Web viewThe base of each triangle once measured 230 meters. ... 6 x 2 = 2 x 6 _____ 7. ... Section...

ALGEBRA 1Teacher’s Name:

Unit 1Chapter 1Chapter 2

This book belongs to:

Updated Fall 2015Algebra 1 Unit 1 Homework Assignments

1

Date Section Homework Assignment

1.1 Variables and Expressions Pg. 7 #12, 13, 14, 16, 22, 26, 28, 30, 34, 40

1.2 Order of Operations Pg. 13 #20, 21, 26, 28, 32, 34, 50, 52, 56, 66

1.3 Properties of Numbers Pg. 19 #10, 12, 14, 16, 30, 34, 36, 50a

1.1 – 1.3 Review Workbook Pg. 26

1.1 – 1.3 Quiz None

1.5 Equations Pg. 36 #16, 18, 20, 22, 24, 26, 28, 30, 34, 36, 50

1.6 Relations Pg. 43 #12, 15, 16, 18, 20 – 23 all, 34, 36

1.7 Functions Pg. 52 #20, 22, 24, 26, 28, 34, 36, 46, 47, 48

1.8 Interpreting Graphs of Functions Pg. 59 #4, 6, 8, 9, 12, 14

1.5 – 1.8 Review Workbook Pgs. 54 – 55

1.5 – 1.8 Quiz None

2.1 Writing Equations Pg. 78 #22, 24, 26, 28, 32, 40 – 43 all

2.3 Solving Multi-step Equations Pg. 94 #12, 14, 18, 20, 24, 32, 48, 50, 52ab

2.3 Solving Multi-step Equations Pg. 94 #11, 13, 16, 22, 25, 33, 49, 51a

2.4 Solving Equations with the Variable on Each Side Pg. 100 #10 – 22 even, 32, 34, 38, 40

2.4 Solving Equations with the Variable on Each Side Pg. 100 #11 – 21 odd, 25 – 28 all, 45a

2.1, 2.3, 2.4 Review Workbook Pgs. 84 – 85

2.1, 2.3, 2.4 Quiz None

2.8 Literal Equations and Dimensional Analysis Pg. 129 #8 – 16 even, 28

2.8 Literal Equations and Dimensional Analysis Pg. 129 #9 – 17 odd, 29

Unit Review Worksheet Handout

Unit 1 Test None

2

CHAPTER 1

4

Algebra 1Section 1.1 Notes: Variables and ExpressionsWarm-up

Algebraic Expression: an expression consisting of one or more along with one or more arithmetic operations.

Variables: symbols or letters used to represent numbers or values. Any may be used as a variable.

Term: a , a , or a of numbers and variables.

Factors: in an algebraic expression, the .

Product: in an algebraic expression, the of quantities being multiplied.

In the equation 5 x=15, are the factors. The product is .

A raised dot or set of parentheses are often used to indicate a product.

Here are several ways to represent the product of x and y.

Power: An expression of the form , read “x to the nth power”.

Exponent: In an expression of the form xn, the exponent is . It indicates the number of times x is

.

Base: In an expression of the form xn, the base is .

6

Example 1: Write a verbal expression for each algebraic expression.

a) 8 x2 b) y5−16 y c) 16u2−3 d) 12

a+ 6 b7

Example 2: Write an algebraic expression for each verbal expression.

a) a number c less than 5 b) 9 plus the product of 2 and a number d c) one third of the area a

Variables can represent quantities that are known and quantities that are unknown. They are also used in

.

Example 3: Write an algebraic expression.

a) Mr. Nehru bought two adult tickets and three student tickets for the planetarium show. Write an algebraic expression that represents the cost of the tickets.

b) Sears charges $35 for a service call on their appliances. After the first hour (h), there is an $18 hourly charge. Materials (m) for the job are an additional cost. Which equation could be used to find the cost (C) to the customer?A) C=35+18 h+mB) C=35+18(h+m)C) C=35+18 (h−1 )+mD) C=35+18(h−1)

c) Melissa plans to create a painting to sell to an art gallery. The expression 10 c+5 b+8 p+2 s represents her cost, in dollars, for the painting when she buys c canvases, b brushes, p colors of paint, and s packages of sponges. Which statement is true?A) The term 10c represents the cost of 10 canvases.B) The coefficient 8 represents the cost of p colors of paint.C) The term 5b represents the cost of b brushes at $5 per brush.

7

D) The coefficient 2 represents the number of packages of sponges she buys.

Algebra 1Section 1.1 Worksheet

Write a verbal expression for each algebraic expression.

1. 23f 2. 73 3. 5m2 + 2 4. 4d3 – 10

5. x3∙ y4 6. b2 – 3c3 7. k5

68. 4n2

7

Write an algebraic expression for each verbal expression.

9. the difference of 10 and u 10. the sum of 18 and a number 11. the product of 33 and j

12. 74 increased by 3 times y 13. 15 decreased by twice a number 14. 91 more than the square of a number

15. three fourths the square of b 16. two fifths the cube of a number

17. BOOKS A used bookstore sells paperback fiction books in excellent condition for $2.50 and in fair condition for $0.50. Write an expression for the cost of buying x excellent-condition paperbacks and f fair-condition paperbacks.

18. GEOMETRY The surface area of the side of a right cylinder can be found by multiplying twice the number π by the radius times the height. If a circular cylinder has radius r and height h, write an expression that represents the surface area of its side.

19. SOLAR SYSTEM It takes Earth about 365 days to orbit the Sun. It takes Uranus about 85 times as long. Write a numerical expression to describe the number of days it takes Uranus to orbit the Sun.

20. TECHNOLOGY There are 1024 bytes in a kilobyte. Write an expression that describes the number of bytes in a computer chip with n kilobytes.

21. THEATER H. Howard Hughes, Professor Emeritus of Texas Wesleyan College and his wife Erin Connor Hughes attended a record 6136 theatrical shows. Write an expression for the average number of shows they attended per year if they accumulated the record over y years.

8

22. TIDES The difference between high and low tides along the Maine coast in November is 19 feet on Monday and x feet on Tuesday. Write an expression to show the average rise and fall of the tide for Monday and Tuesday.

23. BLOCKS A toy manufacturer produces a set of blocks that can be used by children to build play structures. The product packaging team is analyzing different arrangements for packaging their blocks. One idea they have is to arrange the blocks in the shape of a cube, with b blocks along one edge.

a. Write an expression representing the total number of blocks packaged in a cube measuring b blocks on one edge.

b. The packaging team decides to take one layer of blocks off the top of this package. Write an expression representing the number of blocks in the top layer of the package.

c. The team finally decides that their favorite package arrangement is to take 2 layers of blocks off the top of a cube measuring b blocks along one edge. Write an expression representing the number of blocks left behind after the top two layers are removed.

9

1.1 Textbook Homework

11

Algebra 1Section 1.2 Notes: Order of Operations

Warm-up

Evaluate: to or of an expression

Example 1: Evaluate the expressions.

a) 26 b) 24 c) 45 d) 73

Order of Operations: the rule that lets you know .

