Complex numbers Questions and Answers

Question 2 Let p be prime Using Fermat s little theorem prove that n 2P 2 2 x 5P 10P 2 1 is a multiple of p if and only if p 2 5 Hint for p 2 5 consider 10n

20 p 3 Find the solution of the differential equation y 7y 10y satisfying the initial conditions y 0 0 y 0 9

TC f x 1 0 70 2 X 2 f x x 1 cos 2x cos 4 4x T 3 15 2 35 cos 6x 11

5 Find fog and go f and their domains f x x 4 g x x

A luxury car and a mid sized sedan were purchased in 2012 The luxury car was purchased for 90 000 and depreciates loses value at a rate of 6 250 per year The mid sized sedan was purchased for 35 000 and depreciates loses value at a rate of 1 250 per year Write an equation relating yy the luxury car s value to xx the number of years since 2012 Write an equation relating yy the sedan s value to xx the number of years since 2012

The half life of Radium 226 is 1590 years If a sample contains 200 mg how many mg will remain after 4000 years mg Give your answer accurate to at least 2 decimal places

Which inequality has the graph shown below 1 0 Oy x 3 Oy 2x 3 Oy x 3 O y 2x 3

Graph the parabola and find its vertex and the axis of the parabola f x x 4 The vertex is

Suppose there are three delegates to a county convention Abby has 30 votes Brian has 20 votes and Cierra has 10 votes a 3 pts What is the quota Show your calculations b 5 pts Fill in the chart to find the critical voters Total Votes Winning Coalition Yes or No Coalition A 30 B 20 C 10 A 30 B 20 A 30 A 30 C 10 B 20 C 10 B 20 C 10 Critical Voters

Read the passage Finding the Invisible All over the planet ancient tombs and temples lie hidden from view So how do archaeologists know where to begin digging Thanks to satellites that question is becoming easier to answer In the pioneering field of satellite archaeology satellites four hundred miles above Earth can identify structures buried under soil covered by modern construction or obscured by forests For example mud bricks used by ancient Egyptians are more dense than soil and the differences are detected by the satellites Advanced computer programs map buried settlements and distinguish them from water vegetation and farmland Sarah Parcak a pioneer in the field says of the technology It allows you to literally strip away vegetation and see entire cities beneath the rain forest canopy This is the unbelievable future of archaeology What is the main idea of the passage Satellite archaeology is a rapidly expanding new scientific field Archaeologists are uncovering ancient hidden structures by using satellite imagery

Given a 18 and b 20 find the missing side and angles in the right triangle where a is the side across from angle A b across from B and c across from the right angle Round your answers to three decimal places C IN i A i degrees B i degrees

Find the slope of the line passing through the points 7 6 and 7 8 slope Find the slope of the line passing through the points 4 6 and 6 6 slope 8 08 X Und

Find the slope of the line passing through the points 4 9 and 8 9 slope Find the slope of the line passing through the points 3 1 and 3 8 slope 0 0 X

situa 4 Lin s job pays 8 25 an hour plus 10 of transportation allowance each week She has to work at least 5 hours a week to keep the job and can earn up to 175 per week including the allowance Represent this situation mathematically If you use variables specify what each one means How many hours per week can Lin work Explain or show your reasoning

3 A doctor se and 12 patients each day On Mondays and Tuesdays the appointment times are 15 minutes On Wednesdays and Thursdays they are 30 minutes On Fridays they are one hour long The doctor works for no more than 8 hours a day Here are some inequalities that represent this situation 0 25 y 1 7 x 12 xy 8 What does each variable represent Y X What does the expression x y in the last inequality mean in this sit E

Consider the following situation Teegan likes to play golf He has budgeted 64 next month for the driving range It costs him 9 75 for a bucket of balls each time he goes What is the maximum number of times he can go to the driving range next month to stay within his budget Enter the answer to the question in the answer box Enter only a number now words or symbols in the answer box

If the function y ez is vertically compressed by a factor of 6 reflected across the x axis and then shifted down 1 units what is the resulting function Write your answer in the form y cea b Provide your answer below y I 7 4 8 5 9 6 X X y 1 x V X 0

Solve the problem A restaurant serves 8 ounces of soup to each customer How many quarts of soup should be prepared in order to serve 196 customers

D Select X 2 3 4 5 y 250 50 10 2

y x 6x 9 what is the vertex We need vertex f

C y 3x 30x 63 completing the square

Mary Beth has 1500 in a savings account on January 1 She wants to have at least 500 by May 1 She estimates that she can withdraw 38 50 per week w for food clothing and entertainment Which inequality represents her estimate

