Complex numbers Questions and Answers

Find the inverse of the following function g x 2 1 log x 1 3 8 x 1085 5 1 Og x log x 1 3 Og x log 1

Which function below has an asymptote at x b Ax a logs x c d g x b log x d c h x c log x b d P x d log x a b O Question 2 25 points Determine the domain and range of the function f x log2 x 3 shown in the graph Domain All Real Numbers R Range y 0 Domain All Real Numbers R Range y 3 Domain x 3 Range All D 2 1 5 4 3 2 1 1 2 3 1 2 f x log x 3 3 5 6 7

log 9 0 1 2 3 Question 6 12 5 points Use the change of base formula to approximate the following with your calcu log 59049 O 0 1 4 771 10 19683

Perform the indicated operations simplify Add 11 12i 13 14i sum Subtract 11 12i 13 14i difference

The area of a triangle can be found using the formula Area 6m Find the area of the triangle pictured below where the measurements are given in meters m 12 m 1 base height 2 O

Determine the graph that best represents the situation given below Each person who attends the party will be given 2 slices of pizza Number of Pizza Slices Press the hotspot to select the graph that best represents the situation Press the answer box after each selection to save your response 5 Number of People Number of Pizza Slices Number of People Number of Pizza Slices Number of People

Match the following numbers to their equivalents in Scientific Notation 2 500 000 000 000 0 00023 101 2 5 10 2 2 3 10 10 1 10 2 5 10 12 23 10 4 1 01 10

Mr Tyler is 6 feet tall His youngest son Sean is 4 feet tall Which equation correctly represents the relationship between Mr Tyler s height H and Sean s height b

For each table identify the slope and then use the line tool to show what the graph might look like X32401 3 m Y 5 2 4 7 Graph Description m V35T7X 1 Y 12345 4 5 Graph Description

Which of the following equations has no solution O 5x 20 7x 7 3 x 3x O x 20 5x 7 3 x 3x 7 3 x 3x 0 5x 21 x O 5x 20 x 7 3 x 3x

What is the y intercept of y a sin kx c a a c b Not possible to find the y int without the actual values of a k and c O c a c O d c

A trigonometric function of the form f x sin has been transformed to have a maximum at 6 5 and a minimum at 2 5 The equation of the new function would be a f x 2 sin x 4 5 b f x sin x 9 c f x 9 sin x d f x 4 5 sin 2x

1 2 3 4 5 Locate two points on the line make sure they are on gridlines Vertical change Rise Horizontal change Run Use the pen tool to follow the path from one point to the other You must stay on grid lines Write the vertical change up or down over the horizontal change left or right Follow the line from left to right to determine the sign of the slope M

Q 14 Let M denote the determinant of a square matrix M Let g 0 R be the function defined by 9 0 5 0 1 5 0 1 where f 0 1 sin 0 1 sin 8 1 sin 0 A p 3 2 P B p 32 C p 5 2 0 1 sin 1 sin it sin 0 1 cot 0 1 os 0 IT COS COS loge Let p x be a quadratic polynomial whose roots are the maximum and minimum values of the function g 0 and p 2 2 2 Then which of the following is are TRUE tan 0 1 loge tan

The special triangle and has corresponding sides of a 4 4 2 Ob 1 3 2 Oc 9 4 4 O d 1 1 2

DO NOT USE A CALCULATOR ON ANY OF THE FOLLOWING QUESTIONS UNLESS INDICATED 1 Which of the following is a solution to the equation 8x x 9 A 4 7 B 4 2 7 C 8 7 D 8 2 7 3 What is the sum of all values of x that satisfy the equation 2x 9x 4 0 A 5 B 2 25 C 3 5 D 4 5

Three students attempt to define what it means for lines I and m to be parallel m Can you match the teacher s comments to the definitions Definition of parallel lines Daniela s definition Lines I and m are parallel if they intersect at right angles Ori s definition Lines I and m are parallel if they go in the same direction Kaori s definition At every point on line 1 line m is the same distance away Teacher s comments Were you thinking of perpendicular lines Yes Well done Here have a cookie You ve earned it It seems like you ve got the basic idea but your definition could be more precise

on 6343 15 Nofe 4626 646 So m y 4 y 2x ong 4 y x y x 3

The linear function g is defined by g x 4x a Show that g 3 and g 2 have a difference of 4 g t 4 2 X 8 4XL 3 IL 8 4 b Show that when the input value increases from x to x 1 the output values g x 1 and g x have a difference of 4 2 The exponential function h is defined by h x 4 a Show that h 3 and h 2 have a quotient of 4 b Show that when the input value increases from x to x 1 the output values h x 1 and h x have a quotient of 4

To pass the test you must ha least 27 answers correct

The Hatfields are having their annual family reunion They are expecting 175 people and they need to find a place to have the reunion They found The Train Depot as a possible venue The meeting room measures 50 x 75 feet Each person will occupy 15 square feet Based on your calculations can the 175 people fit in the room a Yes b No c There is not enough information to determina