8-3

Example 2: Evaluate using the order of operations.

a) 48÷ 23 ∙3+5 b) 20−7+82−7∙ 11

When one or more grouping symbols are used, evaluate within the .

Grouping symbols such as ( ), [ ], and { } are used to clarify or change the order of operations.

13

Example 3: Expressions with grouping symbols.

a) (8−3 ) ∙3 (3+2) b) 4 [12÷ (6−2 ) ]2 c) 25−6 ∙2

33−5 ∙ 3−2

To evaluate an algebraic expression, the variables with their values. Then find the value of the numerical expression

using the .

Example 4: Evaluate the algebraic expression.

a) 2 ( x2− y )+z2 if x = 4, y = 3, and z = 2 b) 5d+(6 f −g ) if d = 4, f = 3, and g = 12

Example 5:

Each side of the Great Pyramid of Giza, Egypt, is a triangle. The base of each triangle once measured 230 meters. The height of each triangle once measured 187 meters. The area of a triangle is one-half the product of the base b and its height h.

a) Write an expression that represents the area of one side of the Great Pyramid.

b) Find the area of one side of the Great Pyramid.

According to the California Department of Forestry, an average of 539.2 fires each year are started by burning debris, while campfires are responsible for an average of 129.1 each year.

a) Write an algebraic expression that represents the number of fires, on average, in d years of debris burning and c years of campfires.

b) How many fires would there be in 5 years?

14


Evaluate each expression.

1. 112 2. 83 3. 54 4. (15 – 5) •2

5. 9 • (3 + 4) 6. 5 + 7 • 4 7. 4(3 + 5) – 5 • 4 8. 22 ÷ 11 • 9 – 32

9. 62 + 3 • 7 – 9 10. 3[10 – (27 ÷ 9)] 11. 2[52 + (36 ÷ 6)] 12. 162 ÷ [6 (7−4 )2]

13 52• 4−5 •42

5(4)14.

(2 •5)2+432−5

15. 7+32

42 •2

Evaluate each expression if a = 12, b = 9, and c = 4.

16. a2 + b – c2 17. b2 + 2a – c2 18. 2c(a + b) 19. 4a + 2b – c2

20. (a2 ÷ 4b) + c 21. c2 • (2b – a) 22. bc2+ac

23. 2 c3−ab

4

24. 2(a−b)2 – 5c 25. b2−2 c2

a+c –b

26. CAR RENTAL Ann Carlyle is planning a business trip for which she needs to rent a car. The car rental company charges $36 per day plus $0.50 per mile over 100 miles. Suppose Ms. Carlyle rents the car for 5 days and drives 180 miles.

a. Write an expression for how much it will cost Ms. Carlyle to rent the car.

b. Evaluate the expression to determine how much Ms. Carlyle must pay the car rental company.

27. GEOMETRY The length of a rectangle is 3n + 2 and its width is n – 1. The perimeter of the rectangle is twice the sum of its length and its width.

a. Write an expression that represents the perimeter of the rectangle.

b. Find the perimeter of the rectangle when n = 4 inches.

15

28. SCHOOLS Jefferson High School has 100 less than 5 times as many studentsas Taft High School. Write and evaluate an expression to find the number of students at Jefferson High School if Taft High School has 300 students.

29. GEOGRAPHY Guadalupe Peak in Texas has an altitude that is 671 feet more than double the altitude of Mount Sunflower in Kansas. Write and evaluate an expression for the altitude of Guadalupe Peak if Mount Sunflower has an altitude of 4039 feet.

30. TRANSPORTATION The Plaid Taxi Cab Company charges $1.75 per passenger plus $3.45 per mile for trips less than 10 miles. Write and evaluate an expression to find the cost for Max to take a Plaid taxi 8 miles to the airport.

31. GEOMETRY The area of a circle is related to the radius of the circle such that the product of the square of the radius and a number π gives the area. Write and evaluate an expression for the area of a circular pizza below. Approximate π as 3.14.

32. BIOLOGY Lavania is studying the growth of a population of fruit flies in her laboratory. She notices that the number of fruit flies in her experiment is five times as large after any six-day period. She observes 20 fruit flies on October 1. Write and evaluate an expression to predict the population of fruit flies Lavania will observe on October 31.

33. CONSUMER SPENDING During a long weekend, Devon paid a total of x dollars for a rental car so he could visit his family. He rented the car for 4 days at a rate of $36 per day. There was an additional charge of $0.20 per mile after the first 200 miles driven.

a. Write an algebraic expression to represent the amount Devon paid for additional mileage only.

b. Write an algebraic expression to represent the number f miles over 200 miles that Devon drove the rented car.

c. How many miles did Devon drive overall if he paid a total of $174 for the car rental?

16


17

Algebra 1Section 1.3 Notes: Properties of NumbersWarm-up

Example 1: Evaluate

a) Evaluate 14

(12−8 )+3(15 ÷5−2) b) Evaluate 2 ∙3+(4 ∙2−8)

Example 2:

a) Becky made a list of trail lengths to find the total miles she rode. Find the total miles Becky rode her horse.

b) Rafael is buying furnishings for his first apartment. He buys a couch for $300, lamps for $30.50, a rug for $25.50, and a table for $50. Find the total cost of these items.

Equivalent expressions: Expressions that denote the same value for all values of the variable(s).

19

1.3 Extra Practice

_____ 1. Commutative Property of Addition A. 2(3 + 4) = 2(3) + 2(4)

_____ 2. Zero Property B. 5 + 0 = 5

_____ 3. Associative Property of Addition C. 5 + 4 = 4 + 5

_____ 4. Additive Identity Property D. 3 x (2 x 4) = (3 x 2) x 4

_____ 5. Multiplicative Identity E. 5 x 1 = 5

_____ 6. Commutative Property of Multiplication F. 6 x 2 = 2 x 6

_____ 7. Associative Property of Multiplication G. 5 x 0 = 0

_____ 8. Distributive Property H. (5 + 2) + 4 = 5 + (2 + 4)

Word Problem Practice

1. A travel checks into a hotel on Friday and checks out the following Tuesday morning. Use the table to find the total cost of the room including tax.

2. Tickets to a baseball game cost $25 each plus $4.50 hangling charge per ticket. If sharon has a coupon for $10 off and orders 4 tickets, how much will she be charged?

3. The cost of tickets to a local amusment park are shown. a) Write an expression to represent the the total cost given adult and child tickets

b) Find the total cost for 5 adults and 8 children.

4. The XYZ Car Rental Angecy charges a flate rate of $29 per day plus $0.32 per mile driven. a) Write an algebraic expession for the rental cost of a car for x days that is driven y miles.

b) Find the total cost for a car for 3 days that is driven 1,000 miles.

