Formulae 1C. FORMULAE 25
|
|
- Loraine Riley
- 5 years ago
- Views:
Transcription
1 1C. FORMULAE 5 1c Formulae The formulae of science usually contain variable letters other than the variable x. Indeed, formulae in science typically use several letters. Take for example, Isaac Newton s Universal Law of Gravitation, which says that the magnitude of the force of attraction between two celestial bodies is given by the formula F = GMm r, where m usually denotes the mass of the smaller body, M the mass of the larger body, and r is the distance between the two bodies. The letter G represents the universal gravitational constant, having value N(m/kg). Variable case. Note the use of upper and lower case letter M s in Newton s Law of Gravitation. When working with scientific formulae, you must maintain the case of the given letters. You are not allowed to substitute lower forupper case, or upper for lower case in your work. In Section??, we described the goal that must be met when we are asked to solve an equation for x. Solve for x. When asked to solve an equation for x, the goal is to manipulate the equation into the final form x = Stuff, where Stuff is a valid mathematical expression that may contain other variables, mathematical symbols, etc., but it must not contain any occurrence of the variable x. Thus, to solve an equation for x, we need to isolate the terms containing x on one side of the equation, and all remaining terms on the other side of the equation. r x: x c = d EXAMPLE 1. Solve for x: x + a = b. Solution: To undo the effects of adding a, subtracta from both sides of the equation. x = c + d. x + a = b x + a a = b a x = b a Subtract a from both sides.
2 6 MODULE 1. LINEAR EQUATIONS AND INEQUALITIES In Example 1, notethattheanswerx = b a has the required form, x = Stuff, where Stuff is a valid mathematical expression that contains other variables, mathematical symbols, etc., but it does not contain any occurrence of the variable x. Now, what if we were asked to solve the same equation for a, instead of x? EXAMPLE. Solve for a: x + a = b. Solve for x: Solution: We are instructed to solve the equation x + a = b for a. This means that our final answer must have the form a = Stuff, where Stuff is a valid mathematical expression that contains other variables, mathematical symbols, etc., but it does not contain any occurrence of the variable a. This means that we must isolate all terms containing the variable a on one side of the equation, and all remaining terms on the other side of the equation. Now, to undo the effect of adding x, subtractx from both sides of the equation. x c = d x + a = b x + a x = b x a = b x Subtract x from both sides. Note that we have a = Stuff, where Stuff contains no occurrence of a, the variable we are solving for. Answer: c = x d. EXAMPLE 3. The formula F = kx, known as Hooke s Law, predicts the force F required to stretch a spring x units. Solve the equation for k. Solve for m: Solution: We are instructed to solve the equation F = kx for k. This means that our final answer must have the form k = Stuff, where Stuff is a valid mathematical expression that may contain other variables, mathematical symbols, etc., but it may not contain any occurrence of the variable k. This means that we must isolate all terms containing the variable k on one side of the equation, and all remaining terms on the other side of the equation. However, note that all terms containing the variable k are already isolated on one side of the equation. Terms not containing the variable k are isolated on the other side of the equation. Now, to undo the effect of multiplying by x, divide both sides of the equation by x. E = mc F = kx F x = kx x F x = k Divide both sides by x.
3 1C. FORMULAE 7 Saying that F/x = k is equivalent to saying that k = F/x. We can leave our answer in the form shown in the last step, but some instructors insist thatwe write the answer as follows: k = F x F/x = k is equivalent to k = F/x. m = E c. Note that we have k = Stuff, where Stuff contains no occurrence of k, the variable we are solving for. r t: d = st EXAMPLE 4. The formula V = RI is called Ohm s Law. It helps calculate the voltage drop V across a resistor R in an electric circuit with current I. Solve the equation for R. Solution: We are instructed to solve the equation V = RI for R. This means that our final answer must have the form R = Stuff, where Stuff is a valid mathematical expression that may contain other variables, mathematical symbols, etc., but it may not contain any occurrence of the variable R. This means that we must isolate all terms containing the variable R on one side of the equation, and all remaining terms on the other side of the equation. However, note that all terms containing the variable R are already isolated on one side of the equation. Terms not containing the variable R are isolated on the other side of the equation. Now, to undo the effect of multiplying by I, divide both sides of the equation by I. V = RI V I = RI I V I = R Divide both sides by I. This can also be written in the following form: R = V I V/I = R is equivalent to R = V/I. t = d s. Note that we have R = Stuff, where Stuff contains no occurrence of R, the variable we are solving for. Clearing Fractions If fractions occur in a formula, clear the fractions from the formula by multiplying both sides of the formula by the common denominator.
