Complex numbers Questions and Answers

Ex The time t required to empty a tank varies inversely as as the rate of pumping If a pump can empty a tank in 2 5 hours at a rate of 400 gallons per minute how long will it take to empty a tank at 500 gallons per minute

kx Combined Variation y Mixes direct and indirect variation Z

Find all the real fourth roots of 16 Choose all that apply Select one or more a There are no real fourth roots b 2 2 O d 4 Oe 4 c

Simplify 2x y4z6 2 3 8 6 x y z Select one O a 2xy z6 O b 4xy z6 O c 4xz O d 2xz18 18

Find all the real fourth roots of 0 0081 Choose all that apply Select one or more O a There are no real fourth roots of the number O b 0 3 c 0 3 d 0 03 0 e 0 03

Find the real solutions of the equation Choose all that apply 16 81 8 Select one or more O a 4 9 O b 4 9 c 2 3 d 2 3 Oe There are not real solutions Check

tx x 50x 40 Muncion write in tactored form The complex zeros off are Simplity your answer Type an exact answor using radicals and i as needed Use integers or fractions for any numbers in the expression Use a commus to separate answers as

A local flooring company is retiling your kitchen Your kitchen is a rectangle with dimensions of 10 ft by 16 ft You are going to use square tiles that measure 6 by 6 inches Assuming the tiles lay completely flush with one another on the floor no space in between How many tiles will the flooring company need to buy 6 inches feet Area of kitchen Area of 1 tile How many tiles will the flooring company need to buy

Determine the values of a for which the system has no solutions exactly one solution or infinitely many solutions x 3y z 2 3x y 2z 3 5x 5y a 9 z a 4 For a i For a For at there is no solution there are infinitely many solutions the system has exactly one solution

Find the 80th percentile of the IQ scores distribution of 20 to 34 year olds

0 5 a Find the point of intersection of the tangent lines to the curve r t 3 sin at 2 sin t 6 os t at the points where t 0 and t x y z b Find both tangent lines Illustrate by graphing the curve and both tangent lines The tangent lines will be plotted for 1 u 1 Select Update Graph to see your responses plotted on the screen Select the Submit button to grade your responses x u y u z u tangent line at t 0 tangent line at t 0 5 x u y u z u

The instructions say begin by graphing the standard quadratic function f x x 2 then use transformations of this graph to graph the given functions my professor already gives me the answer so I know what the answer is but I have to show my work more importantly I want to understand how to do this question so if you could please take it step by step i would really appreciate it i get that 7 2 is the vertex and thats the first point but how do you get the rest using 1 3 9 g x x 7 2 3 10 8 6 4 10 TO X

3 033 x 10 in decimal form erHow to enter your answer opens in new window 2 Poi Keypad Xx

Divide 7 3i by 5 2i and simplify completely Show Transcribed Text r

Equations and Inequalities Solve multi step inequalities A federal grant can give Chicago Vocational Career Academy 5 000 for the first day of school However that amount decreases by 5 for every student that misses the first day The high school hopes to keep at least 4 650 from the grant If s is the number of students absent on the first day which of the following inequalities correctly models the scenario O 4 650 5s 5 000 less than 70 students miss O 5 000 5s 4 650 no more than 70 students O 5s 4 650 5 000 less than 20 students miss 5 000 4 650 5 s less than 35 students miss

3 1 mark The basic period of 13 sin x 9 is given by a 2 C T a b C b KIN d e 1

Which of the following relationships are true Select one or more a None are true b cos B sec B 1 sin A csc A 1 All are true cos A sin A 1 cot A tan A 1 c Od e Of

When simplifying the following expression 1 1 sing 1 1 sin 0 the denominator is

A Given the above Triangle If a 12 c 16 then the tan A cot C Select one 25 a b C C d w o ula N W 510 12 a B 3

1 2 3 4 5 10 15 15 oz to 16 00 oz 15 85 oz to 16 00 oz 15 85 oz to 16 15 oz 16 15 oz to 16 45 oz TIME REMAINING 01 53 18 A company manufactures 16 oz boxes of cereal Boxes are randomly weighted to ensure the correct amount If the discrepancy in weight is more than 0 15 oz the production is stopped What is the range of acceptable values for production to continue

3 Which of these points is further from the origin 5 2 1 or 3 4i

If 3 1 is a point on the graph of y f x which of the following must be on the graph of y f x Choose the correct answer below O 1 3 O 1 3 O 3 1 O 3 1

c Water leaked from a tank at a rate of r t liters per hour The rate decreased as time passed and values of the rate at three hour time intervals are shown in the table Find lower and upper estimates for the total amount of water that leake out T h 0 3 6 9 12 15 r t l h 9 8 8 6 7 4 6 3 5 1 5 3

The graph below depicts a function Its one asymptote is indicated in re Domain of f y 23

12 At a nursery you pay 6 for 2 plants At this price how much would you pay for 11 plants Type a response

At the same time that a 5ft tall girl casts a 12 ft shadow a flagpole casts a 30 ft shadow How tall is the flagpole Type a response

In 7 hours Marc can package 30 orders At this rate how many orders can he package in 42 hours Type a response Bu Pag