21

Name:



1. 2 + 6(9 –32) – 2 2. 5(14 – 39 ÷ 3) + 4 • 14


3. 13 + 23 + 12 + 7 4. 6 • 0.7 • 5

5. SALES Althea paid $5.00 each for two bracelets and later sold each for $15.00. She paid $8.00 each for three bracelets and sold each of them for $9.00.

a. Write an expression that represents the profit Althea made.

b. Evaluate the expression. Name the property used in each step.

6. SCHOOL SUPPLIES Kristen purchased two binders that cost $1.25 each, two binders that cost $4.75 each, two packages of paper that cost $1.50 per package, four blue pens that cost $1.15 each, and four pencils that cost $0.35 each.

a. Write an expression to represent the total cost of supplies before tax.

b. What was the total cost of supplies before tax?

7. EXERCISE Annika goes on a walk every day in order to get the exercise her doctor recommends. If she walks at a rate of 3 miles

per hour for 13

of an hour, then she will have walked 3 × 13

miles. Evaluate the expression and name the property used.

8. SCHOOL SUPPLIES At a local school supply store, a highlighter costs $1.25, a ballpoint pen costs $0.80, and a spiral notebook costs $2.75. Use mental math and the Associative Property of Addition to find the total cost if one of each item is purchased.

23

9. MENTAL MATH The triangular banner has a base of 9 centimeters and a height of 6 centimeters. Using the formula for area of a

triangle, the banner’s area can be expressed as 12

× 9 × 6. Gabrielle finds it easier to write and evaluate ( 12

×6)× 9 to find the

area. Is Gabrielle’s expression equivalent to the area formula? Explain.

10. ANATOMY The human body has 60 bones in the arms and hands, 84 bones in the upper body and head, and 62 bones in the legs and feet. Use the AssociativeProperty to write and evaluate an expression that represents the total number of bones in the human body.

11. TOLL ROADS Some toll highways assess tolls based on where a car entered and exited. The table below shows the highway tolls for a car entering and exiting at a variety of exits. Assume that the toll for the reverse direction is the same.

a. Running an errand, Julio travels from Exit 8 to Exit 5. What property would you use to determine the toll?

b. Gordon travels from home to work and back each day. He lives at Exit 15 on the toll road and works at Exit 22. Write and evaluate an expression to find his daily toll cost. What property or properties did you use?

24

Entered Exited Toll

Exit 5 Exit 8 $0.50

Exit 8 Exit 10 $0.25

Exit 10 Exit 15 $1.00

Exit 15 Exit 18 $0.50

Exit 18 Exit 22 $0.75


25

Algebra 1 Name_________________________1.1 – 1.3 Review Date _____________ Period ______

1. Write a verbal expression for each of the following:

a. 2m b. w – 24 c. 23

r 4

2. Write an algebraic expression for each of the following: b. One third of a number x b. The product of three and a number r increased by sixteen

3. Evaluate each expression

a. 10+83÷ 16 b. (18−42 )2+8 c. 3∙ 92−32∙ 93 ∙ 9

4. Evaluate a2bc−b2 if a=8, b=4, c=16

5. Evaluate the expression 6 ∙ 16+5 (12 ÷ 4−3 ).

6. Carolyn has 9 quarters, 4 dimes, 7 nickels, and 2 pennies. Write and evaluate the expression to determine how much money she has.

7. Mr. Martinez orders 250 key chains printed with his athletic team’s logo and 500 pencils printed with their Web address. If k represents the cost of each key chain and p represents the cost of each pencil, write an expression that represents the cost of the order.

8. Jocelyn babysat for 25 hours and worked at the grocery store for 15 hours in a week. a. Let b be the amount she earns per hour babysitting and g be the amount she earns per hour at the grocery

store. Write an algebraic expression that represents the total amount she earned.

b. If Jocelyn earns $10 an hour babysitting and $8.25 an hour working at the grocery store, find the total amount she earned that week.

9. A certain smartphone family plan costs $55 per month plus additional usage costs. It costs $2 per each extra megabyte used. Let x represent the number of megabytes of data used above the plan. Interpret the following expressions:

a. 2x27

b. 2x + 55

28

Algebra 1Section 1.5 Notes: Equations

Warm-upUse the distributive property to rewrite the expression without parentheses.1.) 8(x + 5) 2.) 4(y – 7) 3.) (x – 4)(2)

4.) –6(r – 1) 5.) (m – 7)( –3) 6.) –12(n + 3)

7.) (x)(x + 3) 8.) (–a)(a + 3) 9.) (2x + 1)(5x)

Open Sentence: a mathematical statement with one or more .

Equation: a mathematical sentence that contains an .

Solving an open sentence: Finding a for the that results in a true

sentence or an that results in a true statement when substitute into the equation.

Solution: a replacement value for the variable in an open sentence.

Replacement Set: a from which replacements for a variable may be chosen.

Set: a that is often shown using braces.

Element: Each in the set.

Solution Set: the set of elements from the replacement set that make an open sentence .

Example 1:

a) Find the solution set of the equation 4 a+7=23 if the replacement set is {2, 3, 4, 5, 6}.

b) Find the solution set of the equation 28=4 (1+3d ) if the replacement set is {0, 1, 2, 3}.

30

You can often solve an equation by applying the order of operations.

Example 2: Standardized test practice

a) Solve 3+4 (23−2 )=b .

a. 19 b. 27 c. 33 d. 42

b) Solve t=92÷ (5−2 ) .

a. 3 b. 6 c. 14.2 d. 27

Some equations have a unique solution. Other equations do not have a solution.

Example 3: Solve the equation. 4 n− (12+2 )=n (6−2 )−9

Identity: an equation that is true for every value of the variable.

Example 4: Solve (5+8÷ 4 )+3 k=3 (k+32 )−89

Example 5:

a) Dalila pays $16 per month for a gym membership. In addition, she pays $2 per Pilates class. Write and solve an equation to find the total amount Dalila spent this month if she took 12 Pilates classes.

b) Amelia drives an average of 65 miles per hour. Write and solve an equation to find the time it will take her to drive 36 miles.

31


Find the solution of each equation if the replacement sets are a = {0 , 12

,1 , 32

, 2} and b = {3, 3.5, 4, 4.5, 5}.

1. a + 12

= 1 2. 4b – 8 = 6 3. 6a + 18 = 27

4. 7b – 8 = 16.5 5. 120 – 28a = 78 6. 28b

+ 9 = 16

Solve each equation.

7. x = 18.3 – 4.8 8. w = 20.2 – 8.95 9. 37−918−11

= d

10. 97−2541−23

= k 11. y = 4 (22−4)3 (6)+6

12. 5(22)+4(3)

4(23−4 ) = p

13. TEACHING A teacher has 15 weeks in which to teach six chapters. Write and then solve an equation that represents the number of lessons the teacher must teach per week if there is an average of 8.5 lessons per chapter.

14. CELL PHONES Gabriel pays $40 a month for basic cell phone service. In addition, Gabriel can send text messages for $0.20 each. Write and solve an equation to find the total amount Gabriel spent this month if he sends 40 text messages.

