Complex numbers Questions and Answers

Compute the product 7 18 8 18 and write it as b 18 where b is a natural number less than 18 What is b

tree on a hillside casts a shadow c 220 ft down the hill If the angle of Inclination of the hillside is b 24 to the morizontal and the angle of elevation of the sun is a 54 find the height of the tree Round your answer to the nearest oot 303 X ft

Isolate the literal equation A bh for h 2 a h O b b h 26 2A O c h 2Ab d h 2b

Isolate w for the literal equation p 2w 2 O a w P 1 O b w P 21 2 O c w 2Pl w 1 2 O d

Given J X 2log3 x 3 und J a 0 2 b 2 c 9 d O 1 2187 1

For the literal equation d rt you can isolate the variable by dividing d by r t True False

Solve for x 3x 9 9 O a x 6 and x 56 9 O b x 6 O c x 2 and x 1 7 O d x 6 and x 0

Solve for m Select all answers that apply 6m 9 39 mark all correct answers a 22 5 b 2 c 8 O d 4 e 5 1 60 7

Match each equation with its solution a 8 b 0 c 6 d 3 1 3 1 x 2 2 n 6 8n 6 3 2 4 7b 3 117 4 4 7 8x 7 117

Plot the complex number in the complex plane 2 5 21 R

1 Solve the following equations for x 6 pts each a In 4x 15 0 b 2x 4x 32 c 96x 1 274x 3

The length width w and height h of a box change with time At a certain instant the dimensions are 6 m and w h 4 m and and w are increasing at a ra 7 m s while h is decreasing at a rate of 2 m s At that instant find the rates at which the following quantities are changing a The volume m s b The surface area m s c The length of a diagonal Round your answer to two decimal places Im s

Aaliyah needs to bake 42 servings of treats She has cooked 20 servings of treats already She has bars left to make and each bar is 2 servings Howany bars does she need to make Choose the correct equation a x 20 42 Ob 2x 20 42 c 2x 20 42 Od 20x 2 42

andscaping company charges a 12 fee to make a house call plus an hourly rate for labor If the total bill for a job that takes 2 5 hours comes to 95 75 write an uation that can be used to solve for the hourly labor rate Use r to represent the rate Then solve the equation and explain all steps CCO

Let f x ex and g x 4 ln x Find an expression for h x g x 10x a Oh x 4e 0x In x b O h x 40x c O h x x40 d O h x 4e10x e Oh x x f O None of these

10 What is the inverse operation of addition O multiplication O addition O division O subtraction E

7 Solve for y Explain all steps Y 8 15 3 R JU i 11 Font Famil

Simplify Do not use any spaces 8x 10x 5y 3 9y

Value 2 Simplify 1 x y x 3x O a x y b xy O c 2x 3y O d x O b

Use a half angle formula to evaluate the expression without using a calculator 1 2 CSC a What is the measure of the half angle CSC 2 Type an exact answer in terms of Use integers or fractions for any numbers in the expression b What is the measure of angle a X Type an exact answer in terms of Use integers or fractions for any numbers in the expression Show Transcribed Text c The terminal side of the half angle lies in Quadrant d Is the cosecant function and sine function positive or negative in this quadrant The cosecant function and sine function are in this quadrant 3 Use a half angle formula to evaluate the expression without using a calculator 17x 12 The half angle formula e Which half angle formula should be used to evaluate the expression csc 17 12 should be used to evaluate the expression csc 178 17x 12 Submit test

a Multiplicative Identity b Commutative Property of Addition c Commutative Property of Multiplication d Associative Property of Multiplication e Associative Property of Addition f Distributive Property g Additive Identity 1 3 5 4 3 5 4 2 4 2 9 4 2 9 3 10 5 5 10 4 6 5 5 6 5 5 0 5 6 8 1 8 7 5 3 8 15 40

A trigonometric function is given y 6 cos 7x a Find the amplitude period phase and horizontal shift of the function amplitude 6 period phase horizontal shift 0 10 5 10 b Sketch the graph of one complete period y 2n 0 10 y 5 10 0 0 4 Show Transcribed Text X y 10 x 5 10 y 10 5 10 p 7 4 4 X X

Value 3 A secretary was making name tags She made each name tag from an index card which was cut into s How many name tags can the secretary make with 2 index cards O a 8 Since each card will be cut into 1 4s and there are four 1 4s in 1 we can multiply 4 by two since there are two index cards to get the total number of name tags she can make O b 2 The secretary has two index cards and cuts them into 1 4s We can combine the whole number of cards with the fraction she will cut them into to get the number she will have when done O c 3 8 Since we have a fraction she will cut them into and a whole number of cards we need to get two fractions By putting 2 over 4 we can add directly across O d To get the total number of name tags the secretary can make out of two index cards we need to multiply the total number of index cards by the fraction she is going to cut them into

A cook has 4 cups of raisins to make oatmeal cookies The recipe requires cup of raisins for each batch of cookies How many batches of cookies can the cook make O a 1 Each recipe requires cup of raisins and we have four cups We can multiply the whole number by 1 to give us 4 3 which reduces down to 1 3 which is the number of batches of cookies we can make O b 12 To get the total number of batches we would need to divide our total number of cups by the amount the recipe requires To do so we flip our cup to make 3 1 and multiply by 4 Once we do that we then reduce to get the number of batches we can make O c Since we have a whole number of cups we need to make that a fraction by putting it over 3 and multiplying directly across O d 4 Since we have a whole number of cups of raisins and only need a fraction of them for the recipe we can combine the two to give us the number of batches we can make

