Complex numbers Questions and Answers

Solve the inequality algebraically x 7 9 20 List the intervals and sign in each interval Complete the following table Type your answers in interval notation Use ascending order Interval Sign What is the solution Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers

KLMN is a rectangle Select the stateme are congruent Select two N K Opposite sides of a parallelogram are congruent Adjacent sides of a parallelogram are congruent AKLN AKLM by the angle side angle criterion AKLN ALKM by the side angle side criterion AKLN ALMN by the side angle side criterion M L

QRST is a rectangle Select the statements used to prove that its diagonals are congruent Select two T Q U Opposite sides of a parallelogram are congruent AQRT AQRS by the angle side angle criterion AQRT ARQS by the side angle side criterion Adjacent sides of a parallelogram are congruent AQRT ARST by the side angle side criterion S R

ABCD is a parallelogram Select the true statements used to prove that opposite angles of a parallelogram are congruent Select two A D a B Y 50 8 B C Za Zy because same side interior angles are congruent when a transversal crosses parallel lines La 28 because alternate interior angles are congruent when a transversal crosses parallel lines AABD ACDB by the side angle side congruence criterion AABD ACDB by the angle side angle congruence criterion 28 28 because same side interior angles are congruent when a transversal crosses parallel lines

For the triangle below mZA 122 c 36 and mZB 23 Find the length of side b b A C a B C Round your answer to the nearest tenth one decimal place

P h 25 AN Amplitude 47 The equation of the graph is of the form f 2 Asin Ba D where A B and D are real numbers Using the above information write the positive values for A B and D Period Vertical Shift

3 Create a trigonometric function that has an amplitude and a maximum of and a period c f x

3 Consider the parameters provided in the first column Match these with their corresponding trigonometric functions to model periodic phenomenon with specified amplitude frequency and midline Parameter 1 Period 27 Amplitude 1 Contain points 1 Parameter 2 Period 2 Amplitude 1 Contain points 2 1 Parameter 1 Parameter 2 DRAG DROP THE ANSWER f x 2 cos z 2 f x cos z f x f a 2 cos z 2

A y 1 cos x C y 1 sin x Find the equation KIN B y 1 cos x D y 1 sinx

1 2 3 ANNWA 4 Determine the period 4 8 12 16 20 24 28

4 3 2 1 1 2 3 4 Determine the period A 20 4 8 22 16 24 28

3 Area of the square is 49 sq ft 2x 3

Solve by completing the square d 18d 2 65 Enter any rational solutions as integers or reduced fractions If there are multiple solutions separate them using commas For no solution click No solution O No solution

3 Malt is standing on top of a cliff 305 feet above a lake The measurement of the angle of depression to a boat on the lake is 42 How far is the boat from Matt 4 A ladder that is 20 ft long is leaning against the side of a building If the angle formed between the ladder and the ground is 75 how far is the bottom of the ladder from the base of the building

4x Jennifer has a bag of chips that contains 2 red chips and 1 black chip If she also has a fair die what is the probability that she rolls an odd number and pulls a red chip x A B 13 10

4x If two triangles satisfy the SAS criteria which statements describe the rigid motions that would map one onto the other A A rotation and reflection would map one onto the other if the two triangles share a common side B A rotation and reflection would map one onto the other if the two triangles share a single common vertex C A translation rotation and reflection would map one onto the other if the two triangles share a single common vertex D A translation rotation and reflection would map one onto the other if the two triangles are distinct from each other 4x F A reflection would map one onto the other if the two triangles share a common sida

Find the length of BC 4x A 12 B 18 x C 16 G B 6 A 6 4 G E 6 F

11 10 9 8 7 6 5 4 3 2 1 m 19 2 123 to 6 9 10 11 Give the equation for the ellipse graphed above

4x 4x B 60 C 120 Oak Main 120 H 130 A city is planning to start construction of a new street The new street will be named Elm street and is represented by the red dashed line in the diagram Oak street Maple street and Cherry street are parallel to each other If Elm street is constructed so that it is parallel to Oak Maple and Cherry what will be the measure of angle 2 4x D 50 Broad Maple Cherry 3 2 Elm

The quadrilateral shown is a rectangle What is the measure of CE A C 15 10 D 14 E 30 C

ines a and b are parallel What is the measure of 47 if 22 measures 68 4x 4x A B C C 112 56 be 68 1 2 7 8 3 4 5 6