32

15. TIME There are 6 time zones in the United States. The eastern part of the U.S., including New York City, is in the Eastern Time Zone. The central part of the U.S., including Dallas, is in the Central Time Zone, which is one hour behind Eastern Time. San Diego is in the Pacific Time Zone, which is 3 hours behind Eastern Time. Write and solve an equation to determine what time it is in California if it is noon in New York.

16. FOOD Part of the Nutrition Facts label from a box of macaroni and cheese is shown below.

Write and solve an equation to determine how many servings of this item Alisa can eat each day if she wants to consume exactly 45 grams of cholesterol.

17. CRAFTS You need 30 yards of yarn to crochet a small scarf. Cheryl bought a 100-yard ball of yarn and has already used 10 yards. Write and solve an equation to find how many scarves she can crochet if she plans on using up the entire ball.

18. POOLS There are approximately 202 gallons per cubic yard of water. Write and solve an equation for the number of gallons of water that fill a pool with a volume of 1161 cubic feet. (Hint: There are 27 cubic feet per cubic yard.)

19. VEHICLES Recently developed hybrid cars contain both an electric and a gasoline engine. Hybrid car batteries store extra energy, such as the energy produced by braking. Since the car can use this stored energy to power the car, the hybrid uses less gasoline per mile than cars powered only by gasoline. Suppose a new hybrid car is rated to drive 45 miles per gallon of gasoline.

a. It costs $40 to fill the gasoline tank with gas that costs $3.00 per gallon. Write and solve an equation to find the distance the hybrid car can go using one tank of gas.

33

b. Write and solve an equation to find the cost of gasoline per mile for this hybrid car. Round to the nearest cent.


34

Algebra 1Section 1.6 Notes: RelationsWarm-up1. A car is currently 300 miles from its destination and is traveling against the wind. The car travels 60 miles per hour (mph) when there is no wind. The car’s distance from its destination is given by the formula D=300−h(60−c ). Given: D = distance in miles, h = number of hours, c = speed of the wind in mph. What is a correct formula for the car’s distance from its destination after 4 hours?

A) D=17400−290 c B) D=17400−c C) D=54−c D) D=54+4 c

Solve each equation.

2. (6−427 )+ y=4 3. (3+42−9 ) m=90 4. If 8=112

x, then what is 3 x?

Coordinate System: The grid formed by the intersection of two number lines, the axis and the ___ axis.

Ordered pair: a set of used to locate any point on a coordinate plane, written in the form .

x-coordinate: the number in an ordered pair.

y-coordinate: the number in an ordered pair.

Relation: a set of ordered pairs

Mapping: illustrates how each element of the domain is with an element in the range.

Domain: the set of numbers of the ordered pairs in a relation.

Range: the set of numbers of the ordered pairs in a relation.

36

In the relation above, the domain is and the range is .

37

Example 1:

a) Express {(4, 3), (-2, -1), (2, -4), (0, -4)} as a table, a graph, and a mapping.

b) Determine the domain and range of the relation.

Independent variable: the variable in a relation with a value that is .

Dependent variable: the variable in a relation with a value that of the independent variable.

*

Example 3: Identify the independent and the dependent variable for each relation.

a) In warm climates, the average amount of electricity used rises as the daily average temperature increases and falls as the daily average temperature decreases.

b) The number of calories you burn increases as the number of minutes that you walk increases.

A relation can be graphed without a scale on either axis. These graphs can be interpreted by analyzing their shape.

Example 3: Describe what is happening in each graph.

a) b)

38

x y

http://www.google.com/url?sa=i&rct=j&q=coordinate+plane&source=images&cd=&cad=rja&uact=8&docid=qiT2IeMQvFsCTM&tbnid=u8gKK_ic99i_pM:&ved=0CAUQjRw&url=http://www.mathnstuff.com/papers/planes.htm&ei=b0CNU9O5G8SqyATvsoGgCg&bvm=bv.68191837,d.aWw&psig=AFQjCNH-Es4rXELgNvkf0ymqRRFFzdQZsA&ust=1401852392952807

X Y

0 9−8 3

2 −6

1 4


1. Express {(4, 3), (–1, 4), (3, –2), (–2, 1)} as a table, a graph, and a mapping. Then determine the domain and range.

Describe what is happening in each graph.

2. The graph below represents the height of a tsunami as it travels across an ocean.

3. The graph below represents a student taking an exam.

Express the relation shown in each table, mapping, or graph as a set of ordered pairs.

4. 5. 6.

7. BASEBALL The graph shows the number of home runs hit by Andruw Jones of the Atlanta Braves. Express the relation as a set of ordered pairs. Then describe the domain and range.

39

8. HEALTH The American Heart Association recommends that your target heart rate during exercise should be between 50% and 75% of your maximum heart rate. Use the data in the table below to graph the approximate maximum heart rates for people of given ages.

Age (years) 20 25 30 35 40

Maximum Heart Rate(beats per minute) 200 195 190 185 180

Source: American Heart Association

9. NATURE Maple syrup is made by collecting sap from sugar maple trees and boiling it down to remove excess water. The graph shows the number of gallons of tree sap required to make different quantities of maple syrup. Express the relation as a set of ordered pairs.

10. BAKING Identify the graph that best represents the relationship between the number of cookies and the equivalent number of dozens.

11. DATA COLLECTION Margaret collected data to determine the number of books her schoolmates were bringing home each evening. She recorded her data as a set of ordered pairs. She let x be the number of textbooks brought home after school, and y be the number of students with x textbooks. The relation is shown in the mapping.

a. Express the relation as a set of ordered pairs.

b. What is the domain of the relation?

c. What is the range of the relation?

40


41

X Y

7 5

–4 –3

7 6

1 –2

Algebra 1Section 1.7 Notes: Functions

Warm-up1. Express the relation {(−1 , 0 ) , (2,−4 ) , (−3 ,1 ) , (4 ,−3 ) } as a table, a graph, and a mapping. Then determine the domain and range.

2. A student earns $8 for every lawn he mows. Which equation shows the relationship between the number of lawns mowed m and the wages earned d .

A) m=d+8 B) m=8 d C) 8−m=d D) 8 m=d

3. Steve owns a winter snow plow business and charges a standard fee of $20 per driveway. Steven’s expense for each driveway include $2 per day for salt disbursement and $6 for gas. Steve uses the equation p=x [20−(6+2 d )] to determine his profit. Let p=profit ,∈dollars, x=number of driveways, d=number of days. Which equation could be used to find Steve’s profit when he plows 10 driveways?

A) p=14+2d B) p=14−2 d C) p=140−20d D) p=140+20 d

Function: a relationship between . In a function there is output for each input.

*Cannot have two identical inputs in the domain going to two different outputs in the range.

Example 1:Determine whether each relation is a function. Explain.

a) b) c)

43

Discrete function: a function of points that are connected. Continuous function: a function that can be graphed with a line or a curve.

Example 2: Circle the continuous functions below.