0 You can buy 6 pairs of socks for 9 At this price how many pairs can you buy for 36 Type a response

Given the quadratic function f x x 4 3 What point is the symmetric point to the vertical intercept 8 1 8 1 8 1

Plot the following set on the complex plane ze C z 1 1 n z e C Re z 1 Given that z 1 i is one solution solve the equation z 3 8z 10 0

Solve each equation or inequality Check your solutions 6 251 1 6 3 b 0 2 O 2 2 02 00

Solve each equation or inequality Check your solutions 4v Sv v 1 O 1 2 0 2 v 2 O 1 2 v2 3v 2

If y varies directly as z and inversely as x and y 18 and z 3 when x 6 find y when x 5 and z 5 18 9 64 36 1 pts Question 13

Solve each equation or inequality Check your solutions 02 0 2 W 3 O 2 2 7

O If y varies inversely as x and y 16 when x 4 find y when x 3 O 12 Zm 03 4 O 16 Question 6 11

In Quadrant II which functions are negative Select one or more a Sine b Cosine c Cosecant d Tangent

Find the point on the Unit Circle associated with the angle T 3 Select one O a 3 2 1 2 b 1 2 3 2 C 1 2 3 2 d 1 2 3 2 OC

4 9 12 A line has the equation 3x 2y 12 2 points each q 2 2 a Find the x intercept b Find the y intercept 1 2 c Find the slope

7 Find the distance between 2 3 and 1 2 Leave your answer in exact form 2 points 2 6 30 2 5 1 2

b sin 8 cos 8 tan 8 csc 8 8 15 y 0

Find an equation of the line containing the given pair of points 2 4 and 6 7 y Simplify your answer Type your answer in slope intercept form Use integers or fractions for any numbe the expression

pitilsurenl bns proljon 9 The table shows some of Mr Puhas s household Expense Amount expenses for the month of February Mr Puhas has riw esex fue nousupa oru r 500 set aside for utilities Use an equation to Insurance 105 determine how much money he will have after he Utilities pays for February s utilities d bluos for 12 29162 Mortgage 1 10 The city of Montgomery collects 4 times more tons of plastic than tons of glass in their recycling program The city collected 80 tons of glass in June How much plastic did the city collect in June er w a doidWazlobniut srit 910led enit brit of beau ed bluo noitsup9 Tb 192161bul edt 16 beals1 juoms viqqs terit lle toele2 821 b 80S A 11 The table shows the nutrition information for two types of trail mix Cecilia wants to compare the Calories in a single serving of each type of trail mix EOS b 820 Part A Find the number of Calories per serving of each type of trail mix S B destisponA 25lim slim 61 inom br 19f291 Sn119120016 In grit of noltulo2 gril ai 19dmun raidW Sap w noit up Calories Protein g Fiber g Part B Determine which type of trail mix has more Calories per serving and by how much C 8 n 553 D 553 7 n 15 S in noutaupo eru gniau constelb gill m to oulev orti al tertw 12 McKenzie delivers coupons to her neighborhood This week she has 553 coupons to deliver If she wants to give 7 coupons to each neighbor which equation can be used to find the number of neighbors n to whom McKenzie can give coupons A 553n 7 553 7 7 12 Type ASE 3 servings 4 servings DE 375 1 075 319 a w A 2 8 Type Bo2E 520 21 man utbiq St vud nso nobre18 A rose to 1200 or el tariW ST2 101 femmit suic 9 X1018 1022

4 A package of silicon This is 7 less than the cost of a package of metal straws Select the equations that could be used to find the cost c of the package of metal straws A 7 C 6 c 7 6 cx7 6 6 7 C 6 7 C 5 Which algebraic expression represents the phrase eleven centimeters taller than twice the original height Let h represent the original height A 2h 11 2 h 11 2h 11 dola A 15 6x 18 2x 7x 3x 15 12 6 Which expressions are equivalent to 4x 3 Select all that apply 3 2x 4 9 10x 28 x 25 3x 12x 2 3 4x 3 stunt

Find cos a b if sin a 17 where a is in the fourth quadrant and 8 20 tan b 21 where b is in the second quadrant A B 468 493 132 493 C 155 493 D 475 493

Suppose that sin t OA A 529 625 B 336 625 C 527 625 D 527 625 7 where t is in the first quadrant Find Cos 2t 25

Complete the following a The graph of y x is shown Draw the graph of y 2h x 4 TERESES X D G b The graph of y g x is shown Draw the graph of y g x 1

Solve the system of equations by graphing x y 5 4x 3y 18 If there is a unique solution write the solution as an ordered pair One solution O No solution O Infinite number of solutions

The engine in a car has eight cylinders Each cylinder is a right cylinder with a diameter of 3 126 in and a height of 2 in Find the total displacement volume of this engine Use button on your calculator The total displacement volume of this engine is Type an integer or a decimal Round to the nearest hundredth as needed

Given the triangle ABC if angle A is 40 angle B is 70 and side a is 25 ft What is the distance of side b Round to one decimal Select one O a 17 1 ft O b 11 2 ft O c 36 5 ft O d 26 6 ft

Solve for the length of side c C A b 2 Select one a 2 O b 8 4 3 1 2 O c 2 3 Od 4 120 c a 2 B