Algebra Questions

Find the measure of ZN Ko L 61 x M P 75 3x N

In Exercises 1 and 2 complete the proof Example 1 1 Given PQ RS Prove PR QS P Q 2 Given Z1 is a complement of 22 22 23 R Prove 1 is a complement of 23 X In Exercises 3 6 name the property that the statement illustrates Example 2 3 If PQ ST and ST UV then PQ UV 4 LF F 5 If XY UV then UV XY 6 If ZL ZM and ZM ZN then ZL ZN PROVING A THEOREM In Exercises 7 9 write a two column proof for the property Example 3 7 Reflexive Property of Segment Congruence 8 Transitive Property of Angle Congruence 9 Transitive Property of Segment Congruence Because MNLQ and LQPN then MNPN by the Reflexive Property of Segment Congruence STATEMENTS 1 PQ RS 2 PQ QR RS QR 3 4 RS QR QS 5 PR QS 10 ERROR ANALYSIS In the diagram MN LQ and LQPN Describe and correct the error in the reasoning L Q STATEMENTS 1 Z1 is a complement of 22 2 22 23 3 mZ1 m2 90 4 m 2 m23 5 6 Z1 is a complement of 23 M REASONS PN 1 2 3 Segment Addition Postulate 4 Segment Addition Postulate 5 E REASONS 1 Given 2 PROOF In Exercises 11 and 12 write a two column proof Example 4 11 Given ZGFH ZGHF 3 4 Definition of congruent angles 5 Substitution Property of Equality 6 Prove ZEFG and ZGHF are supplementary F D GO DIGITAL 12 Given ABFG BF bisects AC and DG Prove BCDF 13 MAKING AN ARGUMENT In the figure SRCE and ACQR Your friend claims that because of this CB AC by the Transitive Property of Segment Congruence Is your friend correct Explain your reasoning B Q R

The numbered disks shown are placed in a box and one disk is selected at random Find the probability of selecting a 3 given that a green disk is selected Find the probability of selecting a 3 given that a green disk is selected Type an integer or a simplified fraction OOOO green green green green OOO green green green blue

Elizabeth brought a box of donuts to share There are two dozen 24 donuts in the box all identical in size shape and color Two are jelly filled 10 are lemon filled and 12 are custard filled You randomly select one donut eat it and select another donut Find the probability of selecting two lemon filled donuts in a row Type an integer or a simplified fraction

z 11 4 11 6 11 7 The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt Wore Seat No Seat Belt Total Belt 411 551 Driver Died Total Find the probability of surviving a car accident given that the driver wore a seat belt The probability as a decimal is Round to three decimal places as needed Driver Survived The probability as a fraction is Type an integer or a simplified fraction 542 412 093 164 736 2395 167 131 576 287 2937 579 224

QUIZ 11 4 11 6 11 7 Question 8 of 14 The probability of selecting a P or a Z is Type an integer or a simplified fraction The game of Scrabble has 100 tiles The diagram shows the number of tiles for each letter and the letter s point value One tile is drawn from Scrabble s 100 tiles Find the probability of selecting a P or a Z This question 1 point s possible www Submit quiz A F2 K B 2 G 3 L C 2 H 2 D 4 1 19 N 6 S X1 4 E 12 J 1 O 8 T6Y2 P 2 U Z1 Q V 2 M 2 R 6 W2 M 2 Nanb of till 2 A 9 Paint vales

You draw one card from a 52 card deck Then the card is replaced in the deck and the deck is shuffled and you draw again Find the probability of drawing a ten the first time and a club the second time The probability of drawing a ten the first time and a club the second time is Type an integer or a simplified fraction

A single die is rolled twice Find the probability of rolling a 1 the first time and a 6 the second time Find the probability of rolling a 1 the first time and a 6 the second time Type an integer or a simplified fraction

Use the spinner shown to answer the question Assume that it is equally probable that the pointer will land on any one of the colored regions If the pointer lands on a borderline spin again If the spinner is spun once find the probability that the pointer lands in a red region The probability that the pointer lands in a red region is Type an integer or a simplified fraction This question 1 point s possible green red red green yellow red

Quiz 11 4 11 6 11 7 You are dealt one card from a standard 52 card deck Find the probability of being dealt a five The probability of being dealt a five is Type an integer or a simplified fraction

4 Caleece took a science test and an English test yesterday The English test had 30 que tions and she got 21 right On the science test she had 20 questions and got 15 right On which test did she earn the higher percentage grade

cos sin 0 cos e Rewrite sine and or cosine cos 0 sin e sin e cos 8 sin e cos 0 sin e cos e sin 0 over a common denominator Type your answer in terms www Simplify your answer

1 3 ems by substitution Solve each system by substitution 1 2x 7y 1 7x y 20 A 3 1 B Infinite number of solutions C 3 1 D 3 1 3 x 7y 10 3x 7y 2 A 2 4 C 4 2 B 4 2 D 4 2 2 4 2 8x 5y 1 y 3 A 2 3 C 6 3 4 3x 24y 3 x 8y 4 A No solution C 5 5 B 2 3 D 6 3 B 5 6 D 5 6