Example 3: There are three lunch periods at a school. During the first period, 352 students eat. During the second period 304 students eat. During the third period, 391 students eat.

a) Make a table showing the number of students for each of the three lunch periods.

b) Determine the domain and range of the function.

c) Write the data set of ordered pairs then graph the data.

d) State whether the function is discrete or continuous. Explain your reasoning.

Vertical line test: if any line passes through no more than one point of the graph of a relation, then the relation is a function.

*Use when you are given a graph

Example 4: Determine whether the following graphs represent functions.

a) b) c)

44

AB C D E

A function can be represented in different ways.

Function Notation: A way to a function that is defined by an equation. In function notation, the equation y=3 x−8is written f ( x )=3 x−8.

It is said “f of x”. If a number is inside the parenthesis than that is the number you for x.

Example 5: For f ( x )=3 x−4, find each value.

a) f (4 ) b) Find the missing values in the table using the function above.

Nonlinear function: a function with a graph that is not a line.

Example 6: If h ( t )=1248−160t +16 t2, find each value.

a) h(3) b) h(2 z )

45

x f(x)−8−110

X Y

1 5

–4 –3

7 6

1 –2


Determine whether each relation is a function.

1. 2. 3.

4. {(1, 4), (2, –2), (3, –6), (–6, 3), (–3, 6)} 5. {(6, –4), (2, –4), (–4, 2), (4, 6), (2, 6)}

6. x = –2 7. y = 2

If f(x) = 2x – 6 and g(x) = x – 2 x2, find each value.

8. f(2) 9. f (−12 ) 10. g(–1)

11. g (−13 ) 12. f(7) – 9 13. g(–3) + 13

14. f(h + 9) 15. g(3y) 16. 2[g(b) + 1]

17. WAGES Martin earns $7.50 per hour proofreading ads at a local newspaper. His weekly wage w can be described by the equation w = 7.5h, where h is the number of hours worked.

a. Write the equation in function notation.

b. Find f(15), f(20), and f(25).

18. ELECTRICITY The table shows the relationship between resistance R and current I in a circuit.

Resistance (ohms) 120 80 48 6 4

47

Current (amperes) 0.1 0.15 0.25 2 3

a. Is the relationship a function? Explain.

b. If the relation can be represented by the equation IR = 12, rewrite the equation in function notation so that the resistance R is a function of the current I.

c. What is the resistance in a circuit when the current is 0.5 ampere?

19. TRANSPORTATION The cost of riding in a cab is $3.00 plus $0.75 per mile. The equation that represents this relation is y = 0.75x + 3, where x is the number of miles traveled and y is the cost of the trip. Look at the graph of the equation and determine whether the relation is a function.

20. TEXT MESSAGING Many cell phones have a text messaging option in addition to regular cell phone service. The function for the monthly cost of text messaging service from Noline Wireless Company is f(x) = 0.10x + 2, where x is the number of text messages that are sent. Find f(10) and f(30), the cost of 10 text messages in a month and the cost of 30 text messages in a month.

21. GEOMETRY The area for any square is given by the function y = x2, where x is the length of a side of the square and y is the area of the square. Write the equation in function notation and find the area of a square with a side length of 3.5 inches.

22. TRAVEL The cost for cars entering President George Bush Turnpike at Beltline road is given by the relation x = 0.75, where x is the dollar amount for entrance to the toll road and y is the number of passengers. Determine if this relation is a function. Explain.

23. CONSUMER CHOICES Aisha just received a $40 paycheck from her new job. She spends some of it buying music online and saves the rest in a bank account. Her savings is given by f(x) = 40 – 1.25x, where x is the number of songs she downloads at $1.25 per song.

a. Graph the function.

48

b. Find f(3), f(18), and f(36). What do these values represent?

c. How many songs can Aisha buy if she wants to save $30?1.7 Textbook Homework

49

Algebra 1Section 1.8 Notes: Interpreting Graphs of FunctionsWarm-upDetermine whether each relation is a function.1. 2. 3.

4. If f ( x )=3 x+7, find f (10). 5. The graph of y=x3 is shown. What is the approximatesolution if x=1?

y-intercept: the of a point where a graph crosses the y – axis.

x-intercept: the of a point where a graph crosses the x – axis.

Example 1: The graph shows the cost at a community college y as a function of the number of credit hours taken x.

a) Identify the function as linear or nonlinear.

b) Estimate and interpret the intercepts of the function.

c) Approximate the cost of a student taking 4 credit hours.

Line Symmetry: if a vertical line is drawn and each half of the graph on either side of the line matches exactly.

Example 2: The graph shows the cost y to manufacture x units of product. Describe and interpret any symmetry.

51

Example 3: The graph shows the population y of deer x years after the animals are introduced on an island.

Estimate when the deer population is:

A) positive

B) negative

C) increasing

D) decreasing

E) at its maximum population (relative maximum)

F) at its minimum population (relative minimum)

Describe the end behavior of the graph.

How many deer will there be after 0.5 years? 5 years?

The deer population started at about 80 deer. When will the deer population be at 80 again?

52


Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the x–coordinate of any relative extrema (relative max or min), and the end behavior of the graph.

1. 2.

3. 4.

5. HEALTH The graph shows the Calories y burned by a 130-pound person swimming freestyle laps as a function of time x. Identify the function as linear or nonlinear. Then estimate and interpret the intercepts.

53

6. TECHNOLOGY The graph below shows the results of a poll that asks Americans whether they used the Internet yesterday. Estimate and interpret where the function is positive, negative, increasing, and decreasing, the x-coordinates of any relative extrema, and the end behavior of the graph.

7. GEOMETRY The graph shows the area y in square centimeters of a rectangle with perimeter 20 centimeters and width x centimeters. Describe and interpret any symmetry in the graph.

8. EDUCATION Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the x-coordinate of any relative extrema, and the end behavior of the graph.

54


55

Algebra 1 Name_________________________1.5 – 1.8 Review Date _____________ Period ______

1. Find the solution of n2 – 11 = 3 if the replacement set is {26, 28, 29, 30, 31}.

2. Solve the following equation: 4 [32−5(8−6)]

32−7 + 11 = r

3. What is the domain and range of the relation?

4. Determine which relation is a function.

A B y = 15 x + 2 C D {(3, 0), (– 2, – 2), (7, – 2), (– 2, 0)}

5. Which statement best describes the graph of the price of one share of a company’s stock shown at the right?A The price increased more in the morning than in the afternoon. B The price decreased more in the morning than in the afternoon.C The price increased more in the afternoon than in the morning.D The price decreased more in the afternoon than in the morning.

6. If h(r) = 23 r – 6, what is the value of h(–9)?

For Questions 7 and 8, use the graph.7. Interpret the y-intercept of the graph.

8. Interpret the end behavior of the function in terms of social networking.

57

x 3 4 4 5

y – 1 2 3 4

9. A car rental company charges a rental fee of $20 per day in addition to a charge of $0.30 per mile driven. Write and solve an equation to find the total amount Bruce spent if he rents a car for 3 days drives 50 miles.

a) Define your variables given the information in the problem

b) Write an equation to represent the total amount Bruce owes

c) Solve your equation

Use the graph that shows Robert’s bowling scores for his last four games to answer Questions 10 and 11.

