# Chapter 3 & Determine whether the pair of equations represents parallel lines. Work must be shown. 2) 3x - 4y = 10 16x + 8y = 10

Size: px
Start display at page:

Download "Chapter 3 & 8.1-8.3. Determine whether the pair of equations represents parallel lines. Work must be shown. 2) 3x - 4y = 10 16x + 8y = 10"

Transcription

1 Chapter 3 & These are meant for practice. The actual test is different. Determine whether the pair of equations represents parallel lines. 1) = = 39 1) Determine whether the pair of equations represents parallel lines. Work must be shown. 2) 3-4 = = 2) Provide the proper response. 3) Identif whether the slope is positive, negative, zero or undefined. 3) ) Identif whether the slope is positive, negative, zero or undefined. 4) Solve using the substitution method. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. ) + 3 = 80 ) 2 + = 30 6) 3 + = -7 = ) 1

2 7) + 7 = = 34 7) Provide an appropriate response. 8) Does ever straight line have an -intercept? If not, give an eample of an equation whose graph does not have an -intercept. 8) 9) Is it possible for the -intercept and the -intercept of a straight line to be at the same point? Eplain our answer. 9) ) What can ou sa about a line if ever point on the line has the same coordinate? ) 11) Eplain how ou would find the intercept of a line with an equation of the form A + B = C. 11) 12) What can ou sa about the graph of A + B = C if B is equal to zero? 12) 13) What is the -intercept of the line = b? 13) Determine whether the pair of equations represents perpendicular lines. 14) = = 27 14) 1) 3-4 = = -12 1) Find the equation for the graph. 16) 16)

3 17) 17) Solve the sstem graphicall. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. 18) = -3 18) = ) 3-2 = = )

4 Solve the sstem graphicall. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. Label at least two points per line and the solution. 20) = ) = Solve the sstem graphicall. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. 21) = ) 3 = Solve using the elimination method. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. 22) = = 1 22) 4

5 23) 9-6 = = 6 23) 24) 3r - 3s = 2-3r + 3s = 2 24) 2) - 3 = = -39 2) 26) = = ) Answer the question. 27) True or False? In quadrant IV, the -coordinate is alwas positive. 27) 28) True or False? The ordered pair (-6, -9) determines a point in quadrant III with -coordinate -9 and -coordinate ) 29) True or False? The ordered pair (-8, 2) determines a point in quadrant II with -coordinate -8 and -coordinate 2. 29) 30) True or False? In quadrant II, the -coordinate of a point is alwas negative. 30) 31) True or False? The -coordinate is positive in quadrants I and IV. 31) 32) True or False? The ordered pair (0, 0) determines a point in quadrant I with -coordinate 0 and -coordinate 0. 32) Write a slope-intercept equation of the line whose graph is described. 33) Parallel to the graph of = 3-7; -intercept (0, -) 33) 34) Perpendicular to the graph of 2 + = 2; -intercept (0, -) 34) Find the slope and the -intercept of the line. 3) -3 + = - 3)

6 Solve the problem. 36) A sum of mone amounting to \$3.0 consists of dimes and quarters. If there are 17 coins in all, how man are quarters? 36) 37) The sum of two numbers is 72, and twice their difference is 24. What is the smaller of the two numbers? 37) 38) Anne and Nanc use a metal allo that is 24.% copper to make jewelr. How man ounces of an allo that is 23% copper must be mied with an allo that is 2% copper to form 88 ounces of the desired allo? 38) 39) The following graph shows data for a recent train ride from New York to Toronto. At what rate did the train travel? 39) Time of Da (PM) 40) And has 3 coins made up of quarters and half-dollars, and their total value is \$ How man quarters does he have? 40) 41) A student took out two loans totaling \$13,000 to help pa for college epenses. One loan was at 6% simple interest, and the other was at 4%. After one ear, the student owed \$720 in interest. Find the amount of the loan at 4%. 41) 42) At :00 AM, Gavin rented a mountain bike. He returned the bike at 3:00 PM. He biked for 27. miles. He paid \$4.00 for the rental. Find Gavin's average speed, in miles per hour. 42) 43) There were 620 people at a pla. The admission price was \$3.00 for adults and \$1.00 for children. The admission receipts were \$1320. How man adults and children attended? 43) 44) Two angles are complementar. The sum of the first angle plus twice the second angle is 148. Find the measures of the angles. 44) 4) The perimeter of a rectangle is 6 cm. The length is 12 cm longer than the width. Find the dimensions. 4) 6