4 8 MODULE 1. LINEAR EQUATIONS AND INEQUALITIES EXAMPLE 5. The formula K = 1 mv is used to calculate the kinetic energy K of a particle of mass m moving with velocity v. Solve the equation for m. Solve for g: Solution: We re asked to solve the equation K =(1/)mv for m. First, clear the fractions by multiplying both sides by the common denominator. s = 1 gt K = 1 mv ( ) 1 (K) = mv K = mv Multiply both sides by. Cancel s. Note that all terms containing m, the variable we are solving for, are already isolated on one side of the equation. We need only divide both sides by v to complete the solution. K v = mv v Divide both sides by v. K v = m Cancel v for v. Note that the final answer has the form m = Stuff, where Stuff contains no occurrence of the variable m. Answer: g = S t EXAMPLE 6. As mentioned earlier, Newton s Universal Law of Gravitation Solve for q : is described by the formula F = kq 1q 1 F = GMm r. r Solve this equation for m. Solution: We re asked to solve the equation F = GMm/r for m. First, clear the fractions by multiplying both sides by the common denominator. F = GMm r r (F )=r ( GMm r ) Multiply both sides by r. r F = GMm Cancel r for r.
5 1C. FORMULAE 9 q = Fr kq 1 Note that all terms containing m, the variable we are solving for, are already isolated on one side of the equation. We need only divide both sides by GM to complete the solution. r F GM = GMm Divide both sides by GM. GM r F GM = m Cancel GM for GM. Note that the final answer has the form m = Stuff, where Stuff contains no occurrence of the variable m. Geometric Formulae Let s look at a few commonly used formulae from geometry. r W : P =W +L EXAMPLE 7. Let W and L represent the width and length of a rectangle, respectively, and let P represent its perimeter. L W W L The perimeter (distance around) of the rectangle is found by summing its four sides, then combining like terms. P = L + W + L + W P =W +L Summing the four sides. Combine like terms. Solve P =W +L for L. Then, given that the perimeter is 300 feet and the width is 50 feet, use your result to calculate the length. Solution: We re first asked to solve P =W +L for L. First, isolate all terms containing the variable L on one side of the equation. P = W + L P W =W +L W Subtract W from both sides. P W =L P W = L Divide both sides by. P W = L
6 30 MODULE 1. LINEAR EQUATIONS AND INEQUALITIES Note that the final result has L = Stuff, where Stuff contains no occurrence of the variable L. The second part of this example requests that we find the length of the rectangle, given that the perimeter is P = 300 feet and the width is W =50 feet. To calculate the length, substitute P =300andW = 50 in L =(P W )/. L = P W Perimeter formula solved for L. 300 (50) L = Substitute 300 for P,50forW L = Multiply: (50)=100. L = 00 Subtract: = 00. L =100 Divide: 00/ =100. Hence, the length of the rectangle is 100 feet. Answer: W = P L EXAMPLE 8. Let b and h represent the length of the base and the height Solve for W : of a triangle, respectively, and let A represent the area of the triangle. P =W +L h The area of the triangle is computed using the formula: b A = 1 bh That is, the area of a triangle is one-half the base times the height. First, solve this formula for h. Secondly, given that the area is A = 90 in (90 square inches) and the length of the base is 15 in (15 inches), find the height of the triangle. Solution: We re first asked to solve A =(1/)bh for h. Because the equation has fractions, the first step is to clear the fractions by multiplying both sides
7 1C. FORMULAE 31 by the least common denominator. A = 1 bh ( ) 1 (A) = bh A = bh Area of a triangle formula. Multiply both sides by. Now, we already have all terms containing the variable h on one side of the equation, so we can solve for h by dividing both sides of the equation by b. A b = bh b Divide both sides by b. A b = h Note that the final result has h = Stuff, where Stuff contains no occurrence of the variable h. The second part of this example requests that we find the height of the triangle, given that the area is A = 90 in and the length of the base is b = 15 in. To calculate the height of the triangle, substitute A = 90 and b = 15 in h =A/b. h = A b Area formula solved for h. h = (90) 15 Substitute 90 for A, 15forb. h = Multiply: (90)=180. h =1 Divide: 180/15=1. Hence, the height of the triangle is 1 inches.
