years The amount of compound interest earned is Round to the nearest cent as needed Final Amount 2101 68 Compound Interest

The inverse of the logarithmic function f x logo 5x is f x 0 5 What values of a b and e complete the table for the inverse function X C y a DONE 2 4 1 b a 0 b 1 0 5 2 C

3 If 1 was written as x then what would be the value of n Explain your thinking x

The function f has domain 2 x 6 and is linear from 2 10 to 2 0 and from 2 0 to 6 4 A sketch of the graph of y f x is shown in Figure 2 2 iii Find g x YA 10 1 Write down the range of f ii Find ff 0 The function is defined by Figure 2 g x 4 3x 5 x iv Solve the equation gf x 16 6 XER x 5 X

5 This set of questions pertains to graphs of sine and cosine a Please examine this graph 38 12 83 2 128 12 Now please write a sine function which generates this graph In so doing please explain the relevance and calculation of amplitude period vertical shift midline and the variable c which relates to phase shift Please type a summary of your work b Here are the general forms of sine and cosine functions we studied in this class ya sinb 8 c d y a cos b 8 c d Consider the following properties of a graph of sine or cosine vertical shift midline phase shift amplitude period minimum output value maximum output value and value of 0 that generates a maximum output value b 1 Of these properties which ones can you figure out simply by inspection meaning by just visually observing the equation without any meaningful calculation Please justify your answer 4 sentences total please b 2 Of these properties which ones can you figure out simply by inspection and a little basic arithmetic Please justify your answer 3 sentences total please b 3 Of these properties which ones may require more complex calculation Please uld require more complex calculation 3

Write an equation of the line that passes through 3 5 3 2 and is perpendicular to the line defined by 5x 4 y Write the answer in slope intercept form if possible and in standard form Ax By C with smallest integer coefficients Use the Cannot be written button if applicable Part 0 2

Mary is in a boat in the ocean 48 mi from point A the closest point along a straight shoreline She needs to dock the boat at a marina x miles farther up the coast and then drive along the coast to point B 96 mi from point A Her boat travels 10 mph and she drives 60 mph If the total trip took 7 hr determine the distance x along the shoreline Mary 48 mi A Marina 96 mi B Add a VERY GOOD explanation I don t understand it Also tell me the exact algebra

Gion f x x for for x for 0 x obtain the Fourier series of the x interval x 27 to x 37 x 2

Simplify Choose all that apply to the answer 72 32 18 Select one or more a There is an odd number under the radical b There is an odd number outside the radical There is an even number under the radical d There is an even number outside the radical C

25 The larger of two numbers is 16 more than the smaller When added together the sum of the larger number and two times the smaller number is 97 What are the two numbers larger number smaller number

O O O O 8 8 8 one two 20 How many solutions does the following system have 1x 6y 2 3x 18y 6 34 74 3T none infinite 7T 3 A

nalyze the following graph of a system of two equations etermine the x and y values of the solution of the syster y

Use the discriminant to determine the amount real number roots the equation has 3x 5x 3 0 O one real root two real roots three real roots O no real roots 2 For the following equation Decide how many different real number roots the equation has x 8x 6 different real number root s

either the simplest fractional form or as a decimal that i rounded to the nearest hundredth x x 8 2 96 2 76 2 85 3 05 2 90 None of the above For the following equation Decide how many different real number roots the equation has 8 36 9 different real number root s

14 Solve the following by taking the square root 6 11 11 Round your answer to the nearest hundredth b 15 Solve the following by taking the square root 4a 26 68 Round your answer to the nearest hundredth a

8 Solve the following by taking the square root 3x 51 Round your answer to the nearest hundredth x 9 Solve the following by taking the square root 56 32 7 b O 2 79 O 2 70 O 2 76

Solve the equation using the quadratic formula 9x 5x 4 0 0 1 0 9 0

2 Solve the following by taking the square root y 35 Round your answer to the nearest hundredth y

4 Solve the equation by completing the square More than one answer may be correct check all that x 9x 18 X 11 3 0 3 6

3 Solve using the completing the square method More than one answer may be correct check all tha x 10x 22 0 x 07 3 3 O 5 3 5 3 13 0 7 3

2 Identify the number that needs to be added to both sides of the equation x 4x 45 to complete the square O 10 O 6 C

Simplify 1 4 8 3 5 50 5 4 80 7 4 20 9 5 64 11 80 13 3 12 15 3 8 7 2 27 2 3 48 4 4 30 6 2 48 8 3 16 10 45 12 2 64 14 5 18 16 4 50 18 2 18

Factor the following binomial 6 36 b 6 b 6 O b 6 b 6 O b 12 b 3 O b 12 b 3

Round your answer to the nearest hundredth x 8x9 3 1 3 9 29 9 55 1 29

Using the following equation and graph find the x value of the largest root of the quadratic Hint The largest number is the furthest to the right on the x axis or furthest up on the y axis x 10x 24 x

4 Given three consecutive odd integers their sum is two times the third number plus 13 What are the three numbers first number second number third number

For the following function one zero is given Find all other zeros f x x 6x2 13x 10 2 i List the remaining zeros other than 2 i The remaining zero s of f x is are Simplify your answers Type exact answers using radicals and i as needed Use comma to separate answers as needed

5 Using the following equation and graph find all the roots of the quadratic x 3x 4 y

Use synthetic division to perform the division x 4x 7x 6 x 2 x 4x 7x 6 x 2 16

Find missing angles AMC DMB and DBM in the following figure 70 620

10 Multiply out the following expression 4c c 6 c 6 Expanded expression

Match each expression to its simplified form Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE 36 36 24 72 III III III E E 6 2 2 6 61 6

5 The parent function for the graph below is of the form y ab Write the parent function Then write a function for the translation indicated Hi three points on the graph and run an exponential regression to find the parent function Then use the given translations to write the new function ty 20 2 4

Graph the trigonometric function y cos Plot all points corresponding to x intercepts minima and maxima within one cycle Then click on the graph a function butte