7 46) Jill is 13. kilometers awa from Joe. Both begin to walk toward each other at the same time. Jill walks at 2. km/h. The meet in 3 hours. How fast is Joe walking? 46) 47) Two angles are supplementar. One angle is 212 less than three times the other. Find the measures of the angles. 47) 48) In an isosceles triangle, each base angle is less than two times the third angle. Find the measures of all three angles. 48) 49) An orchard operator must dilute 11 quarts of a 60%-insecticide solution b adding water. How man quarts of water should be added to get a miture that is 2% insecticide? 49) 0) John and Ton start from the same place at the same time and head for a town miles awa. John walks twice as fast as Ton and arrives 3 hours before Ton. Find the speed of each. 0) 1) From a point on a river, two boats are driven in opposite directions, one at miles per hour and the other at 6 miles per hour. In how man hours will the be 44 miles apart? 1) 2) In a right triangle, one acute angle is 4 more than twice the other. Find the measure of each acute angle. 2) 3) Mrs. Bod has a desk full of quarters and nickels. If she has a total of 32 coins with a total face value of \$4.60, how man of the coins are nickels? 3) 4) A contractor mies concrete from bags of pre-mi for small jobs. How man bags with % cement should he mi with 4 bags of 13.% cement to produce a mi containing 7% cement? 4) ) In a chemistr class, 4 liters of a 4%-saline solution must be mied with a % solution to get a 6% solution. How man liters of the % solution are needed? ) 6) Joe has a collection of nickels and dimes that is worth \$4.. If the number of dimes was doubled and the number of nickels was increased b 17, then the value of the coins would be \$7.0. How man dimes does he have? 6) 7) A garage owner wants to fill a -gallon drum with a 20% winter miture of antifreeze for his customers. How man gallons of 0% antifreeze should he mi with some % antifreeze miture in order to fill the drum? 7) 8) To the nearest dollar, the average tuition at a public four-ear college was \$3068 in 1997 and \$3283 in Find, to the nearest dollar per ear, the rate at which tuition was increasing. 8) 9) An epress train and a local train leave a station at the same time (on separate tracks) and head for a town 0 miles awa. The epress travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train. 9) 7

8 60) A woman made a deposit of \$187. If her deposit consisted of 63 bills, all \$1 bills or \$ bills, then how man \$1 bills did she deposit? 60) 61) A plane fling the 3922-mile trip from Cit A to Cit B has a 30-mph tailwind. The flight's point of no return is the point at which the flight time required to return to Cit A is the same as the time required to continue to Cit B. If the speed of the plane in still air is 360 mph, how far from Cit A is the point of no return? Round our answer to the nearest mile. 61) 62) To the nearest dollar, the average tuition at a public four-ear college was \$302 in 1997 and \$3249 in Find, to the nearest dollar per ear, the rate at which tuition was increasing. 62) 63) In a basketball game, Will scored 21 points, consisting onl of three-point shots and two-point shots. He made a total of 9 shots. How man shots of each tpe did he make? 63) Solve b graphing. 64) The population, p, in thousands, of one town can be approimated b p = d, where 64) d is the number of ears since 198. Use a graph to estimate the population of the town in the ear Graph the equation. 6) 4 + = 0 6)

9 66) = ) ) = 0. 67) ) = 1 68)

10 69) = ) ) + = 2 70) ) 2 - = -2 71)

11 72) + = 4 72) Find the - and -intercepts for the equation. Then graph the equation. 73) 6-12 = 0 73) ) = 20 74)

12 7) + = 7) ) 20-4 = -8 76) Find the - and -intercepts for the equation. Then graph the equation. Label the intercepts as ordered pairs.on the graph. 77) = 36 77) Find the slope of the line containing the given pair of points. If the slope is undefined, state so. 78) (-2, -2) and (-2, -4) 78) 12

13 79) (2, 3) and (11, 1) 79) 80) (1, 2) and (7, 11) 80) Find an equation of the line containing the given pair of points. Write our final answer in slope-intercept form. 81) (7, -6) and (3, -1) 81) 82) (8, -8) and (2, -1) 82) 83) (7, ) and (0, 3) 83) 84) (-2, 0) and (-9, -4) 84) 8) (-1, 3) and (-4, -6) 8) 86) (-2, 7) and (, -4) 86) 87) (4, 0) and (-6, 7) 87) Decide whether or not the ordered pair is a solution to the equation. 88) + = 8; (4, 2) 88) 89) + 2 = 0; (-2, 6) 89) Find the coordinates of the -intercept and the coordinates of all -intercepts. Write as ordered pairs. 90) 90)

