Algebra Questions

21

2 3i 7

6x 480

x 24 0

x 7x 6 0

x 7x 6 0

y 10 3x 5x y 6

2x 3y 4 x 2y 3

x 16 0

18x 81 0

x 16 0 AIRIE

9 Use the sets U following set a d e f a b c d e f A a b c B a c f to list the elements of the d An B ANB de b B B b d e e An B 10 Use a Venn diagram to illustrate the set AUB nC A We can use Venn Diagrams to identify sets of data and show the equalities of various sets Eventually we will solve problems and identify probabilities using Venn Diagrams Let s do some examples II Use a Venn diagram to illustrate the following equality B C AUB AUB de U f AUB AUB ANB U ANB U ANB A A B B U

Let p and q represent the following statements p 8 4 12 q 10 7 70 Determine the truth value for the statement paq Choose the correct truth value below Op q is false O p q is true

Construct a truth table for the given statement qV p Fill in the truth table P T F q T P qv p

Construct a truth table for the given statement PA P Fill in the truth table P T F p PA P

2 31 2 1 2 2 3 2 2 H 2 y sin x 1 Transformation

Find the x intercepts of the polynomial function State whether the graph crosses the x axis or touches the x axis and turns around at each interce f x 4x x OA 0 crosses the x axis 4 crosses the x axis 4 crosses the x axis OB 0 touches the x axis and turns around 4 crosses the x axis 4 crosses the x axis OC 0 touches the x axis and turns around 4 touches the x axis and turns around D O touches the x axis and turns around 4 crosses the x axis

As age increases so does the likelihood of a particular disease The fraction of people x years old with the disease is modeled by f x 0 8 1 271e 0 122x a Evaluate f 25 and f 65 Interpret the results b At what age does this likelihood equal 60 a Select the correct choice below and fill in the answer boxes within your choice OA 25 and f 65 COLLE This means that among Round to three decimal places as needed people age 25 have the disease while among people age 65 have the disease OB 1 25 and f 65 Round to three decimal places as needed This means that among people age 25 have the disease while among people age 65 have the diconco

Find the value log 355 log 31 log 355 log 31 Round to four decimal places as needed

Let v 0 2 3 and v 3 1 0 V1 Select all vectors v3 such that V V2 V3 is a basis of R A V3 2 3 2 B V3 3 1 3 3 1 0 C V3 D V3 0 0 0 OE V3 3 3 3

Write in logarithmic form 5 125 What is the equivalent logarithmic form log 5 Simplify your answers Type integers or fractions

Write the given statement in an equivalent exponential form log 6216 6 The equivalent exponential form of the given statement is Type your answer using exponential notation Do not simplify

Complete the sentence below The graph of f k gk passes through the points 1 D 0 and 1 Simplify your answers

The graph of a function f is shown Use the graph to find f1 7 10 10 Ay X 2

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

oblem 8 Let V be the set of all ordered pairs of real numbers with u 0 Consider the following addition and scalar multiplication operations on u and v v v u v U v 2 6u v ku ku1 ku Use the above operations for the following parts 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

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 a formula in terms of k for the entries of Ak where A is the diagonalizable matrix below A 19 18 20 19 00

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

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

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

4 Combine like terms in the expression below 2 4x 2 3 2x 6

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

4 Simplify by combining like terms 2 x 4x 5 3 x 3x 4

3 If 3x 4x 10 4x 6x 4 is rewritten in the form ax bx c what is the value of a a 3 b 7 c 3 d 12

2 Which of the following expressions is equivalent to 3 x 10x 4 3x 4 a 3x 18x 16 b 3x 42x 16 c 3x 42x 16 d 3x 18x 16

Exit Ticket 14 1 Which of the following expressions is equivalent to 2 2x 10 3 x 10 a 7x 10 b 7x50 c 7x 10 d x

Simplify the following trigonometric expression by following the indicated direction Multiply cos e cos 0 sin 0 1 sin 0 1 by sin 0 1 sin 0 1 Simplify your answer

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

7 Which of the following expressions is equivalent to 3 x 4x 4 4 x 3x 2 a x 4 b 1x4 12x 20 c x 24x 4 d 1x 24x 20

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