Complex numbers Questions and Answers

23 In six years Rose will be two times as old as Anne Four years ago Anne was one third the age of Rose How old are they now ni aslimi

24 A boat can go 26 miles downstream in the same time it takes to go 6 miles upstream The rate of the water is 5 mph What is the rate of the boat

3 There are 62 miles in 1 kilometer How many miles are there in 10 kilometers

Evaluate 10 4 2 n 1 n 1 S member for a geometric series S 1 r 1 r

Find the area of the figure given to the right Round to the nearest hundredth The area of the figure is approximately 3N m m 6 18 m

Find the missing dimension of the figure shown to the right Round to the nearest tenth The missing dimension is approximately in 11 14

Find the perimeter and area of the figure shown to the right Assume right angles and parallel sides except where obviously otherwise The perimeter of the given figure is 11 m J 11 m 53 m 5

Find the perimeter and area of the figure Assume right angles and parallel sides except where obviously otherwise The perimeter of the figure is Simplify your answer BE 20 8 12 5

Find the perimeter of the polygon shown to the right The perimeter of the polygon is Simplify yo in O Points 0 of 1 12 22 59 37

In the figure shown to the right two parallel lines are cut by a third line Find 4w 4x 4y and 4z 4 w 104 W OF

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For the triangle shown to the right two angles are given Find the third angle without using a protractor The measure of the third angle ZE is D 29 E 16 F

In the figure shown to the right one angle measurement is given Find 4p 4p D P 570

the figure shown to the right one angle measurement is given Find a b and c da O a 151 C

Consider the following triangle C 124 a 36 b 56 Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle Law of Sines Law of Cosines Solve if possible the triangle If two solutions exist find both Round your answers to two decimal pr A B 0

K rev In an effort to control vegetation overgrowth 96 rabbits are released in an isolated area free of predators If the population after 1 year has increased to 288 rabbits what will the population be after another 6 months Round your answer to the nearest rabbit Answer 2 Points rabbits Keypad Keyboard Shortcuts N

f x Answer 2 Points 4 x 1 2 36 x 5 Step 3 of 3 Evaluate this function at x 4 Write the exact answer Do not round If the answer is undefined write Und as your answer f 4 if x 1 8 ifx 1 Keypa Keyboard Short

Prev Blanche has recently inherited 7900 which she wants to deposit into a savings account She has determined that her two best bets are an account that compounds semi annually at an annual rate of 4 2 Account 1 and an account that compounds continuously at an annual rate of 4 3 Account 2 Step 1 of 2 Which account would pay Blanche more interest Answer 2 Points O Account 1 O Account 2 Keypad Keyboard Shortcuts N

ev Use the elementary properties of logarithms to solve the following equation Round your final answer to four decimal places if necessary Use e 2 71828 if necessary If there is no solution write for your answer Answer 2 Points X In 6x 8 5 Keypad Keyboard Shortcuts

Find an equation for the asymptote of the exponential function y 2 2 3 Answer 2 Points y 3

Find all values of a in degrees that satisfy the equation sec 3a 6 5 Show Transcribed Text S C Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The solution set is ala k where k is any integer Simplify your answers Use angle measures greater than 0 and less than or equal to 120 B The solution set is alax kor a Simplify your answers Use angle measures greater than 0 and where k is any integer

points Here are pairs of equivalent expressions one in standard form and the other in factored form Find the missing numbers 1 x 18 x and x 1 x 17

Voltage through a circuit is determined by the formula V PR where P is power measured in watts and R is the resistance measured in ohms Round answers to two decimal places as needed a Determine the amount of resistance that is required for 2 watts of power to produce 4 volts b Determine the voltage produced if 100 watts is supplied with a resistance of 40 ohms c Determine the amount of power that must be supplied in order to produce 50 volts if the resistance is 30 ohms

The diagram below shows a right triangle that has side lengths of 7 45 and 2 31 cm One of the interior angles of the triangle measures 0 degrees Note that this question allows you to use trig functions that evaluate for angle measures in degrees To remind yourself how to evaluate trig functions for angle measures in degrees in this program click here 7 45 cm What is the value of 0 tan 1 2 31 7 45 2 31 1 7 45 tan 2 31 cm Preview 0 30066689878063946 Try again What is the value of tan 0 How can we use that value to determine the value of 02

Circle with center 3 1 and point on the circle 3 7

L Spinner A is spun and then Spinner B is spun Show two ways to represent the sample space for probability experiment Red Blue Spinner A G M F 120 N Spinner B

A B C If log 3 log p D p t rz 2 log t log r then the value of x is

6 The following data sets gives the approximate lengths of Beet and Mahler s nine symphonies in minutes 38 26 68 50 33 30 40 52 85 94 50 72 72 80 90 80 a Find the mean median and range for each of the two data sets Beethoven Mean Beethoven Median Beethoven Mode Beethoven 28 36 Mahler Beethoven Range 71 Mahler Mean Beethoven standard deviation Mahler Median Mahler Mode Mahler Range b Find the standard deviation for each of the data sets

5 The following table shows the average monthly precipita tion in Seattle Washington from March through August a Find the median monthly total for the six month period b Find the mean monthly total c Find the range of the monthly averages March April May June July August Imetres