14 Find the coordinates of the -intercept and the coordinates of all -intercepts. 91) 91) Find the intercepts for the equation. 92) = 7 92) 93) -2 + = -2 93) 94) -4-2 = -4 94) Write an equation of the line containing the specified point and parallel or perpendicular, as indicated, to the given line. Write our final answer in slope-intercept form. 9) (2, 6), parallel to = ) 96) (7, 2), perpendicular to = 4 96) 97) (0, -6), perpendicular to = ) Write the equation of the line on the graph in slope-intercept form. 98) 98)

15 Use the graph to solve the problem. 99) Find the rate of change of Simone's salar. 99) Solve using an appropriate method. If the sstem has an infinite number of solutions, use set-builder notation to write the solution set. If the sstem has no solution, state this. 0) = 3 0) = 18 Determine whether the ordered pair is a solution of the sstem of equations. Remember to use alphabetical order of variables. 1) (-3, -1); - = -2 1) = Find the slope of the line, or state that the slope is undefined if appropriate. 2) 2) 1

16 3) (3, 3) (3, -3) 3) Find the slope of the line. If the slope is undefined, state so. 4) = -4 4) ) = 1 ) Write an equation for the graph. 6) 6) - - Write an equation in slope-intercept form of the line satisfing the given conditions. 7) Parallel to = and the same -intercept as 9 - = 3. 7) 16

17 Graph the specified line. 8) The line with slope 1 6 that passes through the point (0, 6) 8) Find the slope-intercept equation for the line with the indicated slope and -intercept. 9) Slope 1 ; -intercept (0, 3) 9) 2 17

18 Answer Ke Testname: 11CH3&8P 1) Yes 2) No 3) Negative 4) Positive ) (, ) 6) - 1 7, ) (12, -2) 8) The -intercept is the point where the line crosses the -ais. Lines parallel to the -ais do not intercept the -ais. Thus the graph of an equation of the form = b where b 0 has no -intercept. 9) Yes. If the line passes through the origin, then both the -intercept and the -intercept are at (0, 0). ) The line is vertical. 11) Let = 0 and solve for. 12) The graph is a vertical line. 13) (0, b) 14) No 1) Yes 16) = ) = ) (-3, -7) 19) No solution 20) (6, 1) 21) (6, 9) 22) 9 4, -1 23) (0, 3) 24) No solution 2) (6, -1) 26) (4, 0) 27) False 28) False 29) True 30) True 31) True 32) False 33) = 3-34) = 1 2-3) 3 ; (0, -1) 36) 9 37) 30 38) 22 ounces 39) 60 miles per hour 40) 18 41) \$

19 Answer Ke Testname: 11CH3&8P 42). mph 43) Adults: 30; children: ) 32, 8 4) Width: 8 cm; length: 20 cm 46) 2 km/h 47) 98, 82 48) 70, 70, 40 49) 319 quarts 0) Ton: mph; John: 3 3 mph 1) 4 hours 2) 12, 78 3) 17 4) 13 bags ) 2.0 L 6) 21 7) gallons 8) \$21 per ear 9) Epress: 0 mph; local: 2 mph 60) 32 61) 1798 miles 62) \$66 per ear 63) Two-point shots: 6; three-point shots: 3 64) About 16,000 6)

20 Answer Ke Testname: 11CH3&8P 66) ) )

21 Answer Ke Testname: 11CH3&8P 69) ) )

22 Answer Ke Testname: 11CH3&8P 72) ) (0, 0), (0, 0) )

23 Answer Ke Testname: 11CH3&8P 7) (0, ), (, 0) ) 0, - 2, 2, ) (0, -3), (-6, 0) ) Undefined 79) ) ) =

24 Answer Ke Testname: 11CH3&8P 82) = ) = ) = ) = ) = ) = ) No 89) Yes 90) (0, -8), (-8, 0), (8, 0) 91) (0, 8), (-4, 0), (-2, 0), (1, 0) 92) (7, 0) 93) (1, 0), (0, -2) 94) (1, 0), (0, 2) 9) = ) = ) = ) = ) \$3000 per ear 0) No solution 1) Yes 2) ) Undefined 4) Undefined ) 0 6) = 2 7) =

25 Answer Ke Testname: 11CH3&8P 8) ) =

### MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60

MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60 A Summar of Concepts Needed to be Successful in Mathematics The following sheets list the ke concepts which are taught in the specified math course. The sheets

### The Slope-Intercept Form

7.1 The Slope-Intercept Form 7.1 OBJECTIVES 1. Find the slope and intercept from the equation of a line. Given the slope and intercept, write the equation of a line. Use the slope and intercept to graph

