Algebra Questions

9 Which point is on the line 6y 3x 0 A 2 1 B 2 1 C 1 2 D 1 2 Bizi sedy Hind

4n 8n 8n 4n

Exercises 49 64 Complete the following a Find f x for the indicated values of x if possible b Find the domain of f Use words or inequalities to describe the domain 49 f x x for x 2 5 50 f x 2x 1 for x 8 1 51 f x x 3x for x 3 2 52 f x 5 x 2x for x 1 53 f x 12 3x for x 1 4

Which expression represents the area of the rectangle shown a 4x 5 units b 4x 5 units c 3x 7x 4 units d 3x 9x 4 units 3x 4 x 1

What is the most completely factored form of the expression 45x 40x a 40 5x x b 5 9x 8x c 5x 9x 8 d 5x 9 8x

Exercises 43 48 A function g is defined a Write g as a set of ordered pairs b Give the domain and range of g 43 g 1 0 g 2 2 g 5 7 44 g 2 5 g 3 9 g 4 4 45 g 1 8 g 2 8 g 3 8 46 g 5 0 g 0 5 g 5 0 47 g 1 2 g 0 4 g 1 3 g 2 2 48 g 4 5 g 0 5 g 4 5 g 8 0

Exercises 27 42 Graph y f x by hand by first plotting points to determine the shape of the graph 27 f x 3 28 f x 2 29 f x 2x 30 f x x 1 31 f x 4 x 32 f x 3 2x 33 f x x 2 34 f x 2 2x 35 f x x 1

220 attended the FSU Marist game M 185 attended the FSU Butler game B 190 attended the FSU NC State gandle NCS 100 attended the Marist game and the NC State game 60 attended the NC State game and the Butler game attended the Butler game and the Marist game 30 attended all three of the games 65 Sketch a Venn diagram and answer the questions below M NOS B U

15 x x 2 16 x x 1 17 x x 6 18 x x 9 19 xlx 3 x 3 20 x x 4 x 5 21 x x 1 x 6 22 x x 5 x 7

Survey researchers design and conduct surveys and analyze data Some survey researchers design public opinion surveys Other survey researchers market research analysts design marketing surveys which examine products or services that consumers want need or prefer Most survey researchers work in research firms polling organizations nonprofits corporations colleges and universities and government agencies The majority work full time during regular business hours A bachelor s degree may be sufficient for some entry level positions The median annual wage for survey researchers was 49 760 in May 2014 SOURCE Bureau of Labor and Statistics U S Department of Labor Occupational Outlook Handbook 2016 2017 Edition Survey Researchers Surveys for scientific research cover various fields including government health social sciences and education For example a survey researcher may try to capture information about the prevalence of drug use or disease An anonymous survey of college students was taken to determine behaviors regarding alcohol cigarettes and illegal drugs The results were as follows 894 drank alcohol regularly 665 smoked cigarettes 192 used illegal drugs 424 drank alcohol regularly and smoked cigarettes 114 drank alcohol regularly and used illegal drugs 119 smoked cigarettes and used illegal drugs 97 engaged in all three behaviors 309 engaged in none of the behaviors

the value s of x when f x 4 There may be more than one response 1 point Distance away from car Feet 0 2 4 6 8 10 12 14 16 10 2 A B C 10 12 14 16 Time seconds D 18 E 20 22 LL 24 26

14 2 1 0 2

A survey was given asking whether people like dogs and or cats 183 said they like dogs 148 said they like cats 74 said they liked both cats and dogs 48 said they don t like cats or dogs How many people like dogs but not cats people like dogs but not cats

A survey was given to 298 people asking whether people like dogs and or cats 186 said they like dogs 123 said they like cats 67 said they don t like cats or dogs How many said they liked both cats and dogs people liked both cats and dogs

The Venn diagram here shows the cardinality of each set Use this to find the cardinality of the given set A 6 m AL ROC 12 14 B 4

The Venn diagram here shows the cardinality of each set Use this to find the cardinality of the given set A C n An BC 8 11 7 5 9 14 B 6 a

The Venn diagram here shows the cardinality of each set Use this to find the cardinality of the given set A 10 7 B

The Venn diagram here shows the cardinality of each set Use this to find the cardinality given set A 9 6 C 8 B 8

Let the Universal Set be S Let A and B are subsets of S Set A contains 29 elements and Set B contains 99 elements Sets A and B have 24 elements in common If there are 24 elements that are in S but not in A nor B how many elements are in S