THIS or THAT Choose This problem or That problem to answer for a total of 10 points Determine the number of compounding periods n nts Determine the interest rate i per compounding period Determine the values of P n and i in the formula A P 1 i olve the problem THIS 2 points Annual compounding for 10 years Quarterly compounding for 6 years 4 5 compounded semi annually Mays invested 500 for 5 years at 8 compounded annually Hasan invests 925 into a savings account that earns 6 per year compounded quarterly for 3 years Find the total amount in the account THAT 3 points 13 compounded bi weekly Talha borrowed 700 for 2 years at 12 compounded monthly Omer invests 1400 in a GIC that compounded quarterly for 3 years earns 5 interest per year Find the amount of interest earned

X 330 22 18 11 289 97 X 12 740 8 8 m 9 15 10 5 X 152 1 9 3 40 7 4 111 1 12 104 6

1 Identify if the SINE LAW or COSINE LAW should be used 2 List whether angle or side version of the equation should be used 12 marks

4 Water wheels are still used to power lumber mills in historic parks A typical water wheel makes 1 complete revolution every 90 seconds A paddle starts its cycle 1 meter below the level of the water and reaches a maximum height of 4 meters above the water Assume that the timing starts when the paddle is at the top of the water wheel A Make a graph that motion of the wheel represents the B What is the amplitude and period of the water wheel C How high is the center of the wheel above the level of the water 27 D What is the equation of this function 1011 Ay 3 18

Two systems of equations are given below For each system choose the best description of its solution If applicable give the solution System A x 4y 8 0 x 4y 8 System B x 3y 9 x 3y 9 O The system has no solution The system has a unique solution x y D The system has infinitely many solutions They must satisfy the following equation y 2 x O The system has no solution O The system has a unique solution x y D The system has infinitely many solutions They must satisfy the following equation m

Find the exact value of the following without using a calculator in sin 4 tan 4 sin sin tan 4 Simplify your answer Type an exact answer using radicals as needed Rationalize all denominato

Diverges The answer above is NOT correct Sum Diverges Find the sum of the following infinite series If it is divergent type Diverges or D 8 7 2 49

Choose the best term from the Word List Write it on the blank 1 A display that shows how many times an event occurs is a n bar graph compare frequency table overestimate underestimate 2 A display that uses bars to show data is a n 3 Rounding each factor in a multiplication to a greater number gives a n of the actual product 4 You can use the length of the bars in a bar graph to two similar data sets

Use the bar graph to answer the questions 14 Which animal has about 34 teeth 15 About how many more teeth does a dog have than a hyena 16 About how many more teeth does a hyena have than a walrus Number of Teeth 45 40 35 30 25 20 15 10 5 0 Animal Teeth Dog Hyena Walrus Animal

Write number sentences to show your work a What is the largest answer you can find Practice b What is the smallest answer you can find 4 3 2 1 2 4 5 2 8 Using only the unused tiles and any operation 1 3 89 5 99 592 100 100 Pa 0 1 2 3 4 5 6 7 8 9 O 1 2 3 4 5 6 7 8 9

Given the following tables determine which one is not a function x1234 y1234 All of the tables are functions x36912 y1223 x0123 y3210 x 4 202 ly 5 7 9 5

The values in the table represent an exponential function What is the common ratio of the associated geometric sequence X 1 2 3 4 5 y 6 36 216 1296 7776

Level 4 Mastered COMPLETE ONE OF THE FOLLOWING CORRECTLY TO EARN AA 1 Domain ange A x A Graph the function y log x and fill out the table below to help you graph 1 9 b Describe the domain and range of the function c Suppose your graph was transformed 3 units up and 1 unit right Write the equation that would match that graph Match each equation with a graph that represents it y log x yu log10 y loggx y In x 10 100 200

Level 2 Emerging 1 a Select all that are equivalent to tog 8 HL HIL iv V log 20 log 125 log100 log 27 log 0 0001 b Give an example of a logarithmic expression that evaluates to 1 2 Solve the following equations a log 50x log x 2 2 olve Graph the following equations b 2log x 6 Level 3 Proficient 1 A video posted on YouTube initially had 80 views as soon as it was posted The total number views to date has been increasing exponentially according to the exponential growth functi y 80 e where r represents time measured in days since the video was posted How many days does it take until 2500 people have viewed this video 0 28 h log 4 log c 9 5