### Systems of Linear Equations

Sstems of Linear Equations. Solving Sstems of Linear Equations b Graphing. Solving Sstems of Equations b Using the Substitution Method. Solving Sstems of Equations b Using the Addition Method. Applications

### Solving Special Systems of Linear Equations

5. Solving Special Sstems of Linear Equations Essential Question Can a sstem of linear equations have no solution or infinitel man solutions? Using a Table to Solve a Sstem Work with a partner. You invest

### 1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =

Extra Practice for Lesson Add or subtract. ) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = Multiply. 7) (5)(-4) = 8) (-3)(-6) = 9) (-)(2) = Division is

### FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

FINAL EXAM REVIEW MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether or not the relationship shown in the table is a function. 1) -

### Math 152, Intermediate Algebra Practice Problems #1

Math 152, Intermediate Algebra Practice Problems 1 Instructions: These problems are intended to give ou practice with the tpes Joseph Krause and level of problems that I epect ou to be able to do. Work

### Systems of Linear Equations: Solving by Substitution

8.3 Sstems of Linear Equations: Solving b Substitution 8.3 OBJECTIVES 1. Solve sstems using the substitution method 2. Solve applications of sstems of equations In Sections 8.1 and 8.2, we looked at graphing

### Review of Intermediate Algebra Content

Review of Intermediate Algebra Content Table of Contents Page Factoring GCF and Trinomials of the Form + b + c... Factoring Trinomials of the Form a + b + c... Factoring Perfect Square Trinomials... 6

### Graphing Linear Equations

6.3 Graphing Linear Equations 6.3 OBJECTIVES 1. Graph a linear equation b plotting points 2. Graph a linear equation b the intercept method 3. Graph a linear equation b solving the equation for We are

### North Carolina Community College System Diagnostic and Placement Test Sample Questions

North Carolina Communit College Sstem Diagnostic and Placement Test Sample Questions 0 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College

### SLOPE OF A LINE 3.2. section. helpful. hint. Slope Using Coordinates to Find 6% GRADE 6 100 SLOW VEHICLES KEEP RIGHT

. Slope of a Line (-) 67. 600 68. 00. SLOPE OF A LINE In this section In Section. we saw some equations whose graphs were straight lines. In this section we look at graphs of straight lines in more detail

### 135 Final Review. Determine whether the graph is symmetric with respect to the x-axis, the y-axis, and/or the origin.

13 Final Review Find the distance d(p1, P2) between the points P1 and P2. 1) P1 = (, -6); P2 = (7, -2) 2 12 2 12 3 Determine whether the graph is smmetric with respect to the -ais, the -ais, and/or the

### { } Sec 3.1 Systems of Linear Equations in Two Variables

Sec.1 Sstems of Linear Equations in Two Variables Learning Objectives: 1. Deciding whether an ordered pair is a solution.. Solve a sstem of linear equations using the graphing, substitution, and elimination

### INVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4. Example 1

Chapter 1 INVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4 This opening section introduces the students to man of the big ideas of Algebra 2, as well as different was of thinking and various problem solving strategies.

### Linear Equations in Two Variables

Section. Sets of Numbers and Interval Notation 0 Linear Equations in Two Variables. The Rectangular Coordinate Sstem and Midpoint Formula. Linear Equations in Two Variables. Slope of a Line. Equations

### SYSTEMS OF LINEAR EQUATIONS

SYSTEMS OF LINEAR EQUATIONS Sstems of linear equations refer to a set of two or more linear equations used to find the value of the unknown variables. If the set of linear equations consist of two equations

### Summer Math Exercises. For students who are entering. Pre-Calculus

Summer Math Eercises For students who are entering Pre-Calculus It has been discovered that idle students lose learning over the summer months. To help you succeed net fall and perhaps to help you learn

### 5. Equations of Lines: slope intercept & point slope

5. Equations of Lines: slope intercept & point slope Slope of the line m rise run Slope-Intercept Form m + b m is slope; b is -intercept Point-Slope Form m( + or m( Slope of parallel lines m m (slopes

### Midterm 2 Review Problems (the first 7 pages) Math 123-5116 Intermediate Algebra Online Spring 2013

Midterm Review Problems (the first 7 pages) Math 1-5116 Intermediate Algebra Online Spring 01 Please note that these review problems are due on the day of the midterm, Friday, April 1, 01 at 6 p.m. in

### Why should we learn this? One real-world connection is to find the rate of change in an airplane s altitude. The Slope of a Line VOCABULARY

Wh should we learn this? The Slope of a Line Objectives: To find slope of a line given two points, and to graph a line using the slope and the -intercept. One real-world connection is to find the rate

### More Equations and Inequalities

Section. Sets of Numbers and Interval Notation 9 More Equations and Inequalities 9 9. Compound Inequalities 9. Polnomial and Rational Inequalities 9. Absolute Value Equations 9. Absolute Value Inequalities

### For 14 15, use the coordinate plane shown. represents 1 kilometer. 10. Write the ordered pairs that represent the location of Sam and the theater.