Algebra 1-6 Study Guide: Solving for a Variable (pp 49-51) Page! 1 of! 8. Vocabulary
Page 1 of 8 Attendance Problems: Solve each equation. 1. 5 + x = -2 2. 8m = 43 c + 5 3. = 6 4. 0.3s + 0.6 = 1.5 4 5. 10k - 6 = 9k + 2 formula Vocabulary literal equation I can solve a formula for a given
More informationUnit 11 Radical Equations Examples Introductory Algebra Page 1 of 9
Introductory Algebra Page 1 of 9 Questions 1. Solve 12 + 4x + 7. 2. Solve y y 3. 3. Solve 2y 4 + 2 y. 4. Solve 3 3 x 2.. Solve 8x + 17 2x + 8 + 3. 6. Solve 2x + 9 x + 1 2. 7. In geology, the water depth
More informationThere are two main properties that we use when solving linear equations. Property #1: Additive Property of Equality
Chapter 1.1: Solving Linear and Literal Equations Linear Equations Linear equations are equations of the form ax + b = c, where a, b and c are constants, and a zero. A hint that an equation is linear is
More informationIntermediate Algebra Semester Summary Exercises. 1 Ah C. b = h
. Solve: 3x + 8 = 3 + 8x + 3x A. x = B. x = 4 C. x = 8 8 D. x =. Solve: w 3 w 5 6 8 A. w = 4 B. w = C. w = 4 D. w = 60 3. Solve: 3(x ) + 4 = 4(x + ) A. x = 7 B. x = 5 C. x = D. x = 4. The perimeter of
More informationMATH ALGEBRA AND FUNCTIONS
Students: 1. Use letters, boxes, or other symbols to stand for any number in simple expressions or equations. 1. Students use and interpret variables, mathematical symbols and properties to write and simplify
More informationEureka Math Module 4 Topic C Replacing Letters and Numbers
Eureka Math Module 4 Topic C Replacing Letters and Numbers 6.EE.A.2c: Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.A.4: Identify when two expressions are equivalent. Copy
More informationT f. en s. Unit 1 Rates and Proportional Relationships 9. Unit 2 The Number System 31. Unit 3 Expressions and Equations 53. Unit 4 Geometry 79
T f a ble o Co n t en s t Introduction to Get Set for Math.... 4 How to Answer Test Questions.... 5 Unit 1 Rates and Proportional Relationships 9 7.RP.1 Lesson 1 Ratios and Rates.... 10 7.RP.2.a, b Lesson
More informationNo Brain Too Small PHYSICS
Level Physics: Mechanics Hooke s Law Answers The Mess that is NCEA Assessment Schedules. Level Physics: AS 97 replaced AS 9055. In 9055, from 003 to 0, there was an Evidence column with the correct answer
More informationMathB65 Ch 1 I,II,III, IV.notebook. August 23, 2017
Chapter 1: Expressions, Equations and Inequalities I. Variables & Constants II. Algebraic Expressions III. Translations IV. Introduction to Equations V. The Additive/Multiplication Principles VI. Strategy
More informationSect Formulas and Applications of Geometry:
72 Sect 2.6 - Formulas and Applications of Geometry: Concept # Solving Literal Equations for a particular variable. Now, we will examine solving formulas for a particular variable. Sometimes it is useful
More informationChapter 4: Solving Literal Equations
Chapter 4: Solving Literal Equations 1 Day 1: The Basics of Literal Equations A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
More informationMATH 125 ELAC SPRING 2018 TEST 2 REVIEW SHEET NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
MATH 125 ELAC SPRING 2018 TEST 2 REVIEW SHEET NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve. 1) 5x + 5 + 3 = 12 1) 2) 3 5x + 4 + 5 = 0 2)
More informationMultiplication and Division
UNIT 3 Multiplication and Division Skaters work as a pair to put on quite a show. Multiplication and division work as a pair to solve many types of problems. 82 UNIT 3 MULTIPLICATION AND DIVISION Isaac
More informationTABLE OF CONTENTS. Introduction to Finish Line Indiana Math 10. UNIT 1: Number Sense, Expressions, and Computation. Real Numbers
TABLE OF CONTENTS Introduction to Finish Line Indiana Math 10 UNIT 1: Number Sense, Expressions, and Computation LESSON 1 8.NS.1, 8.NS.2, A1.RNE.1, A1.RNE.2 LESSON 2 8.NS.3, 8.NS.4 LESSON 3 A1.RNE.3 LESSON
More informationChapter 1. Solving Algebraic Equations for a Variable
www.ck1.org CHAPTER 1 Solving Algebraic Equations for a Variable Here you ll learn how to isolate the variable in an equation or formula. Problem: You are planning a trip to Spain in the summer. In the
More informationLiteral Equations Manipulating Variables and Constants
Literal Equations Manipulating Variables and Constants A literal equation is one which is expressed in terms of variable symbols (such as d, v, and a) and constants (such as R, g, and π). Often in science
More informationThis question was generally well done, although some students treated it as if the car was doing a vertical loop.
