Complex numbers Questions and Answers

31 REASONING Consider a function of the form f x a x h k Describe when the function is increasing or decreasing when a a 0 and b a 0 33 Let the graph of g be a reflection in the x axis of the graph of f x x 5 32 COLLEGE PREP In Exercises 33 36 write a rule for g described by the transformations of the graph of f Ay x 12 By x 12 Cy x 12 Dy x 12 y 161 8 8 34 Let the graph of g be a translation 4 graph of f x x 7

Use the box method to distribute and simplify 5x 4 5 2 Drag and drop the terms to the correct locations of the table c u t 12

The monthly payment p on a mortgage varies directly with the amount borrowed B If the monthly payment on a 30 year mortgage is 6 95 for every 1000 borrow ind a linear equation that relates the monthly payment p to the amount borrowed B for a mortgage with the same terms Then find the monthly payment p when the amount borrowed is 245 000 What is the general formula describing the variation Use k for the constant of proportionality Op kB O p B O p kB k PE B

Determine the following function h x 6 3 2x 5 Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The function has one horizontal asymptote Type an equation Use integers or fractions for any numbers in the equation OB The function has two horizontal asymptotes The top asymptote is and the bottom asymptote is Type equations Use integers or fractions for any numbers in the equation OC The function has no horizontal asymptotes

Find the absolute maximum and minimum values of f x y z 2x2y given that x y 16

Determine if the following function Answer

For the given functions f and g find the requested composite funct f x x 6 g x 8x 10 Find fog x A 2 2X 1 B 8 x 6 10 C 2 2x 1 D 8 x 4

Every complex number has a conjugate partner For instance a bi and a bi are conjugate pairs This is significant because whenever you multiply conjugate pairs the imaginary terms will cancel out leaving you with a product that is a Real number a bi a bi a bi a b i a b 1 a 6 We can take advantage of this when attempting to divide Complex numbers because it is preferable to have a denominator that is a Real number instead of Complex Rewrite the expression in a bi form Practice 2 4i 4 i

Simplify each expression using complex numbers a 233 b 282 C 151 d 248 11 0

Simplify the expression using complex numbers 9 i 9 i

Simplify the expression using complex numbers 1 i 2 52

Write the following expression in the standard form a bi zz where z 5 4i zz Simplify your answer

i Comment whether the sequence is Converges or diverges Obtain the first five terms of that sequence ii 1 np p 0

P2 Eliminate the cross product term by a suitable rotation of axes and identify the conic or th limiting form represented by the given equation a b c d 3x 10xy 3y 10 0 3 3 x xy y x y 13 2 4x 3xy 18 16x 24xy 9y 20x 15y 150

Match each phrase with its description uniform unimodal bimodal Choose Choose no peaks in the shape of the data 1 peak in the shape of the data 2 peaks in the shape of the data Choose

Consider the following a Write the ratio of red ma b Write the ratio of blue m

1 c 3 Yes it can be represe Yes it can be represe Yes it can be represe

1 Find the absolute values for each of the following complex numbers a 12 5 1 b 13 411 c 1 6 10 1 2 Simplify each of the following complex numbers b 9 0 12 c 98 6 8 10 1 c 24 g 45 10 28 4 4 12 12 24 1 6 2 m 6 3 n 2 10 0 15 10 p 8 6 k d 1 9 311 d 32 h 80

2A A 23 The dimensions in inches of 2 rectangular prisms are shown in the figure below The volume of the large prism is the same as the volume of how many of the small prisms A B C 246 X y N A 2r 2y 3z 4

Many calculations related to retirement planning are based on percentages A percentage is a part of 100 and is the same as a fraction or decimal For example 15 percent is the same as 15 100 which is 15 To calculate the percentage of a number change the percentage to a decimal and multiply by the number For example 15 percent of 200 15 100 x 200 or 15 x 200 30 Solve the following problems 1 Riley has been working as a high school principal for 30 years The formula for calculating retirement pensions in his school system is based on 2 percent multiplied by each year worked What is the percentage that will be used to calculate his retirement pension 2 Riley s annual retirement pension is based on his average salary over his career If his average salary is 50 000 what will be his annual retirement pension