Name Class Date 12.1 Independent Practice CMMN CRE 6.NS.6, 6.NS.6b, 6.NS.6c, 6.NS.8 m.hrw.com Personal Math Trainer nline Assessment and Intervention For 10 13, use the coordinate plane shown. Each unit

### 1. a. standard form of a parabola with. 2 b 1 2 horizontal axis of symmetry 2. x 2 y 2 r 2 o. standard form of an ellipse centered

Conic Sections. Distance Formula and Circles. More on the Parabola. The Ellipse and Hperbola. Nonlinear Sstems of Equations in Two Variables. Nonlinear Inequalities and Sstems of Inequalities In Chapter,

### Solution of the System of Linear Equations: any ordered pair in a system that makes all equations true.

Definitions: Sstem of Linear Equations: or more linear equations Sstem of Linear Inequalities: or more linear inequalities Solution of the Sstem of Linear Equations: an ordered pair in a sstem that makes

### 6. The given function is only drawn for x > 0. Complete the function for x < 0 with the following conditions:

Precalculus Worksheet 1. Da 1 1. The relation described b the set of points {(-, 5 ),( 0, 5 ),(,8 ),(, 9) } is NOT a function. Eplain wh. For questions - 4, use the graph at the right.. Eplain wh the graph

### Direct Variation. 1. Write an equation for a direct variation relationship 2. Graph the equation of a direct variation relationship

6.5 Direct Variation 6.5 OBJECTIVES 1. Write an equation for a direct variation relationship 2. Graph the equation of a direct variation relationship Pedro makes \$25 an hour as an electrician. If he works

### 5.1. A Formula for Slope. Investigation: Points and Slope CONDENSED

CONDENSED L E S S O N 5.1 A Formula for Slope In this lesson ou will learn how to calculate the slope of a line given two points on the line determine whether a point lies on the same line as two given

### EQUATIONS OF LINES IN SLOPE- INTERCEPT AND STANDARD FORM

. Equations of Lines in Slope-Intercept and Standard Form ( ) 8 In this Slope-Intercept Form Standard Form section Using Slope-Intercept Form for Graphing Writing the Equation for a Line Applications (0,

### Systems of Equations and Matrices

Sstems of Equations and Matrices A sstem of equations is a collection of two or more variables In this chapter, ou should learn the following How to use the methods of substitution and elimination to solve

### GED Practice Test #3 (34 Questions - each question is worth 2.94 points)

GED Practice Test #3 (34 Questions - each question is worth 2.94 points) 1) Pickins community will be constructing fourteen identical rectangle gardens below. How many feet of fencing will they need? 1)

### FSCJ PERT. Florida State College at Jacksonville. assessment. and Certification Centers

FSCJ Florida State College at Jacksonville Assessment and Certification Centers PERT Postsecondary Education Readiness Test Study Guide for Mathematics Note: Pages through are a basic review. Pages forward

### ( ) ( ) Math 0310 Final Exam Review. # Problem Section Answer. 1. Factor completely: 2. 2. Factor completely: 3. Factor completely:

Math 00 Final Eam Review # Problem Section Answer. Factor completely: 6y+. ( y+ ). Factor completely: y+ + y+ ( ) ( ). ( + )( y+ ). Factor completely: a b 6ay + by. ( a b)( y). Factor completely: 6. (

### NAME DATE PERIOD. 11. Is the relation (year, percent of women) a function? Explain. Yes; each year is

- NAME DATE PERID Functions Determine whether each relation is a function. Eplain.. {(, ), (0, 9), (, 0), (7, 0)} Yes; each value is paired with onl one value.. {(, ), (, ), (, ), (, ), (, )}. No; in the

REVISED 7/4/205 Released Form North Carolina READY End-of-Grade Assessment Mathematics Grade 8 Student Booklet Academic Services and Instructional Support Division of Accountabilit Services Copright 203

### Skills Practice Skills Practice for Lesson 1.1

Skills Practice Skills Practice for Lesson. Name Date Tanks a Lot Introduction to Linear Functions Vocabular Define each term in our own words.. function A function is a relation that maps each value of