5 5 2x 2y 16 x 6 8 A 8 2 B 8 0 C Infinite number of solutions D 8 3 7 y 6 6x 4y 6 A 5 6 C 5 6 B 5 6 D 5 2 6 8 6 4x 3y 21 x 5y 12 A 3 5 G 3 3 8 81 5y 22 5x 3y 23 A 1 6 C 1 6 B 5 3 D 5 3 B 1 6 D 1 6

In bungee jumping a bungee jump is the amount the cord will stretch at the bottom of the fall The stiffness of the 2W S L where W is the weight of the jumper s cord is related to the amount of stretch by the equation K in pounds K is the cord s stiffness in pounds per foot L is the free length of the cord in feet and S is the stretch in feet Use this equation to answer parts a and b O B exactly 25 feet O C less than 26 feet O D more than 25 feet O E between 25 and 26 feet b If safety requirements will not permit the jumper to get any closer than 6 feet to the ground what is the minimum height required for the ledge in part a

Determine where the graph of f is on or below the graph of g by solving the inequality f x g x Graph f and g together 4 f x x 1 2 g x 8x 8 The graph of f is on or below the graph of g over Type your answer in interval notation Choose the graph which correctly shows f and g together O A Q M B g x Q 37 O C Q G D Q o Ly

In bungee jumping a bungee jump is the amount the cord will stretch at the bottom of the fall The stiffness of the 2W S L where W is the weight of the jumper cord is related to the amount of stretch by the equation K s in pounds K is the cord s stiffness in pounds per foot L is the free length of the cord in feet and S is the stretch in feet Use this equation to answer parts a and b a A 140 pound person plans to jump ott a ledge attached to a cord of length 33 feet It the stiffness of the cord is no less than 26 pounds per foot how much will the cord stretch O A less than 25 feet O B exactly 25 feet O C less than 26 feet O D more than 25 feet O E between 25 and 26 feet

What is the domain of the following function 4 f x x 256 Choose the correct domain O A xl 4 x 4 O B xl 4 x 4 OC xlx 4 or x 4 O D xlxs 4 or x 4 O E 0 00 OF

The game of Scrabble has 100 tiles The diagram shows the number of tiles for each letter and the letter s point value One tile is drawn from Scrabble s 100 tiles Find the probability of selecting a Q or a C The probability of selecting a Q or a C is Type an integer or a simplified fraction Points 0 of 1 GECOID A 9 B 2 C 2 D 4 available until you sign in again F 2 K G 3 L Q V 2 H 2 M 2 R 6 W2 1 12 J 9 N S 6 0 8 T X 1 6 Y 2 Z 2

The mathematics faculty at a college consists of 10 full professors 10 associate professors 7 assistant professors and 10 teaching assistants TAS If one faculty member is randomly selected find the probability of choosing a full professor or a TA The probability is Type an integer or a fraction Simplify your answer

8 Fred s Furniture has a sale Before the sale a couch cost 500 a Fred decreases the price to 450 What is the percent decrease b Fred increases the price back to 500 What was the percent increase c Why are your answers to B and C not the same

K The game of Scrabble has 100 tiles The diagram shows the number of tiles for each letter and the letter s point value One tile is drawn from Scrabble s 100 tiles Find each probability a Find the probability of selecting a U b Find the probability of not selecting a U Part 1 of 2 a The probability of selecting a U is Type an integer or a simplified fraction HW Score 0 0 of O Points 0 of 1 A F2K1 B 2 G3 L Q V M 6 W2 C 2 H D 4 N S X E 12 JOT Y 6 2 UZ how

You are dealt one card from a 52 card deck Find the probability that you are dealt a diamond or a picture card The probability is Type an integer or a simplified fraction

Male Female Total 11 6 41 The probability is Type an integer or a simplified fraction The table shows the educational attainment of the population in a certain country ages 25 and over expressed in millions Find the probability that a randomly selected person aged 25 or over has not completed four years or more of college Years of High School Less than 4 4 only 11 28 16 25 27 53 HW Score 0 0 of 20 points O Points 0 of 1 Years of College Some less than 4 22 18 40 RECEI 4 or more 16 21 37 Total 77 80 157 Save

5 10 4 4 7x x 6x 5 A 4 3 2 012 3 6 11 11 7 4 x 4 18 7x 10 8 6 2 0

Today the population of the town of Wallingford Pennsylvania is 11 300 people In 1980 ere were 10 000 people while in 1990 there were 10 500 people By what percent did the opulation grow from 1990 to today

10 9 X g x 4 3 J 4 10 2 A 7 6 5 7 7 4 A 2 4 4 S 6 7 4 10 12 ve 15 56 17 18 12 30 25 22 22 set 2 1 0 1 0 1 2 2 2 3 4 2 7 2 2 20 From the graph of f x and the table of g x find fog 2