4 A graph of f x x 2 is shown a Evaluate f 1 f 2 f 3 2 0 2 y NO 2 H f x x 2 4 6 b Find the domain and range of f 00 8

Functions and Their Representations HW 3 11 13 17 35 41 45 53 61 68 73 75 95 97 100 101 105 113 115 121 126 131 133 137 page 44 Sec 1 3 I Relations A relation is a set of ordered pairs If we denote the ordered pairs by x y then the set of all x values is the DOMAIN and the set of all y values is the RANGE Example 1 A physics class measured the time y that it takes for an object to fall x feet as shown in the table The object was dropped twice from each height x feet y seconds 20 1 2 20 1 1 a Express the data as a relation S D 20 40 R 1 1 1 2 1 5 1 6 S 20 1 2 20 1 1 40 1 5 40 1 6 b Find the domain and range of S 40 1 5 Find the domain and range of this relation 40 1 6 Example 2 Complete the following for the relation S 1 2 5 5 3 3 0 7 5 4

Identify a function symbolically Example 5 Determine if y is a function of x a y x 2 b x2 y 25

2 Let a function f be represented symbolically by f a Evaluate f 3 f 1 and f a 3 b Find the domain of f 2 3 A function g is given by g x x 2x and its graph is shown 3 2 1 y 32 7 1 1 3 2 g x x2 2x 3 a Find the domain and the range of g b Use g x to evaluate g 0 g 2 g 3 x 1 X

A function is a relation in which each element of the domain corresponds to exactly one element in the range The ordered pairs for a function can be either finite or infinite Diagrammatic Representation of Functions Example 3 Domain 10 D 15 20 Write f as a set of ordered pair f 5 1 Domain Range 2 f D R 2 3 4 R 3 5

1 How many planned to only grade papers 2 How many planned to grade papers or do household chores 3 How many did not plan to do any of these activities 4 How many planned to do at least two of these activities 5 How many planned to attend a football game and do household chores but did not have any plans to grade 6 How many planned to attend a football game or grade papers but did not plan to de household chores 7 How many planned to do at most one of these activities

Let S be the universal set where S 1 2 3 18 19 20 Let sets A and B be subsets of S where Set A 1 2 3 7 9 12 13 14 15 16 17 18 Set B 3 4 6 7 9 10 12 13 14 15 17 Set C 3 6 7 8 12 13 15 18 19 20 Find the number of elements in the set AUBUC n AUBUC Find the number of elements in the set An BnC n AnBnC

Let S be the universal set where S 1 2 3 23 24 25 Let sets A and B be subsets of S where Set A 1 2 5 10 14 16 21 22 25 Set B 3 8 9 14 16 22 24 25 Set C 2 5 6 7 10 12 13 15 19 20 23 25 Find the number of elements in the set An B n An B Find the number of elements in the set BNC n BNC Find the number of elements in the set An C n Anc

Let the Universal Set S have 150 elements A and B are subsets of S Set A contains 28 elements and Set B contains 88 elements If Sets A and B have 5 elements in common how many elements are in A but not in B

The Venn diagram here shows the cardinality of each set Use this to find the cardinality of each given set 13 n A n ANC M 5

20 points A car s stopping distance in feet is modeled by the equation d v 58 4f where v is the initial velocity of the car in miles per hour and f is a constant related to friction If the 2 15v initial velocity of the car is 47 mph and f 0 34 what is the approximate stopping distance of the car 239 miles 21 miles 239 feet 21 feet

A skydiver jumps from an airplane at an altitude of 2 500 ft He falls under the force of gravity until he opens his parachute at an altitude of 1 000 ft Using the initial velocity of zero approximately how long does the jumper fall before he opens his chute For this quadratic model we will let the y axis be the axis of symmetry h t 16t2 vt ho 9 7 s 2 4s 12 5 s 14 8 s

A softball pitcher throws a softball to a catcher behind home plate The softball is 3 feet above the ground when it leaves the pitcher s hand at a velocity of 50 feet per second If the softball s acceleration is 16 ft s which quadratic equation models the situation correctly h t at vt ho 3 50t 16t ho h t 16t2 50t 3 h t 5012 16t 3 3 1612 50t ho