### Florida Algebra I EOC Online Practice Test

Florida Algebra I EOC Online Practice Test Directions: This practice test contains 65 multiple-choice questions. Choose the best answer for each question. Detailed answer eplanations appear at the end

### Example 1: Model A Model B Total Available. Gizmos. Dodads. System:

Lesson : Sstems of Equations and Matrices Outline Objectives: I can solve sstems of three linear equations in three variables. I can solve sstems of linear inequalities I can model and solve real-world

### Name Class Date. Additional Vocabulary Support

- Additional Vocabular Support Rate of Change and Slope Concept List negative slope positive slope rate of change rise run slope slope formula slope of horizontal line slope of vertical line Choose the

### Exponential and Logarithmic Functions

Chapter 6 Eponential and Logarithmic Functions Section summaries Section 6.1 Composite Functions Some functions are constructed in several steps, where each of the individual steps is a function. For eample,

### Assessment For The California Mathematics Standards Grade 3

Introduction: Summary of Goals GRADE THREE By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication,

### SECTION 2-2 Straight Lines

- Straight Lines 11 94. Engineering. The cross section of a rivet has a top that is an arc of a circle (see the figure). If the ends of the arc are 1 millimeters apart and the top is 4 millimeters above

### Systems of Linear Equations in Three Variables

5.3 Systems of Linear Equations in Three Variables 5.3 OBJECTIVES 1. Find ordered triples associated with three equations 2. Solve a system by the addition method 3. Interpret a solution graphically 4.

### LINEAR FUNCTIONS OF 2 VARIABLES

CHAPTER 4: LINEAR FUNCTIONS OF 2 VARIABLES 4.1 RATES OF CHANGES IN DIFFERENT DIRECTIONS From Precalculus, we know that is a linear function if the rate of change of the function is constant. I.e., for

### COMPONENTS OF VECTORS

COMPONENTS OF VECTORS To describe motion in two dimensions we need a coordinate sstem with two perpendicular aes, and. In such a coordinate sstem, an vector A can be uniquel decomposed into a sum of two

### Solving Systems. of Linear Equations

Solving Sstems 8 MODULE of Linear Equations? ESSENTIAL QUESTION How can ou use sstems of equations to solve real-world problems? LESSON 8.1 Solving Sstems of Linear Equations b Graphing 8.EE.8, 8.EE.8a,

### D.2. The Cartesian Plane. The Cartesian Plane The Distance and Midpoint Formulas Equations of Circles. D10 APPENDIX D Precalculus Review

D0 APPENDIX D Precalculus Review SECTION D. The Cartesian Plane The Cartesian Plane The Distance and Midpoint Formulas Equations of Circles The Cartesian Plane An ordered pair, of real numbers has as its

XIV. Mathematics, Grade 8 Grade 8 Mathematics Test The spring 0 grade 8 Mathematics test was based on standards in the five domains for grade 8 in the Massachusetts Curriculum Framework for Mathematics

### ALGEBRA 1 SKILL BUILDERS

ALGEBRA 1 SKILL BUILDERS (Etra Practice) Introduction to Students and Their Teachers Learning is an individual endeavor. Some ideas come easil; others take time--sometimes lots of time- -to grasp. In addition,

### Solving Quadratic Equations by Graphing. Consider an equation of the form. y ax 2 bx c a 0. In an equation of the form

SECTION 11.3 Solving Quadratic Equations b Graphing 11.3 OBJECTIVES 1. Find an ais of smmetr 2. Find a verte 3. Graph a parabola 4. Solve quadratic equations b graphing 5. Solve an application involving

### Section 7.2 Linear Programming: The Graphical Method

Section 7.2 Linear Programming: The Graphical Method Man problems in business, science, and economics involve finding the optimal value of a function (for instance, the maimum value of the profit function

### ACT Math Vocabulary. Altitude The height of a triangle that makes a 90-degree angle with the base of the triangle. Altitude

ACT Math Vocabular Acute When referring to an angle acute means less than 90 degrees. When referring to a triangle, acute means that all angles are less than 90 degrees. For eample: Altitude The height

### Linear Inequality in Two Variables

90 (7-) Chapter 7 Sstems of Linear Equations and Inequalities In this section 7.4 GRAPHING LINEAR INEQUALITIES IN TWO VARIABLES You studied linear equations and inequalities in one variable in Chapter.