16 A bird feeder is full of seed Written as a decimal how full is the bird feeder 1 17 Which expression is equivalent to 5 2 5 2 5 2 13 F13 6 15 3 7 I3 10 2 3 3

12 A tee box is 48 feet above its fairway Starting with an initial elevation of 48ft at the tee box and an initial velocity of 32 ft s the quadratic equation 0 16t 32t 48 gives the time t in seconds when a golf ball is at the height 0 feet on the fairway a Solve by factoring to determine how long the ball is in the air b What is the height of the ball at 1 second C What is the maximum height the ball reaches and when is it at its maximum height

Solve each problem and check all solutions Answer using a complete sentence 1 A boat goes 240 miles downstream in the same time it can go 160 miles upstream The speed of the current is 5 miles per hour What is the speed of the boat in still water Upstream Downstream Distance Rate Time

In Exercises 3 6 graph the quadratic function Label the vertex axis of symmetry and x intercepts Describe the domain and range of the function 3 f x x 3 x 1 4 y x 5 x 1 5 f x 2x 16x 6 y x 8x 7

3 Find all 3rd roots of 8 and show them on the complex plane

1 If Z 2 3i and Z 1 2i find Z Z2 using rectangular form

Consider the following letter to Dear Abby from The Tennessean on January 20 1973 Dear Abby You wrote in your column that a woman is pregnant for 266 days Who said so I carried my baby for ten months and 5 days and there is no doubt about it because I know the exact date my baby was conceived Please print a retraction about this 266 day carrying time because otherwise my friends won t believe me San Diego Reader Dear San Diego Reader The average gestation period is 266 days Some babies come early others come late Yours was late Task The length of human pregnancies is normally distributed with a mean of 266 days and a standar deviation of 16 days Was San Diego Reader s length of pregnancy unusual Explain your answer usin lodge of normal distributions

Use the mixed constraint simplex method to maximize subject to If there are no solutions enter None for P Maximum value is P where 1 P 8x1 4x2 x1 I2 28 4x1 5x2 120 x1 2x 37 1 20 T 20

3 Use the spinners below to answer the following questions P Q R 1 3 2 24 8 6 13 11X5 97 a 3pts If you were required to create a complete organized list how many members would the list have representing the three spinners above spinners P Q and R b 3pts What is the probability sum of the spinners six write you answer to the nearest 1000ths

Q7 Given the function f x ex f 0 5 can be estimated using backward finite divided difference with h 0 1 and 0 h as A 0 607 B 0 638 C 0 706 D 0 607 E 0 503

Is y 3t cos t 3t a solution of the initial value problem below dy y 3t sin t Y 0 dt Yes No Is this differential equation pure time autonomous or nonautomonous O pure time O autonomous

1 Follow the steps below to help you prove or disprove that the point 1 V15 lies on the circle that is centered at the origin and contains the point 0 4 To earn fu credit you must show your work Step 1 Plot a point at the origin and at 0 4 Use these to help you draw the circle centered at the origin that contains 0 4 Step 2 Determine the radius Step 3 Use the radius and the coordinates of the center to write the equation of the circle Step 4 Substitute the x and y coordinates of the point 1 V15 in the equation of the circle to check whether they satisfy the equation

Find all zeros of the polynomial function f z 2z 92 3z 34z 24 by answering each part a Using the Rational Zero Test list all possible rational zeros b Show that 2 is a zero of f x Solution Paper c Find the remaining zeros of f x Solution Paper d Write the complete linear factorization of f x Solution Paper

Answer x 6y 4 4x 24y 18 O Only One Solution O Inconsistent System O Dependent System Keypar Keyboard Shortc

1 The stem and leaf plot below shows the number of kilometers walked by participants in a benefit walk Find the median mode and range of the data Number of Kilometers Walked by Participants 12 0 3 7 9 9 13 0 1 5 5 14 0 0 2 3 3 8 15 1 2 2 2 2 57 16 05 59 99 17 0 4 5 1213 means 12 3 A median 15 1 km mode 15 2 km range 5 5 km OB median 15 2 km mode 12 9 km range 5 km C median 15 1 km mode 16 9 km range 5 km D median 14 8 km mode 16 9 km range 5 5 km