Algebra Questions

a Let D Z EC z 1 Prove that for any a ED the map z a f z 1 az maps the unit circle to the unit circle b Determine with proof the image of the line 1 it t R under the map

To qualify for Gold status at Awesome Airlines one must fly at least 8400 and less than 35000 miles each year If Gerald takes a 700 mile round trip flight to visit his parents how many times does Gerald need to visit his parents each year to attain Gold status Express your answer in interval notation Answer Keypa

1 Graph a line with a slope of that contains the point 6 3 4 4 7 6 5 4 3 2 CO C Y 4 3 2 2 3 4 5 6 7 1 2 3 4 5 6 7 I

Greg takes a 300 mile round trip flight to visit his parents To qualify for Gold status at Awesome Airlines one must fly at least 6600 and less than 13800 miles each year How many times would Greg need to visit his parents each year to attain Gold status Express your answer in interval notation Answer 3

are given that kx kx 6 0 Then an expression for as a function of k is Itiple choic A CO CDE A B C D E 24k 2k k k 24k 2 k 24 2 k k 24 2k k k 6k 2k 1 1

ich of the following describes all the values of a satisfying 4 5 tiple choic view My An ABCDEFGH Submit A x 1 B x 1 C D E 1 x 1 1 or x 1 3 F G H I J x 3 3 x 3 3 or x 3 all x ER no real solutions for a

Given the expression solve for r in terms of p and q only Multiple choic ABC D B T EF G H I A T review My Answers C T D T 2q p q 2q pq 1 2g r pq 2pq pr 9 2 2 E 7 Submit Answers 2q r qr F r pqr 2q 2q p q 1 2pq 9 P G T H r I T is canceled out so it is impossible to solve for r

ve 3x x 22x 8 0 given that is is a root

Suppose A is an invertible matrix with A LU where L is lower triangular and U is upper triangular In terms of L U please find L and U such that A U L U is upper triangular L is lower triangular

3 Suppose a triangle has angle A 58 side a 11 4 and side b 12 8 Solve for the remaining side and angles for the triangle If more than one triangle exists solve for both If no triangle exists say so Sketch each solution triangle if they exist

ph of a function f is given Use the graph to answer the question For what numbers x is f x 0 201 04 O 12 te 20 I 12 14 12 14 20 20 12 14 20

The graph of a function f is given Use the graph to answer the question For what numbers x is f x 0 51 O 3 00 0 3

For x Bx C x a x b x a x b 0 which of the following must be true O ab C and a b B Oa b C and a b B Oab B and a b C Oab Band a b C

For the function find the average rate of change of 1 from 1 to 3 165 HD f x X 4 5 14 07 10 O 7

Find the value for the function Find f x h when f x 2x 4x 5 2x 4xh 2h 4x 4h 5 2x 2xh 2h 4x 4h 5 O2x2 2h2 8x 8h 5 2x 2h 4x 4h 5

Answer the question about the given function Given the function f x x 4x 96 list the x intercepts of the graph of t 12 0 1 0 12 0 8 0 12 0 8 0 12 0 8 0

What number should be added to complete the square of the expression x2 18x 9 162 81 41

graph of a function fis illustrated Use the graph of f as the first step toward graphing the function F x where F x f x 2 1 6 ET 1 1 3 2 X 6 3 4

Ak O 14344 even odd neither a function is given Decide whether it is even odd or neither

completely the given expression 3x 5 x 4 3x 5 3 O5 3x 5 3x 1 O5 3x 5 3x 1 O 15x 5 3x 5 3x 5 15x 5 The polynomial is prime

etermine whether the graph is that of a function If it is use the graph to find its domain and range the intercepts if any and any symmetry with respect to the x axis the y axis or the origin

Graph of a piecewise defined function is given Write a definition for the function O 2 3 7x 4 Nebcam x 4 if 3 x 0

4 12 The local minimum occurs at x

Use the graph to find the intervals on which it is increasing decreasing or constant 5 4 3 2 1 Decreasing on 00 00 Increasing on 0 00 Decreasing on 0 increasing on 0 10 ml

decreasing or constant on the given interval ph of a function is given Determine whether the function is increasing 0 1 24 L EV cam

ve the inequality Express your answer using interval notation 21x 3 3 6x 7 0 6 6 00 0 0 6 6 00 2 76 11 12 Webcam

Find the exact value of csc 0 given that cot 0 A Select the correct choice below and if necessary fill in the answer box to complete your choice csc 8 26 5 and 0 is in quadrant IV Rationalize denominators when applicable B The function is undefined Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

hswer the question about the given function Given the function f x x 6 is the point 2 2 on the graph of f X 3 No Yes

Find the domain of the function g x 3x 2 4 x x 2 2 all real numbers O x x 4 O x x 0

Espa When Christine had 5 years left in college she took out a student loan for 19 246 The loan has an annual interest rate of 4 2 Christine graduated 5 years after acquiring the loan and began repaying the loan immediately upon graduation According to the terms of the loan Christine will make monthly payments for 5 years after graduation During the 5 years she was in school and not making payments the loan accrued simple interest Answer each part Do not round intermediate computations and round your answers to the nearest cent If necessary refer to the list of financial formulas a If Christine s loan is subsidized find her monthly payment Subsidized loan monthly payment 0 b If Christine s loan is unsubsidized find her monthly payment Unsubsidized loan monthly payment S S E