### The Point-Slope Form

7. The Point-Slope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope

### American Diploma Project

Student Name: American Diploma Project ALGEBRA l End-of-Course Eam PRACTICE TEST General Directions Today you will be taking an ADP Algebra I End-of-Course Practice Test. To complete this test, you will

R. Polnomials In this section we want to review all that we know about polnomials. We start with the basic operations on polnomials, that is adding, subtracting, and multipling. Recall, to add subtract

### 1.6. Piecewise Functions. LEARN ABOUT the Math. Representing the problem using a graphical model

. Piecewise Functions YOU WILL NEED graph paper graphing calculator GOAL Understand, interpret, and graph situations that are described b piecewise functions. LEARN ABOUT the Math A cit parking lot uses

### Teacher Page. 1. Reflect a figure with vertices across the x-axis. Find the coordinates of the new image.

Teacher Page Geometr / Da # 10 oordinate Geometr (5 min.) 9-.G.3.1 9-.G.3.2 9-.G.3.3 9-.G.3. Use rigid motions (compositions of reflections, translations and rotations) to determine whether two geometric

### Blue Pelican Alg II First Semester

Blue Pelican Alg II First Semester Teacher Version 1.01 Copyright 2009 by Charles E. Cook; Refugio, Tx (All rights reserved) Alg II Syllabus (First Semester) Unit 1: Solving linear equations and inequalities

### THIS CHAPTER INTRODUCES the Cartesian coordinate

87533_01_ch1_p001-066 1/30/08 9:36 AM Page 1 STRAIGHT LINES AND LINEAR FUNCTIONS 1 THIS CHAPTER INTRODUCES the Cartesian coordinate sstem, a sstem that allows us to represent points in the plane in terms

### Warm Up. Write an equation given the slope and y-intercept. Write an equation of the line shown.

Warm Up Write an equation given the slope and y-intercept Write an equation of the line shown. EXAMPLE 1 Write an equation given the slope and y-intercept From the graph, you can see that the slope is

### THE POWER RULES. Raising an Exponential Expression to a Power

8 (5-) Chapter 5 Eponents and Polnomials 5. THE POWER RULES In this section Raising an Eponential Epression to a Power Raising a Product to a Power Raising a Quotient to a Power Variable Eponents Summar

What five coins add up to a nickel? five pennies (1 + 1 + 1 + 1 + 1 = 5) Which is longest: a foot, a yard or an inch? a yard (3 feet = 1 yard; 12 inches = 1 foot) What do you call the answer to a multiplication

### CHAPTER 1 Linear Equations

CHAPTER 1 Linear Equations 1.1. Lines The rectangular coordinate system is also called the Cartesian plane. It is formed by two real number lines, the horizontal axis or x-axis, and the vertical axis or

### Slope-Intercept Form and Point-Slope Form

Slope-Intercept Form and Point-Slope Form In this section we will be discussing Slope-Intercept Form and the Point-Slope Form of a line. We will also discuss how to graph using the Slope-Intercept Form.

### M122 College Algebra Review for Final Exam

M122 College Algebra Review for Final Eam Revised Fall 2007 for College Algebra in Contet All answers should include our work (this could be a written eplanation of the result, a graph with the relevant

### MATH 185 CHAPTER 2 REVIEW

NAME MATH 18 CHAPTER REVIEW Use the slope and -intercept to graph the linear function. 1. F() = 4 - - Objective: (.1) Graph a Linear Function Determine whether the given function is linear or nonlinear..

### How many of these intersection points lie in the interior of the shaded region? If 1. then what is the value of

NOVEMBER A stack of 00 nickels has a height of 6 inches What is the value, in dollars, of an 8-foot-high stack of nickels? Epress our answer to the nearest hundredth A cube is sliced b a plane that goes

### MATD 0390 - Intermediate Algebra Review for Pretest

MATD 090 - Intermediate Algebra Review for Pretest. Evaluate: a) - b) - c) (-) d) 0. Evaluate: [ - ( - )]. Evaluate: - -(-7) + (-8). Evaluate: - - + [6 - ( - 9)]. Simplify: [x - (x - )] 6. Solve: -(x +

### Section V.2: Magnitudes, Directions, and Components of Vectors

Section V.: Magnitudes, Directions, and Components of Vectors Vectors in the plane If we graph a vector in the coordinate plane instead of just a grid, there are a few things to note. Firstl, directions

### Graphing Linear Equations

Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope

Quadratic Equations and Functions. Square Root Propert and Completing the Square. Quadratic Formula. Equations in Quadratic Form. Graphs of Quadratic Functions. Verte of a Parabola and Applications In

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 24, 2012 9:15 a.m. to 12:15 p.m.