Value of p Select Focus Select Directrix Select Vertex Select 6 A 2 2 Line of Symmetry Select 10

e table shows the number of boys and girls that have black blonde brown or red hair color at is the probability that one of the boys has blonde hair round to nearest hundredth x x x A 0 10 B 0 20 C 0 25 D Hair Color Boys Girls Black 5 Blonde 6 Brown 8 Red 1 0 15 4 4 10 2

Sandeep and Ann want to buy the condo they are currently renting They have some money in a savings account but the condo costs twice that much If the account earns 6 interest compounded continuously how long will it take for their money to double Round your answer to the nearest month years and months

4x The numbers 4 5 6 and 7 are on a spinner You spin the spinner twice Which calculation proves that landing on an even number for the first spin and the second spin are independent events x x x Xx A B C D 111 x E P A and B P A and B P A and B P A and B P A and B 2 2 24 2 4 1 1 44 22 44 24 11 24 24 4

4 Sketch a graph of a function g that satisfies each of the following Feel free to use the circles to check off each condition as you graph it or you can check them off to double check your graph Og is continuous everywhere except at three points x 4 x 1 and x 6 Og has vertical asymptotes at both x 4 and x 6 g has a jump discontinuity at x 1 Olim g x 2 Olim g x 1 O g 1 3 Og is decreasing on the interval 1 1 U 1 6 g is increasing on the interval 4 U 4 1 U 6 00 Og has a local maximum at x 0

Kari wanted to buy a new guitar Kari deposited 929 00 into a new savings account that earns interest compounded continuously After 5 months she withdrew the entire balance of 944 00 and bought the guitar What was the interest rate on the account Round your answer to the nearest tenth of a percent

In Marvel comics T Challa aka The Black Panther as the king of Wakanda is estimated to be worth 90 trillion 9 x 1013 dollars Tony Stark aka Iron Man is only worth about 30 billion 3 x 1010 dollars If Tony Stark could somehow add a 10 increase in his wealth to his current worth each year 30 billion 63 billion 99 3 billion etc how many years would it take to reach T Challa Round your answer to the nearest year

2 You are given that ABEL APUZ and the following m B 51 mZZ 66 BE 11 in BL 20 in PU 352 in Using the similarity relationship between these two triangles determine as much information as possib about the triangles angle measures and side lengths

Destiny deposits some money into a new savings account that earns 7 interest compounded continuously How long will it take for the money to double Round your answer to the nearest month years and months

5 Line SD is a line of symmetry for figure ASMHZDPX Tyler says that ASDPX is congruent to SMDZH because sides AS and MS are corresponding S M A Z H X D a Why is Tyler s congruence statement incorrect b Write a correct congruence statement for the pentagons

1 What is found near at a subduction zone Cascadia Subbuction zom Use the chart on the earth s interior complete the following table Depth km 500 2000 Page 10 2900 Pressure millions of atmosphere Temperature C Density g cm PHEPE PLA Region Lower MANTLE Asthenosphere Middle of outer core Center of the Earth

Question 24 A tourist in a sightseeing balloon drops his cell phone from a height of 670 feet above the ground see picture Find the time t in seconds for the object to reach the ground The height above ground of the object is modeled by Height 16t 670 670 feet t How many seconds will it take the object to hit the ground seconds round to 5 decimal places Check Answer If you are curious about the terminal velocity of an object go to http en wikipedia org wiki Terminal velocity

Let f x 7x 6 and g x x 5x 6 Then fog x f

Cameron deposited 3 000 00 into a new savings account that earns 13 interest compounded continuously How long will it take for the balance to grow to 3 266 00 Round to nearest month 4 Port

1 Rearrange so x terms and y terms are grouped together and write after each group to leave space for completing the square 2 Complete the square for the x terms Remember to add your new constant to the right side of the equal sign 3 Compete the square for the y terms Remember to add your new constant to the right side of the equal sign 4 Rewrite the x terms as a perfect square then rewrite the y terms as a perfect square Combine all constants on the right side of the equal sign 5 State the center and radius of the circle then graph Center Radius x y 4x 2y 11

g x 7 Drag the sets into the boxes to identify the domain and range of the function Show Hints domain range

DIRECTIONS Use this information to answer Parts A B C and D f x 2 x 2 22 32 10 Dotted lines represent any asymptotes on the graph An open circle represents any holes of the graph Part A Choose the graph of the rational function Which is the correct graph D US 10 35 O Show Hints 15 E 15 TO 10 G AA W M A 10 5 81 45 y 10 10 s

Which of the following transformations can you apply to the graph of f x to produce the graph of g x Show Hints O a reflection across the line y x O a translation down 1 unit a reflection across the line y x O a reflection across the x axis Use a graphing calculator to verify the transformation

Find the midpoint of the line segment from 1 1 to 5 4 Midpoint m

Members of the Gigantic State U football team are being chosen at random for steroids use testing using a JuiceDetector test and Hugo Huge gets selected The test comes negative for 97 of subjects who do not use steroids Take E The test gives a positive result F Hugo uses steroids given information tells us that A P EF 0 97 BP EF 0 97 CP EF 0 97 DP E F 0 97

14 Mr Banks deposited 5000 into an account that earns 3 5 interest compounded annually and he will let it accrue money for 7 years About how much more money would he get if he deposited the same sum of money in an account that compounds interest continuously Compound Interest Formula T A P 1 nt 72 Continuous Compound Formula A Pert A It would be the same amount B 25 12 29 23