A quarterback throws an incomplete pass The height of the football at time t is modeled by the equation h t 16t2 40t 7 Rounded to the nearest tenth the solutions to equation when h t 0 feet are 0 2 s and 2 7 s Which solution can be eliminated and why The solution 0 2 s can be eliminated because the pass was not thrown backward The solution 2 7 s can be eliminated because a ball cannot be in the air for that long due to gravity The solution 2 7 s can be eliminated because the pass was thrown backward The solution 0 2 s can be eliminated because time cannot be a negative value

1 A straight waterslide is 175 feet above ground and is 200 feet long What is the angle of depression to the bottom of the slide oldiroq

gles A 53 112 90 CS 36 978 9 to the est tenth 2 findside tan 6 ho B 12 5 B 38 C J A C Sin 38 of C 12 5 T CYSin 38 12 5 12 50 a 12 5 b Siss

3 5 O search 3 81 A 2 3x C 2x 3x 5 54m A 3m 2m C 3 3m II B 3 3x D 2 3x B 3 2 D 2m 3m 4 6 4 27a A 3 3a C 3 2a 6 81n A 3nN2n C 3 3 B 2V2 D 2 3 B 2n D 3

12 B 2 7 C 72 19 A

B 3 2m D 2m 3m B 2v 3uv D 2 2uv 4 B 3 2x y D 3y 3xy 6 8 6 81n A 3n 2n C 3n 3 8 64a7b A 2a 3ab4 C 2ab 3b 1010 24x y A 3xy 2x C 3 2x y B 2n 3 D 3 3n B 2a2a b D 2b 2a B 2x 3y D 2x 3x y

12 From a 200 foot observation tower on the beach a man sights a whale in difficulty The angle of depression of the whale is 7 How far is the whale from the shoreline

5 5 54m4 A 3m2m C 3 3m 7 24ux4 A 2u 3uv C 3uv 2 9 32x y4 A 2 3x y C 2y 2x B 3 2m D 2m 3m B 2v 3uv D 2 2uv B 3 2x y D 3y 3xy

20 24 Kuta Software LLC All rights reserved Simplify Single Radicals Simplify 1 500 A 5 4 C 10 3 81x A 2 3x B 2 5 D 2 2 B 3 3x 2 2 96 4 A 3 7 C 2 2 4 27a A 3 3a B 2V D 21 B 2

2 4 2 x A x C 8x6 3 4 36x6 A 216x C 343x6 B x6 D 20 B x 2 D x

e base of a 8 John wants to measure the height of a tree He walks in the cliff exactly 100 feet from the base of the tree and looks up The angle from the ground to the top of the tree is 33 How tall is the tree

Iding 30 by 6 You are standing 50 meters from a hot air balloon that is preparing to take off The angle of elevation to the top of the balloon is 28 Find the height of the balloon

A 6 C 12 B

Let the Universal Set S have 154 elements A and B are subsets of S Set A contains 30 elements and Set B contains 84 elements If Sets A and B have 3 elements in common how many elements are in neither A nor B

In a loan database there are 14 loans to clients with 20 years of business experience Also there are 72 loans made to clients with a High School education In the database there are 82 loans to clients with 20 years of experience or who have a High School education How many loans were made to clients with a High School education who also had 20 years of experience

In a survey of 149 pet owners 57 said they own a dog and 66 said they own a cat 23 said they own both a dog and a cat How many owned neither a cat nor a dog

x 0 x a Find the limit If it does not exist express your answer as either or o b Compute lim arcsin x 1 x 1 lim x 5 5 x X x 1 Page 2 of 2

B 5 2024 Kuta Software LLC All rights reserved Simplify Single Radicals Simplify 1500 A 5 4 C 10 3 81x A 2 3x C 2x 3x 5 54m4 A 3m 2m C 3 3m 24uv4 7 V A 2u 3uv C 3uv 2 9 32x y4 A 2 3x y C 2y 2x B 2 5 D 2 B 3 3x D 2 3x B 3 2m D 2m 3m B 2v 3uv D 2 2uv B 3 2x y D 3y 3xy 2 2 96 4 6 8 A 3 7 C 2 2 4 27a A 3 3a C 3 2a 6 81n A 3n 2n C 3n 3 8 64a b A 2a 3ab4 C 2ab 3b B 2 7 2 V 2 6 D 100 V 24x y A 3xy 2x y C 3 2x y B 2 2a D 2 3a B 2n 3 D 3 3n B 2a 2a b D 2b 2a B 2x 3y D 2x 3x y