INTEGRATED ALGEBRA The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Tuesda, Januar 4, 01 9:15 a.m. to 1:15 p.m., onl Student Name: School Name: Print our name and

### 1.1 Practice Worksheet

Math 1 MPS Instructor: Cheryl Jaeger Balm 1 1.1 Practice Worksheet 1. Write each English phrase as a mathematical expression. (a) Three less than twice a number (b) Four more than half of a number (c)

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Thursday, August 16, 2012 8:30 to 11:30 a.m.

INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name

### Answers for the lesson Write Linear Equations in Slope-Intercept Form

LESSON 4.1 Answers for the lesson Write Linear Equations in Slope-Intercept Form Skill Practice 1. slope. You can substitute the slope for m and the y-intercept for b to get the equation of the line..

### Slope-Intercept Equation. Example

1.4 Equations of Lines and Modeling Find the slope and the y intercept of a line given the equation y = mx + b, or f(x) = mx + b. Graph a linear equation using the slope and the y-intercept. Determine

### Solving Systems of Equations

Solving Sstems of Equations When we have or more equations and or more unknowns, we use a sstem of equations to find the solution. Definition: A solution of a sstem of equations is an ordered pair that

### x x y y Then, my slope is =. Notice, if we use the slope formula, we ll get the same thing: m =

Slope and Lines The slope of a line is a ratio that measures the incline of the line. As a result, the smaller the incline, the closer the slope is to zero and the steeper the incline, the farther the

1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points

### To Be or Not To Be a Linear Equation: That Is the Question

To Be or Not To Be a Linear Equation: That Is the Question Linear Equation in Two Variables A linear equation in two variables is an equation that can be written in the form A + B C where A and B are not

### FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby

### Geometry and Measurement

The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

### 3-2 Solving Linear Equations by Graphing. Solve each equation by graphing. 2x + 6 = 0. f (x. The graph intersects the x-axis at 3. So the solution is

- Solving Linear Equations by Graphing Solve each equation by graphing. + 6 = The related function is f () = f ( ) = f ( ) = f ( ) = f () = f () = f () = f () = + 6 ( ) + 6 ( ) + 6 () + 6 () + 6 () + 6

### MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

### LESSON EIII.E EXPONENTS AND LOGARITHMS

LESSON EIII.E EXPONENTS AND LOGARITHMS LESSON EIII.E EXPONENTS AND LOGARITHMS OVERVIEW Here s what ou ll learn in this lesson: Eponential Functions a. Graphing eponential functions b. Applications of eponential

### Final Word Problem Practice #1

Final Word Problem Practice #1 Beginning Algebra / Math 100 Fall 2013 506 (Prof. Miller) Student Name/ID: Instructor Note: Assignment: Set up a tutoring appointment with one of the campus tutors or with

### In this this review we turn our attention to the square root function, the function defined by the equation. f(x) = x. (5.1)

Section 5.2 The Square Root 1 5.2 The Square Root In this this review we turn our attention to the square root function, the function defined b the equation f() =. (5.1) We can determine the domain and

### SECTION 5-1 Exponential Functions

354 5 Eponential and Logarithmic Functions Most of the functions we have considered so far have been polnomial and rational functions, with a few others involving roots or powers of polnomial or rational

### TSI College Level Math Practice Test

TSI College Level Math Practice Test Tutorial Services Mission del Paso Campus. Factor the Following Polynomials 4 a. 6 8 b. c. 7 d. ab + a + b + 6 e. 9 f. 6 9. Perform the indicated operation a. ( +7y)

### Solving Absolute Value Equations and Inequalities Graphically

4.5 Solving Absolute Value Equations and Inequalities Graphicall 4.5 OBJECTIVES 1. Draw the graph of an absolute value function 2. Solve an absolute value equation graphicall 3. Solve an absolute value

### of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

### North Carolina Community College System Diagnostic and Placement Test Sample Questions

North Carolina Community College System Diagnostic and Placement Test Sample Questions 01 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College

### Chapter 8. Lines and Planes. By the end of this chapter, you will

Chapter 8 Lines and Planes In this chapter, ou will revisit our knowledge of intersecting lines in two dimensions and etend those ideas into three dimensions. You will investigate the nature of planes

### Let s explore the content and skills assessed by Heart of Algebra questions.

Chapter 9 Heart of Algebra Heart of Algebra focuses on the mastery of linear equations, systems of linear equations, and linear functions. The ability to analyze and create linear equations, inequalities,

### Lecture 9: Lines. m = y 2 y 1 x 2 x 1

Lecture 9: Lines If we have two distinct points in the Cartesian plane, there is a unique line which passes through the two points. We can construct it by joining the points with a straight edge and extending