10. Identify the independent and dependent variables.

11. Describe what may have happened between the first and fourth games.

For Questions 12–14, use the table that shows 2006 airmail letter rates to New Zealand.

12. Write the data as a set of ordered pairs.

13. Draw a graph that shows the relationship between the weight of a letter sent airmail and the total cost.

*Use the graph to the right

14. Interpret the end behavior of the function.

For Questions 15 – 20, use the graph at the right.

15. Is the function linear or nonlinear (circle one)?

16. Estimate the intercepts. Explain what they represent.

17. Does the function have symmetry?

18. What is the x-coordinate of any relative extrema? What does it represent?

19. Estimate and interpret where the function is positive, negative, increasing, and decreasing.58

Weight (oz) Rate ($)2.0 1.803.0 2.754.0 3.705.0 4.65

20. Interpret the end behavior of the function

59

CHAPTER 2

60

Algebra 1Section 2.1 Notes: Writing Equations

Warm-up1. Write an algebraic expression for the verbal expression twice the sum of a number and 7.

2. In 2008 there were 25 iPad’s at Oswego East High School. Starting in 2009 the school bought 12 more iPads at the end of each year. The equation T=12 x+25 can be used to determine T, the total number of iPads at the school x years after 2008. What was the total number of iPad’s at Oswego East High School at the end of 2014?

3. Rewrite (5 b−6 ) 2+3b in simplest form.

To write an equation…

1) Identify the for which you are looking and assign a variable to it. 2) Write the sentence as an

* Look for key words that indicate where to place the equal to sign.Examples: is, is as much as, is the same as, is identical to

Example 1: Translate the sentence into an equation.

a) A number b divided by three is equal to six less than c.

b) Fifteen more than z times six is y times two minus eleven.

c) Two plus the quotient of a number and 8 is the same as 16.

d) Twenty-seven times k is h squared decreased by 9.

Example 2:

a) A jelly bean manufacturer produces 1,250,000 jelly beans per hour. How many hours does it take them to produce 10,000,000 jelly beans?

b) Mark wants to purchase five notebooks and a folder. If the folder costs $0.50, which equation represents the situation in which x denotes the cost per notebook purchased and y denotes the total cost of Mark’s purchase?A) y=0.50 xB) y=x+0.50C) y=0.50 x+5D) y=5 x+0.50

Now find Mark’s total cost if each notebook is $1.

62

Formula: a rule for the relationship between certain quantities.

Example 3: Translate the sentence into a formula.

a) The perimeter of a square equals four times the length of a side.

b) In a right triangle, the square of the measure of the hypotenuse c is equal to the sum of the squares of the measures of the legs, a and b.

If you are given an equation you can write a sentence or create your own word problem.

Example 4: Translate the equation into a verbal sentence.

a) 12−2 x=−5 b) a2+3b= c6

When given a set of information, you can create a problem that relates a story.

Example 5: Write a problem based on the given information.

a) f =¿ cost of fries f +1.50=¿ cost of burger 4 ( f +1.50 )−f =8.25

b) p=¿ Beth’s salary 0.1 p=¿ bonus p+0.1 p=525

63


Translate each sentence into an equation. Then solve the equation.

1. Fifty-three plus four times b is as much as 21.

2. The sum of five times h and twice g is equal to 23.

3. One fourth the sum of r and ten is identical to r minus 4.

4. Three plus the sum of the squares of w and x is 32.

Translate each sentence into a formula.

5. Degrees Kelvin K equals 273 plus degrees Celsius C.

6. The total cost C of gas is the price p per gallon times the number of gallons g.

7. The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.

Translate each equation into a sentence.

8. r – (4 + p) = 13

r 9. 35

t + 2 = t

10. 9(y2 + x) = 18 11. 2(m – n) = x + 7

Write a problem based on the given information.12. a = cost of one adult’s ticket to zoo 13. c = regular cost of one airline ticket

a – 4 = cost of one children’s ticket to zoo 0.20c = amount of 20% promotional discount2a + 4(a – 4) = 38 3(c – 0.20c) = 330

14. GEOGRAPHY About 15% of all federally–owned land in the 48 contiguous states of the United States is in Nevada. If F represents the area of federally–owned land in these states, and N represents the portion in Nevada, write an equation for this situation.

15. FITNESS Deanna and Pietra each go for walks around a lake a few times per week. Last week, Deanna walked 7 miles more than Pietra.

a. If p represents the number of miles Pietra walked, write an equation that represents the total number of miles T the two girls walked.

b. If Pietra walked 9 miles during the week, how many miles did Deanna walk?

c. If Pietra walked 11 miles during the week, how many miles did the two girls walk together?

16. HOUSES The area of the Hartstein’s kitchen is 182 square feet. This is 20% of the area of the first floor of their house. Let F represent the area of the first floor. Write an equation to represent the situation.

64

17. FAMILY Katie is twice as old as her sister Mara. The sum of their ages is 24. Write a one-variable equation to represent the situation.

18. GEOMETRY The formula F + V = E + 2 shows the relationship between the number of faces F, edges E, and vertices V of a polyhedron, such as a pyramid. Write the formula in words.

19. WIRELESS PHONE Spinfrog wireless phone company bills on a monthly basis. Each bill includes a $29.95 service fee for 1000 minutes plus a $2.95 federal communication tax. Additionally, there is a charge of $0.05 for each minute used over 1000. Let m represent the number of minutes over 1000 used during the month. Write an equation to describe the cost p of the wireless phone service per month.

20. TEMPERATURE The table below shows the temperature in Fahrenheit for some corresponding temperatures in Celsius.

Celsius Fahrenheit

–20° –4°

–10° 14°

0° 32°

10° 50°

20° 68°

30° 86°

a. Write a formula for converting Celsius temperatures to Fahrenheit temperatures.

65

b. Find the Fahrenheit equivalents for 25ºC and 35ºC.


66

Algebra 1Section 2.3 Notes: Solving Multi-Step Equations

Warm-up

Multi-Step Equation: an equation that requires to solve.

To solve a multi-step equation, we must .

Example 1: Solve and check your solution.

a) 2 q+11=3 Check b) k+912

=−2 Check

c) Consider the procedure used below to solve the given equation.Given: 3 ( x−8 )−9 x−5=19

Step 1: 3 x−24−9 x−5=19

Step 2: −6 x−29=19

Step 3: −6 x=19+29

Step 4: −6 x=48

Step 5: x=−8

Which statement about the solution of the given equation is true?1. The first mistake was made in Step 1.2. The first mistake was made in Step 2.