Name 1 Tell whether the given point is a solution y 2x 3 6 0 y x 6 2 Graph the system y 2x 1 y x 3 3 7 A

olve the following system of equations graphically on the set of axes below 10 y x 8 2x y 1 Plot two lines by clicking the graph Click a line to delete it 103 3 5 10

8 3 X a 10 c 11 b 8 d 9 is 14a2 then the value of nen x spansion 1 1 13 a 4 If the second term of the expansion 11 11 C is a 4 c 12 5 The co efficient of x in the expansion of b 3 d 6 1 2x 3x 1 is 1 2x 3 x 1

11 Write the expression as a complex number in standard form 7 81 3 57 i U Font Family AAA E 13 1

2 2x 8 0

2 Find the absolute value of the complex number

Write a polynomial function of least degree that has rational coefficients a leading coefficient of 1 and the given zeros Write he function in standard form 2 3 6 f x

Inequality Statement 3 3 8 3x 5 24 2 2 1 1 0 0 1 1 2 2 3 3

Let E 0 sin2 24 0 Let P 2 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 1 be a partition of the interval 1 2 Calculate UE P and LE P Explain your reasoning paying attention to why the constant 24 makes this question computationally easier than you might think at first glance

Find the Period amplitude and translation of 3 A Y Sin 9xX 6 B Y 4CSC2X 1 Vertical

1 1 point The graph of y 2x 4 is a right side up parabola True False

1 point Given the following f x 30x7 g x 13 2x Complete the following f g x 33 6x O O 60x 392 390 13x 60x 383 D

11 1 point The domain of the graph of this equation is all real numbers y 2x 12x 1 True False

18 1 point The graph of this equation is shifted 6 units down y x 2 6 True False Previous

12 1 point The domain of the graph of this equation is 3 0249 o y x 10x x 3 True False Previous

11 1 point Given the following f x 3x 7x 8x g x 3x 12x 5x and h x 12x 6 Complete the following f g x 21x 45x5 15x4 9x 9x 84x 40x7 40x7 61 45x5 15x 9x 8x 2x 15x 3x

The general solution for x Answer G 21 a X t q 1 e a 1 b x 1 q 1 e c 1 te c x 1 a j e a i e X 1 a e 5 1 21 6 A B 3 O C 1 e 5 5 x is

olve the equation Give a general formula for all the solutions List six solutions 1 sin 0 Write the general formula for all the solutions to sin 0 k is any integer Simplify your answer Use angle measures greater than or equal to 0 and less than 2x Type an exact answer using as needed Use integers or fractions for any numbers in the expression Type an expression using k as 1 Write the general formula for all the solutions to sin 0 based on the larger angle 2 0 Cilif based on the smaller angle 2 k is any integer exe

iam had 215 Then he and his classmates bought a present for their teacher evenly splitting the 50 cost among the x of them How much money does Liam have left Write your answer as an expression

Given the function z Find the difference quotient 3z f z h f z h Find f 0 Find f 1 Graph the function f z are 2 0 and 1 f x h f x h Find f 2 This slope should match the tangent line you drew above Find f z by determining lim h 0 3h 6z 3z and draw the tangent lines to the graph at points whose x coordinat

e information given about the angle 0 0 0 2x to find the exact value of cos 21 5 3x 52 0 2

Find the inverse Fourier Transform of the functions e 20 4 3 5 w i A B w 10sin 3w W A

1 Find the 2 Show that n 8 n 1 1 6n 5 1 n II 6

x y z TH Need Help W 1 Points DETAILS HARMATHAP12 4 3 035 MY NOTES ASK YOUR TEACHER Use the simplex method to maximize the function if possible subject to the given constraints If there is no solution indicate this if multiple solutions exist find one of them enter NO SOLUTION Maximize 3x 2y subject to 10y 20 Y 40 PAR

Solve each of the following over 0 x 360 Express your answer accurate to the nearest hundredth a degree a cos 0 5998 c cot 5 2236 b sin 0 2665 d csc0 1 6880

00 00 09 Question 1 of 60 The type of listing that places listing brokers in a position of competing with their own clients to find a buyer is OA net listing B none of these OC exclusive right to sell listing OD exclusive agency listing

Which expression is missing from the proof O loga O log O log

1 point 4 Listen A painting was purchased for 10 500 in 2000 The painting increases in value by 1 2 per year How much will it have increased in value by 2015 O a 54 735 66 b 12 557 32 Oc 3 057 32 d 12 643 34 Question 21 1 point Saved Listen Which is a property of the exponential function f x 6

How much more acidic is a solution of pH 2 1 than a solution of pH 2 2 a 1 3 times more acidic Ob 10 times more acidic c 0 1 times more acidic d 2 times more acidic