Quadratic equations Questions and Answers

Determine whether the function is one to one If so a write an equation for the inverse function in the form y f x b graph f and f on the same axes and c give the domain and the range of f and f1 If the function is not one to one say so f x X a Write an equation for the inverse function in the form y f x Select the correct choice below and if necessary fill in any answer boxes to complete your choice OA The function f x is one to one and f x OB The function is not one to one Simplify your answer

If the function defined by the following is one to one find its inverse 4 6 3 5 4 8 Select the correct choice below and fill in the answer box if necessary A The inverse function is Type ordered pairs Use a comma to separate answers as needed B The function is not one to one

roblem 11 Let v 1 2 1 and v 1 2 4 1 ii 5 6 0 iii 7 10 2 3 Which of the following vectors are in span v1 V2 A all of them B none of them C i and iii only D i only E ii and iii only F ii only G iii only H i and ii only Problem 11 Select

Find the all solutions of this equation in the interval 0 2 G X 500 27 3 Give your answers in radians Do not use decimal approximations Use pi to represent 7 Use commas to separate your answers tan x 3 0

5 Which of the following is equivalent to 3x 10 a 2 3x 4 2x 2 b x x x 10 c 5 x 2 2 x 10 d x x 10

Mark bought a new van for 140 000 but it will depreciate by 25 every year a Write an equation for the current value of the van v in dollars to the time t in years let the van which bought to 100 00 be vand year it will be depreciate be int the b Use the equation to find the value of the van after 11 years Round final answer to nearest dollar 14000 1 14000 210 00048828 A 140000 1 B c ON h 2 He can get 500 when he sells it for scrap metal After how many years to the nearest month should he sell it for scrap

10 Combine like terms in the expression below x 2x 4x 2x 3x 4x 10

7 A radioactive sample with an initial mass of 72 mg has a half life of 10 days a Write a function to relate the amount remaining A in milligrams to the time t in days b What amount of radioactive sample will remain after 20 days c What amount of radioactive sample was there 30 days ago 10 07 mg of the initial sample remaining

Graph the following function Based on the graph state the domain and the range and find any intercepts f x In In X X 8 if 0 x 8 if x 8 OB The domain is x xz X Simplify your answer Use a comma to separate answers as needed C The domain is x x X Simplify your answer Use a comma to separate answers as needed

12 Distribute then combine like terms 2x x 10 3x 4x10

1 Combine like terms in the expression below 2 x 4x 10 3x 4x 12

5 Combine like terms in the expression below 3 2x 4x5 4x 4x 2

6 Find the sum of 3x 4x and 2x 2x

i Question 1 Make a table Constant of Proportionality is 8 Question 3 Make a table Constant of Proportionality is 1 4 Question 2 Make a table Constant of Proportionality is 2 i Question 4 Make a table Constant of Proportionality is 1 2 7

The atmospheric pressure p on a balloon or an aircraft decreases with increasing height This pressure measured in millimeters of mercury is related to the height h in kilometers above s 0 145h level by the formula p 760e a Find the height of an aircraft if the atmospheric pressure is 231 millimeters of mercury b Find the height of a mountain if the atmospheric pressure is 605 millimeters of mercury a The height of the aircraft is kilometers Round to two decimal places as needed

10 Combine like terms in the expression below x 2x 4x 2x 3x 4x 10

a Which expression below is equivalent to 30 2x 5 50 2x 5 b 3x 3x 2 5 7x 1 0 2x 7 x 1 d 20x 2x 3 5 10 Combine like terms in the expression below x3 2x 4x 2x

8 Find the difference of 3x 10 and 4x 4

Find the difference of 3x 10 and 4x 4

6 Find the sum of 3x 4x and 2x 2x Which of the following expressions is equivalent to 3

3 Which expression below is equivalent to x 4x a 2x 7x 14 b x 7x 14 c 21x d 23x 10 x 3x 47 4 Combine like torms in the expression below 2 x 2x 4 4x 3x 2

4 Combine like terms in the expression below x 2x 4 4x 3x 2

2 Combine like torms to simplify the expression below x 2x 6 2 3x 4 3 Which expression below is equivalent to 4 10 a 2 7x 14 b 8 7 14 6 21

Change the exponential statement to an equivalent statement involving a logarithm ex 17

2 Combine like terms to simplify the expression below x 2x 6 2x 3x 4

Use the given function f to answer parts a through f below f x In x 6 1 f Graph f Choose the correct graph below O A Q G B 10 10 K7 10

Use the given function f to answer parts a through f below X 4 f x 3 2 b Choose the correct graph of f below O A 10 B 10 57 C 10 D

Graph the following function Based on the graph state the domain and the range and find any intercepts f x X In if 0 x 8 if x 8 x Q E

Use the given function f to answer parts a through f below f x In x 6 b Graph f Choose the correct graph below O A 10 B www Q K X 10

Change the logarithmic statement to an equivalent statement involving an exp In 11 x

Find the exact value of the logarithm without using a calculator In Ve

Solve the equation log 4256 2x 2 Change the given logarithmic equation to exponential otic Do implif 1

9 7 99x 119x 76x 96 11x 12 A 9r 1 6 2 11x 12 3 11x 12 B 91 x 8 C 9x x 8 D 9x x 7 2 11x 12 9 21 154p 104p 172p 2 14p A 11p 9p 12 B 11p 7p 10 C 11p 6p 8 D 11p 9p 11 2 1 7p 5 2 14p 1 2 14p 1 2 14p 88 12 153 48 45 12v 9 A 12v 8 3 B v 12v 4 10 C 12v 7 D y 12v 5 10 224x 49 90 14x 14x 7 8 14x 7 1 2x 1 4 A 4 14 B 4x 15 4 3 4v 3 2 3 4v 3 1 4v 3 C x 4x 11 D x 4x 13 14x 7 10 14x 7

i want to calculate theta 3 and theta 4 please 0 712 Cos 3 Cos 04

Exercise 27 5 Let f A B be an injective function and let S be an arbitrar subset of A a Prove that fls SB is injective b Prove that f is a bijection