68

3. The first mistake was made in Step 3.4. Each step is correct.

69

Example 2: Write and solve a multi-step equation.

a) Susan had a $10 coupon for the purchase of any item. She bought a coat that was 12

its original price. After using the coupon,

Susan paid $125 for the coat before taxes. What was the original price of the coat? Write an equation for the problem. Then solve the equation.

b) Len read 34

of a graphic novel over the weekend. Monday, he read 22 more pages. If he has read 220 pages, how many pages does

the book have. Write and solve a multi-step equation.

Example 3: Using equations in real life.

On balances greater than $10,000, a savings account pays an annual interest rate of 1% on the first $10,000 and 2% on the amount of the balance exceeding $10,000. The amount of interest after 1 year when the balance is over $10,000 is given by the formula below, where I is the interest in dollars, and x is the present balance in dollars.

I=0.01 (10,000 )+0.02(x−10,000)

a) What is the interest amount earned in the account if the present balance is $22,000?

b) What is the present balance needed in the account in order for the amount of interest to be $300?

70

2.3 Day 1 Textbook Homework

71

2.3 Day 2 Warm-upSolve each problem.1. If 15 added to 4 times a number is −9, what is the number? Hint: Write an equation.

2. 5 x+3=23 3. 4=3 a−14

4. w7

+3=−1

73


Solve each problem by working backward.

1. Three is added to a number, and then the sum is multiplied by 4. The result is 16. Find the number.

2. A number is divided by 4, and the quotient is added to 3. The result is 24. What is the number?

3. Two is subtracted from a number, and then the difference is multiplied by 5. The result is 30. Find the number.

4. BIRD WATCHING While Michelle sat observing birds at a bird feeder, one fourth of the birds flew away when they were startled by a noise. Two birds left the feeder to go to another stationed a few feet away. Three more birds flew into the branches of a nearby tree. Four birds remained at the feeder. How many birds were at the feeder initially?

Solve each equation. Check your solution.

5. –12n – 19 = 77 6. 17 + 3f = 14 7. 15t + 4 = 49

8. u5

+ 6 = 2 9. d

−4 + 3 = 15 10.

b3

– 6 = –2

11. 12

y – 18

= 78

12. –32 – 35

f = –17 13. 8 – 38

k = –4

14. r+13

12 = 1 15.

15−a3

= –9 16. 3 k−7

5 = 16

17. x7

– 0.5 = 2.5 18. 2.5g + 0.45 = 0.95 19. 0.4m – 0.7 = 0.22

75

Write an equation and solve each problem.

20. Seven less than four times a number equals 13. What is the number?

21. GEOMETRY A rectangular swimming pool is surrounded by a concrete sidewalk that is 3 feet wide. The dimensions of the rectangle created by the sidewalk are 21 feet by 31 feet.

a. Find the length and width of the pool.

b. Find the area of the pool.

c. Write and solve an equation to find the area of the sidewalk in square feet.

77


78

Algebra 1Section 2.4 Notes: Solving Equations with the Variable on Each Side

Warm-up

To solve an equation that has variables on each side, use the to write an equivalent equation with the variable terms on one side.

Example 1: Solve the equation. Check your solution.

a) 8+5 c=7 c−2 b) 5 a+2=6−7a

c) x2+1=1

4x−6 d) 1.3 c=3.3 c+2.8

If equation containing grouping symbols, such as parentheses or brackets, use the to remove the grouping symbols.

Example 2: Solve each equation and check your solution.

a) 13

(18+12 q )=6 (2 q−7 ) b) 7 (n−1 )=−2 (3+n )

80

Example 3: Equivalent Equations

a) Which equation is equivalent to 2 (4 x−1 )+3=8(2 x−3)

A) 8 x+1=16 x−24B) 8 x+2=16 x−3C) 8 x+4=16 x−24D) 8 x+5=16 x−24

b) Which equation is equivalent to 0.2 x+0.5 (10−x )=1.5

A) 5+.3 x=1.5B) 5−.3 x=1.5C) 5+.7 x=1.5D) 5−.8 x=1.5

81


82

Section 2.4 DAY 2 Notes: Solving Equations with the Variable on Each SideWarm-upSolve the equation.1. 7 (1− y )=−3( y−2) 2. 10 (−4+x )=2 x

3. 8 a−4 (5 a−2 )=12a

Some equations have meaning there is no value of the variable that will result in a true equation.

Some equations are of the variable. We call these identities.

Example 3: Solve each equation.

a) 8 (5 c−2 )=10(32+4 c) b) 4 (t+20 )=15(20t +400)

Example 4: Solve each equation.a) 2 ( x−3 )=−6+2 x b) 12+4 x=2(2 x+5)

Example 5: Standardized test practice.

a) Find the value of h so that the figures have the same area.

A. 1 B. 3 C. 4 D. 5

b) Find the value of x so that the figures have the same perimeter.

84

F. 1.5 G. 2 H. 3.2 J. 4

85


Solve each equation. Check your solution.

1. 5x – 3 = 13 – 3x 2. –4r – 11 = 4r + 21

3. 1 – m = 6 – 6m 4. 14 + 5n = –4n + 17

5. 12

k – 3 = 2 – 34

k 6. 12

(6 – y) = y

7. 3(–2 – 3x) = –9x – 4 8. 4(4 – w) = 3(2w + 2)

9. 9(4b – 1) = 2(9b + 3) 10. 3(6 + 5y) = 2(–5 + 4y)

11. –5x – 10 = 2 – (x + 4) 12. 6 + 2(3j – 2) = 4(1 + j)

13. 52

t – t = 3 + 32

t 14. 1.4f + 1.1 = 8.3 – f

15. 23

x – 16

= 12

x + 56

16. 2 – 34

k = 18

k + 9

17. 12

(3g – 2) = g2

18. 13

(n + 1) = 16

(3n – 5)

19. 12

(5 – 2h) = h2

20. 19

(2m – 16) = 13

(2m + 4)

21. 3(d – 8) – 5 = 9(d + 2) + 1 22. 2(a – 8) + 7 = 5(a + 2) – 3a – 19

23. NUMBERS Two thirds of a number reduced by 11 is equal to 4 more than the number. Find the number.

24. NUMBERS Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twice the number. What is the number?

25. NUMBER THEORY Tripling the greater of two consecutive even integers gives the same result as subtracting 10 from the lesser even integer. What are the integers?

26. GEOMETRY The formula for the perimeter of a rectangle is P = 2ℓ, + 2w, where ℓ is the length and w is the width. A rectangle has a perimeter of 24 inches. Find its dimensions if its length is 3 inches greater than its width.

86

27. OLYMPICS In the 2010 Winter Olympic Games in Vancouver, Canada, the United States athletes won 1 more than 4 times the number of gold medals won by the French athletes. The United States won 7 more gold metals than the French. Solve the equation 7 + F = 4F + 1 to find the number of gold medals won by the French athletes.

28. AGE Diego’s mother is twice as old as he is. She is also as old as the sum of the ages of Diego and both of his younger twin brothers. The twins are 11 years old. Solve the equation 2d = d + 11 + 11 to find the age of Diego.