Determine the signs of the six trigonometric functions of an angle in standard position with the given measure 592 Determine if the value of sin 592 is positive or negative Positive Negative Is the value of cos 592 positive or negative Positive Negative What is the sign of the value of tan 592 Negative Positive Is the sign of the value of csc 592 positive or negative Positive Negative Determine if the value of sec 592 is positive or negative O Negative Positive www

Sketch the angle in standard position and draw an arrow representing the correct amount of rotation Find the measure of two other angles one positive and one negative that are coterminal with the given angle and closer to the given angle than any other coterminal angle Give the quadrant of the angle if applicable A 67 Choose the correct graph below where the curve on each graph traces the angle beginning at the positive x axis and ending at the ray O A OB 67 0 Q The least positive coterminal angle is Simplify your answer Type an integer or a fraction 0 67 Q 0 Save Q

Click here to watch the video Sketch an angle 8 in standard position such that has the least possible positive measure and the point 6 8 is on the terminal side of 0 Then find the exact values of the six trigonometric functi for 0 B The function is undefined sin 8 Simplify your answer Type an integer or a fraction 5 A Select the correct choice below and if necessary fill in the answer box to complete your choice cos 0 A B The function is undefined 35 tan 0 Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer Type an integer or a fraction OA csc 8 413 CXXE Simplify your answer Type an integer or a fraction B The function is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer Type an integer or a fraction

Find the exact value of cos 0 given that sin 0 1 4 and 0 is in quadrant III Rationalize denominators when applicable 5 COCCE Select the correct choice below and if necessary fill in the answer box to complete your choice OA cos 0 Simplify your answer Type an exact answer using radicals as needed Type an integer or a fraction OB The function is undefined

Find the measure in degrees not equal to the given measure of the least positive angle that is coterminal with A A 8 Points 0 of 1 The measure of the least positive coterminal angle is Simplify your answer

Find the next two positive and two negative angles that are coterminal with the given quadrantal angle A 630 The two positive angles are Use a comma to separate answers as needed Do not include the degree symbol in your answer

Convert the following angle to decimal degrees x 79 39 17 X Points 0 Round to 3 decimal place

Convert the angle to degrees minutes and seconds form 60 24 60 24

Convert the following angle to decimal degree notation 26 36 Points 0 of 1 26 36 7 Round to two decimal places as needed

Convert the following angle to decimal degree notation 69 54 0 Points 0 of 1 69 54 Round to two decimal places as needed

Convert the following angle to decimal degree notation 71 60 Question 1 1 1 53 Points 0 of 1 71 60 Round to two decimal places as needed

Algebra Prep 2022 Kuta Software LLC All rights reserved EXTRA CREDIT Sum 1 Solve each question Round your answer to two digits 11 Working alone Nicole can pick forty bushels of apples in 9 7 hours One day her friend Wilbur helped her and it only took 5 26 hours Find how long it would take Wilbur to do it alone A 11 49 hours B 9 04 hours C 12 52 hours D 12 8 hours

Select one answer A person must enter a 4 digit code to gain access to his cell phone He will enter codes until he 10 points is successful however he cannot try more than 3 times or the phone will lock him out Let S denote a successful attempt and F denote a failed attempt What is the sample space for this random experiment A B C D E SSS SSF SFS FSS SFF FSF FFS FFF S FS FFS S FS FFS FFF S SS SSS S SF SSF SSS

3 The cost in dollars of producing x units of a certain commodity is C x 100 50x 0 02x a Find the average rate of change of C with respect to x when the production level is changed from x 100 to 105 b Find the instantaneous rate of change of C with respect to x when x 100 and interpret the value of it

Find an equation for the plane that is tangent to the given surface at the given point z y x 3 4 1 WA Find the equation for the tangent plane to the surface z y x at the point 3 4 1 Use a coefficient of 1 for

3 A jet made a trip to Dublin and back The trip there took eight hours and the trip back took 12 hours It averaged 150 mph faster on the trip there than on the return trip Find the jet s average speed on the outbound trip A 180 mph B 450 mph C 510 mph D 640 m

2 A jet and a passenger plane left Nairobi at the same time The planes flew in opposite directions The passenger plane flew 260 mph faster than the jet After four hours they were 2320 mi apart Find the jet s speed A 183 mph B 155 mph C 160 mph D 245 mph

4 5 4 2 5x 3 6 3 8 18 9 A 1 6 x 2 46 B 5 62 x 2 9 C x 5 7 or x 3 7 D 7 48 x 4 6 HO Find each quotient 5 J Tw at inequality and graph its solution A 1 B 39 35 35 5 4 3 2 1 0 1 2 3 4 5 6 7 9 8 7 6 5 4 3 2 1012 10 7 e 6 0

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15 Use your ruler and protractor to draw a triangle with one side 9 cm long and an adjacent angle measuring 45 Explain your method Can you draw a second triangle with the given measures that is not congruent to the first Sketch your results 16 Use your ruler and protractor to draw a triangle with one angle measuring 40 and an opposite side 10 cm long Explain your method Can you draw a second triangle with the given measures that is not congruent to the first Sketch your results