Consider the following function table that represents a linear function What is the slope and y intercept of the line it represents O The slope is 1 and the y intercept is 9 The slope is 9 and the y intercept is 2 The slope is 9 and the y intercept is 7 The slope is 2 and the y intercept is 9 X 1 2 3 4 5 6 Y 7 16 25 34 43 52

There are some dimes and quarters on a desk The number of dimes is 2 less than 5 times the number of quarters Let q represent the number of quarters Write an expression for the number of dimes O5 2 q O2 5q O5q 2 5 q 2

If the figure pattern shown below were continued which figure number would have 250 sma squares in it Note Enter only a number no words or letters in the answer box E 2 1 3 4

Write an expression to represent the following statement eight times the sum of y and 9 OB y 9 8y 9 OB y 9 8 9y

Question 2 of 10 A student performed the following steps to find the solution to the equation x 2x 15 0 Where did the student go wrong Step 1 Factor the polynomial into x 3 and x 5 Step 2 x 3 0 and x 5 0 Step 3 x 3 and x 5 A in Step 2 B in Step 1 C The student did not make any mistakes the solution is correct D in Step 3

During batting practice two pop flies are hit from the same location 2 s apart The paths are modeled by the equations h 16t 56t and h 16 156t 248 where t is the time that has passed since the first ball was hit Explain how to find the height at which the balls meet Then find the height to the nearest tenth

5 If A 6x 10x and B 11x 6x 10x4 Find B A

Consider the subspace U of P3 R defined as U span 1 x Find a basis of U

6 Find the following for the data set below 14 3 23 21 40 14 a mean b median c mode taken d midrange noitsived bamug2 TOM odmor i How many classes with you ared to take to make the us

2 Sort the edges from least to greatest Apply the Sorted Edges Algorithm to find a Hamilt the graph below If an edge is not used state the reason why e g creates 3 edges at a vertex cle without all vertices Find the cost 18 16 20 10 12 trud e 15 B

Evaluate L 8 t sin x t Select one 1 82 1 8 O O 1 O 1 O 1 82 1 1 82 1 8 82 1

Find the area of the shaded sector given that each side of the hexagon is 7 cm long Note that each side of the hexagon touches the circle exactly once and the lines bounding the shaded sector are radial lines

As the prize in a contest you are offered 24 000 now or 45 300 in 8 years If the money can be invested at 9 compounded annually which prize will be worth more in 8 years Choose the option that is most profitable after 8 years accepting the 24 000 prize now accepting the 45 300 prize in 8 years

8 A soccer coach plans to order a few extra t shirts for her team Each t shirt costs 9 85 She has 77 left in her uniform budget Write and solve an inequality to determine the possible numbers of shirts she can buy 6 pts

An initial population of 4 500 undergoes a growth of 4 each month What will the population be in 5 years OA 15 300 OB 36 023 OC 5 475 OD 47 338

y year m minimum wage 1950 1960 1970 1980 1990 6 80 7 05 8 89 8 10 6 59 he table shown to estimate the minimum wage in the year 1967 7 23 OB 8 67 OC 8 51 OD 8 34

11p 1 A pharmacist wants to mix a 20 saline solution with a 30 saline solution to get 20 L of a 26 aline solution How much of each solution should she use

Fill in the blanks The domain of f is equal to the The domain of f is equal to the of f1 and the range of f is equal to the 4 of f and the range of f is equal to the of f

7 Paula received a holiday bonus of 1350 and invests the money in a certificate of deposit CD at a 3 6 annual interest rate compounded monthly for 18 months How much money will the CD be worth in 18 months a b How much interest will she earn during the 18 months

Use the graph to determine the intervals on which the function is increasing decreasing or constant Enter your answers using interval notation If an answer does not exist enter DNE increasing decreasing constant 5 4 3 2 1 y 5 4 3 2 1 1 2 3 1 2 3 4 X 5

5 You deposit 1 000 000 at 3 per year What is the balance at the end of one year if the interest paid is a simple interest b compounded annually c compounded quarterly d compounded daily

Solve the equation for x og 256 4 CIL The solution set is Simplify your answer Type an in fraction

Use the figure below to approximate the value f 1 f x 5 4 3

Determine whether the relation represents a function 9 1 4 6 4 1 8 7 This relation is a function This relation is not a function

National City Corporation quoted a rate of 4 5 simple interest for the 2019 20 school year It offers an interest only repayment option under which you make monthly interest payments for the year and pay on the principal only after graduation How much monthly interest would you pay for a 10 000 loan

Rewrite this number in appropriate scientific notation 5 450 answer

5 x y 5 8 x 4y 28 0 6 6x 3y 1 9 2y 1 x 7x 7 0 2y8x 10 10 y 4 3x Sy

Choose the proportion that is fa 16 26 8 0 O 13 O 30 48 8 0 9 21 O 10