29. GEOMETRY Supplementary angles are angles whose measures have a sum of 180º. Complementary angles are angles whose measures have a sum of 90º. Find the measure of an angle whose supplement is 10º more than twice its complement. Let 90 – x equal the degree measure of its complement and 180 – x equal the degree measure of its supplement. Write and solve an equation.

30. NATURE The table shows the current heights and average growth rates of two different species of trees. How long will it take for the two trees to be the same height?

Tree Species Current Height Annual growth

A 38 inches 4 inches

B 45.5 inches 2.5 inches

31. NUMBER THEORY Mrs. Simms told her class to find two consecutive even integers such that twice the lesser of two integers is 4 less than two times the greater integer.

a. Write and solve an equation to find the integers.

b. Does the equation have one solution, no solutions, or is it an identity?Explain.

87


88

Algebra 1 Name:

2.1, 2.3, 2.4 Review Period:

1. Translate the sentence into an equation and then solve.a) The product of two and a number increased by b) Five plus the quotient of a number and −1 is

four is the same as 12. equal to eight.

2. Adam is on the track & cross country team and he runs 5 miles each day. His coach will give him a prize if he logs 200 miles. How many days will it take Adam to earn his prize?

3. Carla bought a pair of jeans that was 12 its original price. She also had a $5 coupon for the purchase of any

item. After using the coupon, Carla paid $40 for the jeans before taxes. What was the original price of the pair of jeans? Write an equation for the problem. Then solve the equation.

Equation:

Solution:

4. Translate the sentence into a formula: “The perimeter is equal to the sum of twice the length and twice the width.”

5. Using the formula above, find the width if you know the perimeter is 14 feet and the length is 3 feet.

6. Translate the equation into a verbal sentence. Then solve the equation.

a) x2=−6 b) 4 x+3=−13

90

Solve the equation. Write “no solution” or “all solutions” if necessary.

7. −x5

−3=2 8. 4 (b−2 )=2(5−b) 9. 4 (4−4k )=−10−16 k

10. 15=11+12 x 11. 8q+12=4 (3+2 q) 12. 14

x+3=7

13. Drew has saved three times the number of bottle caps that Liz has saved plus 2. The number of bottle caps Drew saved is also seven times the difference of the number of bottle caps and 10 that Liz has saved. Write and solve an equation to find the number of bottle caps they each have saved.

Equation:

L =

Liz has bottle caps

Drew has bottle caps

14. Find the value of x so the rectangles have the same area.

91

15 10

x x + 3

Algebra 1Section 2.8 Notes: Literal Equations and Dimensional Analysis

Warm-upSolve each equation. Check your solution.1.) 8 y+3=5 y+15 2.) 2.8w−3=5w−0.8

3.) 5 ( x+3 )+2=5 x+17 4.) 12 x+4 (6−x )=2 x+60

Some equations contain more than one . At times, you will need to solve these equations for one of the variables.

Example 1: Solve for the specific variable

a) Solve 5b+12 c=9 for b b) Solve 15=3 n+6 p for n

c) Solve k−2

5=11 j for k d) Solve a (q−8 )=23 for q

92

Literal Equation: a or equation with variables.

Example 3: A car’s fuel economy E (miles per gallon) is given by the formula E=mg

, where m is the number of miles driven and g

is the number of gallons of fuel used.

a) Solve the formula for m.

b) If Quanah’s car has an average fuel conception of 30 miles per gallon and she used 9.5 gallons, how far did she drive?

93


94

2.8 Day 2 Warm-up1. The formula for the perimeter (P) of a rectangle is P=2 L+2W .

What should be the first step when solving for L?

Now solve the formula for L.

2. If solving for x in the following equation, which operation should be performed first to solve for the variable x using the fewest possible steps? 2 ( x−1 )=3 y

Now solve completely for x.

96


Solve each equation or formula for the variable indicated.

1. d = rt, for r 2. 6w – y = 2z, for w

3. mx + 4y = 3t, for x 4. 9s – 5g = –4u, for s

5. ab + 3c = 2x, for b 6. 2p = kx – t, for x

7. 23

m + a = a + r, for m 8. 25

h + g = d, for h

9. 23

y + v = x, for y 10. 34

a – q = k, for a

11. rx+9

5 = h, for x 12.

3 b−42

= c, for b

13. 2w – y = 7w – 2, for w 14. 3ℓ + y = 5 + 5ℓ, for ℓ15. ELECTRICITY The formula for Ohm’s Law is E = IR, where E represents voltage measured in volts, I represents current

measured in amperes, and R represents resistance measured in ohms.

a. Solve the formula for R.

b. Suppose a current of 0.25 ampere flows through a resistor connected to a 12-volt battery. What is the resistance in the circuit?

16. MOTION In uniform circular motion, the speed v of a point on the edge of a spinning disk is v = 2 πt

r, where r is the radius of

the disk and t is the time it takes the point to travel once around the circle.

a. Solve the formula for r.

b. Suppose a merry–go–round is spinning once every 3 seconds. If a point on the outside edge has a speed of 12.56 feet per second, what is the radius of the merry-go-round? (Use 3.14 for π.)

17. HIGHWAYS Interstate 90 is the longest interstate highway in the United States, connecting the cities of Seattle, Washington and Boston, Massachusetts. The interstate is 4,987,000 meters in length. If 1 mile = 1.609 kilometers, how many miles long is Interstate 90?

18. INTEREST Simple interest that you may earn on money in a savings account can be calculated with the formula I = prt. I is the amount of interest earned, p is the principal or initial amount invested, r is the interest rate, and t is the amount of time the money is invested for. Solve the formula for p.

98

19. DISTANCE The distance d a car can travel is found by multiplying its rate of speed r by the amount of time t that it took to travel the distance. If a car has already traveled 5 miles, the total distance d is found by the formula d = rt + 5 . Solve the formula for r.

20. ENVIRONMENT The United States released 5.877 billion metric tons of carbon dioxide into the environment through the burning of fossil fuels in a recent year. If 1 trillion pounds = 0.4536 billion metric tons, how many trillions of pounds of carbon dioxide did the United States release in that year?

21. PHYSICS The pressure exerted on an object is calculated by the formula P = FA

, where P is the pressure, F is the force, and A is

the surface area of the object. Water shooting from a hose has a pressure of 75 pounds per square inch (psi). Suppose the surface area covered by the direct hose spray is 0.442 square inch. Solve the equation for F and find the force of the spray.

22. GEOMETRY The regular octagon is divided into 8 congruent triangles. Each triangle has an area of 21.7 square centimeters. The perimeter of the octagon is 48 centimeters.

a. What is the length of each side of the octagon?

b. Solve the area of a triangle formula for h.

99

c. What is the height of each triangle? Round to the nearest tenth.

100


101

Web viewThe base of each triangle once measured 230 meters. ... 6 x 2 = 2 x 6 _____ 7. ... Section...

Documents

Transcript of Web viewThe base of each triangle once measured 230 meters. ... 6 x 2 = 2 x 6 _____ 7. ... Section...