Value 6 Match the problem to its reduced answer a N WA 00 ulawla ula b C 6 d e 24 1 5 1 8 2 2 14 7 3 3 10 20 4 5 5 m 3 4 5 6 25 18

The unknown triangle ABC has angle A 18 and sides a 6 and c 5 How many solutions are there for triangle ABC If there are infinitely many enter o Provide your answer below

Complete the table for the given function and then plot the resulting graph y 5 sin x X A 3 4 T 2 R4 0 R4 RIN A 2 y Type integers or decimals rounded to the nearest tenth as needed 3x 4

A coin is biased to show 40 heads and 60 tails The coin is tossed twice What is the probability that the coin turns up heads once and tails once OA 48 OB 40 OC 24 OD 60

84 voters are asked to rank four brands of cereal A B C and D The votes are summarized in the following preference table Determine the winner using the Borda count method Number of Votes 38 25 11 10 DABC A B CB First Choice Second Choice Third Choice Fourth Choice B CAA CD DD Select the winner below O O O C AD

14 6i 4 real and imaginary numbers

The following function is given f x x 1 3 x 6 x 5 x 5 a What is its derivative f x for x 0 2 x 1 3 6 b What is the derivative f x for x 0 2 x 4 7 c Give the x value where the derivative is not defined 0 d List the a coordinate of all the critical points of f x in increasing order for example 1 0 1 2 35 0 3 65 e Which other a values can give the maximum and minimum values of f x List them in increasing o 3 65 f Give the x coordinate of a point where f x takes its maximum value 5 g Give the x coordinate of a point where f x takes its minimum value

The graph of two functions f and g is illustrated below Use the graph to answer parts a through f 10 f x 10 y 21 2 1 4 1 g x 4 5 6 1 6 3 X 10 Q a f g 2 Simplify your answer b f g 4 Simplify your answer c f g 6 Simplify your answer d g f 6 Simplify your answer e f g 2 Simplify your answer f 4 Simplify your answer

Find the surface area of that portion of the sphere x y 2 8 which lies in the firs octant inside the cylinder x y 8y

Solve the equation for the given variable If your answer is a fraction write it in reduced fractional form Do not convert the answer to a decimal 2 4x4 x 5 16

The cone has the same radius as the hemisphere and that radius forms a 36 degree angle with the slant height of the cone Show Transcribed Text Find the total vol maining

valuate the combination C 44 25 44 25 Use scientific notation Round to three decimal places as needed Use the multiplication symbol in the m eeded

Simplify Assume all variables represent positive values 3 112x 7 28x

se a tree diagram for the following Find the number of ways 2 letters can be choosen from the set U V W if order is important and repetition is lowed Reconsider part a if no repeats are allowed Find the number of combinations of 3 elements taken 2 at a time Does this answer differ from part a or b The number of ways to select 2 letters from the set U V W if order is important and repetition is allowed is D The number of ways to select 2 letters from the set U V W if no repeats are allowed is

Question 7 of 23 Step 1 of 2 Consider the following system of equations 4x 5y 3 0 4x 2y Step 1 of 2 Determine if the point 1 2 lies on both of the lines in the system of equations by substituting the ordered pair into both equations Answer 2 Points 00 58 31 Yes No Key Keyboard Shor

Question 15 of 16 Step 1 of 1 R Divide using the division algorithm Write your answer in the form Q D Answer 2 Points where the degree of R is less than the degree of D 12 26r 11 41 2 00 45 1 Keyboard

A group of 10 workers decides to send a delegation of 3 to their supervisor to discuss their grievances Complete parts a through c below a How many delegations are possible There are 120 delegations possible b If it is decided that a particular worker must be in the delegation how many different delegations are possible There are 36 delegations possible c If there are 5 machinists in the group how many delegations would include at least 1 machinist delegations posible There are

Question 9 of 16 Step 1 of 1 Y Perform the indicated operation by removing the parentheses and combining like terms x 3x 6x 6x Answer 2 Points

Give the values of the radius r the measure of 0 in both degrees and radians the arc length s and the coordinates of the point P sh in the figure y 8 r 8 Round your answers to four decimal places if needed i e i S i P P 0 1 3 rad i X radians or i degrees

Multiply Write your answer as a fraction or as 2 1 4 times 1 1 3

Systems of equations that have different slopes and different y intercepts have Select Choice

Objective Function z 8x y Constraints x 0 y 0 3x 2y 3 a Graph the system of inequalities representing the constraints

5 For the complex number shown to the right give a its rectangular form and b its trigonometric polar form with r 0 0 s8 360 a The rectangular form is b Determine the polar form Select the correct choice below and fill in the answer box to complete your choice OA B O C O D cos sin cos sin isin icos isin icos Aimaginary rea

What is the radius of a sector when 0 2 radians and the 3 100T 27 sq units area is

Consider the figure to the right Determine the amplitude and midline of the periodic function and whether its graph is a vertical stretch and or vertical shift of the graph of y sint or y cost Midline y Amplitude The function is a vertical of Choose one Choose one shift stretch shift and stretch 4 5 9 y 13 5 2m 3x 47 m X

O Use the polygon to the right to complete parts a and b a Name the polygon If the polygon is a quadrilateral give its specific name b State whether or not the polygon is a regular polygon a What is the name of the polygon Hexagon Dodecagon Pentagon