Slope and Intercepts 1 Determine the slope and y intercept of the line segment 8 6 9 8 7 6 5 Slope 4 2 8 6 6 Ty 9 8 7 6 Slope y intercept 3 Determine the slope of the line that passes through 3 5 and 1 5 State the y intercept 4 3 2 1 TY 3 6 7 8 9 2 h 4 6 4 3 2 1 1 2 3 4 5 6 7 8 9 2 3 4 8 X 2 Draw a line that is steeper than the line to the left and passes through the same y intercept 914 8 7 6 3 4 3 2 1 3 2 1 1 2 3 4 5 6 7 8 9 2 3 4 9 8 7 6 5 4 3 9 8 7 6 5 4 3 2 1 5 6 7 8 Slope of the new line 4 Draw a line that is less steep than the line to the left and has a y intercept that is greater 8 7 6 5 4 3 2 1 X 2 1 1 2 3 4 5 6 7 8 9 24 3 4 5 6 7 8 Slope of the new line

10 nts 01 56 40 TB MC Qu 06 55 Static Which of Which of the following is not a common Inter Multiple Choice O A receipt should be provided to e

a Find the matrix for a shear in the that transforms the triangle with vertices 0 0 2 1 and 3 0 into a right triangle with the right angle at the origin x direction D Draw a figure that shows the image of the triangle with vertices 0 0 1 0 and 0 5 1 under a shear by a factor of 2 in the r direction

28 pts Note for this problem you are to select the values to be used in your calculation per the instructions in the bold sections in the following problem statement consider this a choose your own adventure or MADLIB style problem You have been tasked with collecting fast response pressure measurements with a Kulite XCQ 100 pressure transducer to be installed in a Mach 3 supersonic wind tunnel facility The critical unsteady flow physics you wish to study occur over a frequency band Hz equal to the 123 digits of your abc123 multiplied by 300 800 Design an active bandpass filter that will provide an amplification equal to the 123 digits of your abc123 multiplied by 2 while filtering out unwanted noise one decade above and below your measurement band a List the measurement frequency band in Hz and amplification per the instructions above 2 points b Draw a layout of your circuit 7 points c List your chosen target cutoff frequency values 4 points d List the chosen electronic components required to build this circuit i e op amp resistors capacitors inductors transistors flux capacitors etc Be specific if you require a resistor list the resistance value necessary and include it in your drawing 9 points e Recalculate your true cutoff frequencies based on your chosen components How do these compare to your target values 2 points f Calculate your final amplification factor in dB 2 points g If your op amp has a GBP of 5M would you achieve the design gain with this circuit 2 points

Find all zeros of the function f x 4r 28x 571 36 Entry tip Enter the zeros exact values not decimal approximations separated by comm

Find all zeros of f x x 2r 17x 28 Enter the zeros separated by commas Enter exact value not decimal approximations

a rectangualr prism has a volume of 60 and a width of 5 what are possible dimenstions for the length and width

List the possible rational zeros of 10 5x 8 Use to indicate the symbol So 1 becomes 1

1 y varies inversely as x y 4 when x 2 Determine the inverse variation equation Then determine y when x 16

Find any vertical asymptotes as we x 3x 28 f x x 7x 12 X Select the correct choice below ar

Find the greatest common factor of 6x and 15y x The greatest common factor is

25 Which is a factored form of 2x 32x 128 a 2 x 8 x 8 c 2 x 8 b 2 x 8 d 2 x 16 x 4 26 What is the GCF of 48ab and 32a b a 16ab c 4ab b 32a b d 32ab