For each of the following you must show all work in setting up and solving a quadratic equation and clearly state the answer to the given question Please note that trial and error or successive guessing is not awarded marks 1 The area of a rectangular field is 3400m The field is enclosed by 236m of fencing What are the dimensions of the field 5 marks

Write short answers Consider the inverse tangent function defined by y tan x or y arctan x Complete parts a d a What is its domain 0 00 Type your answer in interval notation Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression b What is its range T 2 2 Type your answer in interval notation Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression c Is this function increasing or decreasing CLE increasing decreasing d Is there any real number x for which arctan x is not defined If so what is it or what are they Yes No Use a comma to separate answers as needed

Suppose that you earned a bachelor s degree and now you re teaching middle school The school district offers teachers the opportunity to take a year off to earn a master s degree To achieve this goal you deposit 1500 at the end of every three months in an account that pays 6 5 compounded quarterly Value of Annuity A P 1 T 11 n ext 1 a How much will you have saved at the end of 6 years b Find the interest a 31 617 b 4383 a 135 910 b 99 910 a 43 602 b 7602 a 41 429 b 5429

Which of the following are possible rational roots for the given polynomial f x x 8x x 146x 15 146 3 2 15 2 1 3 3 73 8 U 4 5 8 000 5 15 0 1 POSSIBLE POINTS 73 146 4

Find the mean for the data items in the given frequency distribution Round to the nearest tenth if necessary Score x 1 2 3 4 5 6 7 8 9 10 5 5 7 4 6 2 06 7 Frequency f 5 2 1 6 7 10 9 12 11 11

K Question 5 6 2 11 Use the unit circle shown here to solve the trigonometric equation Solve over 0 360 2 2 sin 8 HW Score 0 0 of 15 points O Points 0 of 1 4 1 0 180 The solution set is Do not include the degree symbol in your answer Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed 150 210 120 LAS 270

Solve the equation for all exact solutions where appropriate Round approximate answers in degrees to the nearest tenth Write answers using the least possible nonnegati csc 0 1 0 Choose the correct answer below O A 270 360 n 315 360 n where n is any integer O B 270 360 n where n is any integer OC 270 180 n where n is any integer OD 270 180 n 315 180 n where n is any integer

K Solve the equation in radians for all exact solutions where appropriate Round approximate answers to four decimal places Write answers using the least possible nonnegative ang 2 sin 2x 3 sin x 1 0 Choose the correct answer below OA The solution set is OB The solution set is OC The solution set is OD The solution set is 3A 2 7 6 3x 2 2nx 2nx 2n 7T 75 6 2nx 11x 6 12x 5 12x 5 11x 6 2n 2nx 2nx 2n 2nx where n is any integer integer 2 3n 3 2 3x 2 F 3 2 2nx where n is any integer eger 2nx where n is any integer 2nx where n is any integer COLLE

The city council of a small town needs to determine if the to support the building of a new library The council decides to conduct a survey of a sample of the town s residents Which one of the following procedures would be most appropriate for obtaining a sample of the town s residents Survey a random sample of persons within each neighborhood of the town Survey every 14th person who enters the old library on a given day Survey a random sample of librarians who live in the town Survey 400 individuals who are randomly selected from a list of all people liv

Numbered disks are placed in a box and one disk is selected at random If there are 6 red disks numbered 1 through 6 and 2 yellow disks numbered 7 through 8 find the probability of selecting a red disk given that an odd numbered disk is selected O 3 4 01 8 300

Exercise 14 3 1 Compute a u v where u 1 b x y where x 10 c 2u v v using u and v above 1 the following inner products 2 2 T v 3 5 14 y 0 49 0 0

oblem 9 Which of the following sets are closed under scalar multiplication i The set of all vectors in R of the form a b where a 5b 0 ii The set of all 2 2 matrices whose trace is equal to 0 iii The set of all polynomials in P2 of the form ao a x a2x where the product ao a a2 0 Problem 9 A none of them B all of them C i and ii only D ii and iii only E iii only F 1 only G ii only H i and iii only Select v

oblem 7 Which of the following statements are always true for vectors in R i If u vxw 4 then w vxu 4 ii 5u v x u 6v 31 u V iii If u is orthogonal to v and w then u is also orthogonal to w v v u A all of them B iii only C i and iii only D i only E none of them F G ii and iii only H i and ii only only

1 Suppose you invest 5 000 in an account that carns 1 interest on the amount in the account month If you make no withdrawals or deposits to the account how much will you have in the

oblem 8 Let V be the set of all ordered pairs of real numbers u with u 0 Consider the following addition and scalar multiplication operations on u u U and v v V u v u v 2 6u2v2 ku ku ku Use the above operations for the following parts Problem 8 a Problem 8 b Problem 8 c a Compute u v for u 6 2 and v 4 7 b If the set V satisfies Axiom 4 of a vector space the existence of a zero vector what would be the zero vector c If u 3 8 what would be the negative of the vector u referred to in Axiom 5 of a vector space Don t forget to use your answer to part b here enter your answer in the form a b Enter your answer symbolically as in these examples Enter your answer symbolically as in these examples enter your answer in the form a b enter your answer in the form a b