Independent Practice Mixed Percentage Skills Read each problem carefully to determine if you are solving for percent change or per cent of 1 The coal consumption of a factory at April was 460 tons And the coal consumption of the factory at May decreased to 345 tons What was the percentage decrease in the coal consump tion of the factory

7 7 y 6 9 6x 4y 6 A 5 6 C 5 6 9 8x 5y 23 3x 5y 12 B 5 6 D 5 2 C 8 10 8 8x5y 22 5x 3y 23 A 1 6 C 1 6 B 1 6 D 1 6 10 5x 4y 19 5x 2y 17

Fork 11 6 You randomly select one card from a 52 card deck Find the probability of selecting a four or a five The probability is Type an integer or a fraction Simplify your answer

Pizza slices are on special this week Normally the pizza parlor charges 3 per slice of piz a but this week they cost 2 50 What is the percent change in the price from last week to this

The table shows the distribution by age of a random sample of 3370 moviegoers ages 12 74 If one moviegoer is randomly selected from this population find the probability expressed as a simplified fraction that the moviegoer s age is at least 25 The probability is Type an integer or a simplified fraction Age Distribution of Moviegoers Ages 12 24 25 44 45 64 65 74 Number 1050 850 750 720 Save

The table shows the distribution by age of a random sample of 3680 moviegoers ages 12 74 If one moviegoer is randomly selected from this population find the probability expressed as a simplified fraction that the moviegoer is not in the 25 44 age range The probability is Type an integer or a simplified fraction GWWwR Age Distribution of Moviegoers Ages 12 24 25 44 45 64 65 74 Number 550 1300 930 900

Extra Credit Verify the identity 1 1 cos 0 1 1 cos 0 2 2 cot 0

2 In the summer Cate works at the pool as a lifeguard In June she works 74 hours In July she works 85 hours What is the percent increase in her number of hours worked

You are dealt one card from a 52 card deck Find the probability that you are not dealt a red picture card The probability is Type an integer or a simplified fraction

552x 2y 16 x 6y 8 7 A 8 2 B 8 0 C Infinite number of solutions D 8 3 7 y 6 6x 4y 6 A 5 6 C 5 6 B 5 6 D 5 2 6 8 6 4x 3y 21 x 5y 12 A 3 5 C 3 3 8 8x 5y 22 5x 3y 23 A 1 6 C 1 6 B 5 3 D 5 3 B 1 6 D 1 6

work 11 6 Question 1 You are dealt one card from a 52 card deck Find the probability that you are not dealt a two The probability is Type an integer or a fraction Simplify your answer www

1 Solve each system by substitution 1 2x 7y 1 7x y 20 2 2 8x 5y 1 y 3 B2

3 3 x 7y 10 3x 7y 2 A 2 4 C 4 2 B 4 2 D 4 2 4 4 3x 24y 3 x 8y 4 A No solution C 5 5 B 5 6 D 5 6

2 A jacket went on sale for 60 last week but then went back to its original price of 80 this week What was the percent increase in price from last week to this week What was the percent increase in price

P 6 male children Type an integer or a simplified fraction Points 0 of 1 You select a family with three children If M represents a male child and F represents a female child the set of equally likely outcomes for the children s genders is MMM MMF MFM MFF FMM FMF FFM FFF Find the probability of selecting a family with 6 male children Save

A single die is rolled twice The 36 equally likely outcomes are shown to the right Find the probability of getting a first number that is greater than the second number The probability of getting a first number that is greater than the second number is Type an integer or a simplified fraction First Roll Second D B 1 1 1 2 1 3 2 1 2 2 2 3 3 1 3 2 3 3 4 1 4 2 4 3 5 1 5 2 5 3 6 1 6 2 6 3

7 Two competing bakeries are both selling birthday cakes Store A decreased the cost of its cake from 18 to 15 50 Store B decreased the cost of its cake from 21 to 18 Which store decreased the price of its cake by the larger percent

6 At the end of a season Chris records a 100 meter sprint time of 12 5 seconds At the begin ning of the season his time was 14 2 seconds What was the percent decrease in his time over the course of the season

Try it Last year Penncrest High School had 300 students in its freshmen class This year they have 250 students in their freshmen class What is the percent change in size of the freshmen class

5 20 of the books in a book shelf are mysteries 30 are science fiction and the rest are historical fiction If there are 10 mysteries on the shelf how many historical fiction books are there

3 If there are 20 students who are late to school on Monday 15 students who are late to school on Tuesday and 25 who are late to school on Wednesday what is the percent increase in tardiness from Tuesday to Wednesday

2 If there are 20 students who are late to school on Monday 15 students who are late to school on Tuesday and 25 who are late to school on Wednesday what percent of lateness oc curred on Tuesday

4 The average American family of 4 uses 400 gallons of water each day To try to save water the Smith family plans to only use 250 gallons of water a day By what percentage are they de creasing their water consumption