Apply 15 At the grocery store Mr Arnett allowed each of his children to fill their own bag with trail mix for their hike The table shows the amount of trail mix for each child The trail mix costs 4 50 per pound How much will Mr Arnett pay for all the trail mix 4 5 15 75 3 5 17 FIND THE ERROR A student s work for converting 4 gallons to cups is shown A 8 Find the mistake and correct it e worl 16 gallons 4 gallons 1 cup d 16 A hockey player needs to shoot a puck 60 yards from his current location to his opponent s goal to score a goal After the shot the puck is 48 inches from his opponent s goal How many feet did the puck travel So d is equal to cup 4 od na 4 OF 19 The table shows the metric system conversions of length Larger Unit Smaller Unit 1 kilometer km 1 000 meters m 1 meter on 00s 100 centimeters cm 1 centimeter 10 millimeters mm Child How can you use ratio reasoning to find the number of centimeters in 2 2 kilometers Ava Grayson Mason Tyler Amount of Trail Mix oz 15 14 10 17 5102 3 51 16 AU 18 USE STRUCTURE When converting from larger units such as quarts to smaller units such as cups will the number of smaller units be greater than the number of larger units Explain your reasoning apn io to noting zeri vimet sout one Sholatophten orii ni se s opra 20 USE EFFICIENT METHODS There are 60 minutes in one hour and 60 seconds in one minute Using this information explain how you could convert 20 miles per hour to feet per second

Use any 7 Mrs Menary made 4 quarts of lemonade for a school party How many fluid ounces of g ad inu lemonade did she make dans 144 oz 3 9 The Martinez family has gallon of orange 4 juice in the refrigerator How many cups of orange juice are in the refrigerator Domsman POOHTAM THE 1 05 190 201 102 blues voy 11 A female hippopotamus can weigh 48 000 ounces How many tons can a female hippopotamus weigh 13 An elephant can drink up to 6 400 fluid ounces of water a day How many gallons of water can an elephant drink per day 8 A class walked 2 5 miles for a walk a thon How many yards did the class walk bi enollag A anollap at b quo que of isupe el b 02 10 A grand piano can weighton How many ounces can a grand piano weigh matayz ontem orit zworta eldst ritonal to enclave linu vallom2 12 At soccer practice Tracey s best kick m traveled a distance of 1 200 inches For how many yards did she kick the ball erit brit of pninbalian Saistomotol SS ni anatomin 14 A recipe for ice cream calls for 56 fluid ounces of milk How many pints of milk are there in the recipe

Find the vertical asymptote s of the graph of the function x 7 3 x h x

Find the vertical asymptote s of the graph of the function g x 1 x 3

Which equation is the inverse of 5y 4 x 3 6 11 10 X O y x 5 x 7 Oy 3 5x 2 0 5y 4 x 3 12 5x 7 O y 3 5x

01 20 O O x20 x 10 3 which inequality can be used to find the domain of f x x 1020 1 X 10 320

86 O x 1 O x 1 X 3 O x23 7 2 8 CO 6 4 TO 2 10 00 6 8 2 S 6 8 X

3 Arpi took a poll of the weights of 24 seniors The following data consist of the weights in pounds 195 206 100 98 150 210 195 106 195 108 180 212 104 195 102 99 206 116 83 142 100 135 98 160 Should she use a histogram or bar graph to display the data Create an appropriate graph chart Interval Frequency 51 100 101 150 151 200 201 250

test ion 1 Points 3 dimensions of the frame in the coordinate 1 inch 2 feet O 16 inches by 12 inches

Use the Remainder Theorem and synthetic division to evaluate the function at the given value f x 415 9x 9 6x 5x 3 f 5

Question 7 12 5 points Simplify the logarithmic expression log7 21 7 0 1 3 21 O 147 Question 8 12 5 points Simplify the logarithmic expression log 96 01 6

Consider the graph of f x 2x 4x 5x 5x 6 shown at the right How many zeros of the function must be imaginary 0 01 02 oo 5 f x 2x 4x 5x 5x 6 65432 123 2 1 co 95 1 2 3

Use Synthetic Division to evaluate 2x 3x x 1 when 3 O 25 23 8 25

5 points Factor 3x x 4 5 x 4 x 4 3x 5 x 4 3x 5 15x x 4 2 x 4 3x 5

Factor 9 r 3 x 3 x 3 x 3 x 3 x 3

Simplify 3 x2 52 5 x 8x 15 Rubric 2 points for the correct work 1 point for the correct answer

Identify the numerical coefficient of the term 7x

Identify all of the real cube roots of 343