2010 Physics GA 1: Written examination 1 GENERAL COMMENTS The number of students who sat for the 2010 Physics examination 1 was 6989. With a mean score of 62 per cent, it was evident that students generally
More information2007 Assessment Report Physics GA 1: Written examination 1
2007 Physics GA 1: Written examination 1 GENERAL COMMENTS The number of students who sat for the 2007 Physics examination 1 was 6544. With a mean score of 55 per cent, students generally found the paper
More informationMAT 1033 Final Review for Intermediate Algebra (Revised April 2013)
1 This review corresponds to the Charles McKeague textbook. Answers will be posted separately. Section 2.1: Solve a Linear Equation in One Variable 1. Solve: " = " 2. Solve: "# = " 3. Solve: " " = " Section
More informationReview for the Final Exam MAT 0024 College Prep Algebra Class
Review for the Final Eam Name MAT 00 College Prep Algebra Class Chapter 1 1) Simplify: 6 ( ) + ( ) 1 1 11 ) Simplify: 8 + ( ) ) Simplify: 7 + ( 1) 16 17 10 ) Simplify: () + 1 ) Simplify: + + ( ) ( ) 1
More informationFractions. Review R.7. Dr. Doug Ensley. January 7, Dr. Doug Ensley Review R.7
Review R.7 Dr. Doug Ensley January 7, 2015 Equivalence of fractions As long as c 0, a b = a c b c Equivalence of fractions As long as c 0, a b = a c b c Examples True or False? 10 18 = 2 5 2 9 = 5 9 10
More informationMultiple Choice. Test A, continued. 19. Which is the solution to 3 2y + 4y = 7? A y = 0 C y = 2 B y = 1 D y = 4
Name Date Class Multiple Choice Test A Choose the best answer. 1. A family swimming pool membership costs $55 per month plus a one-time registration fee of $25. If a family has paid a total of $465, how
More informationMATH Spring 2010 Topics per Section
MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line
More informationb) What is its position when its velocity (magnitude) is largest? When it is at x=0 all the energy is kinetic.
Question 1. The electrostatic force between two charges, Q 1 and F 1 /4 Q 2 a separated by a distance D, is F 1. What is the force between them after they are moved to a distance 2D apart? (Give in terms
More information56 CHAPTER 3. POLYNOMIAL FUNCTIONS
56 CHAPTER 3. POLYNOMIAL FUNCTIONS Chapter 4 Rational functions and inequalities 4.1 Rational functions Textbook section 4.7 4.1.1 Basic rational functions and asymptotes As a first step towards understanding
More informationC Expressions and Equations, Lesson 5, Transforming Formulas (r. 2018) LEARNING OBJECTIVES. Overview of Lesson
C Expressions and Equations, Lesson 5, Transforming Formulas (r. 2018) EXPRESSIONS AND EQUATIONS Transforming Formulas Common Core Standard A-CED.A.4 Rearrange formulas to highlight a quantity of interest,
More informationCollecting Like Terms
MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARM-UP Example 1: Simplify each expression using exponent laws.
More informationWords to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression
1 Words to Review Give an example of the vocabulary word. Numerical expression 5 12 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression
More informationCN#5 Objectives 5/11/ I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed.
CN#5 Objectives I will be able to describe the effect on perimeter and area when one or more dimensions of a figure are changed. When the dimensions of a figure are changed proportionally, the figure will
More informationCHAPTER 1 POLYNOMIALS
1 CHAPTER 1 POLYNOMIALS 1.1 Removing Nested Symbols of Grouping Simplify. 1. 4x + 3( x ) + 4( x + 1). ( ) 3x + 4 5 x 3 + x 3. 3 5( y 4) + 6 y ( y + 3) 4. 3 n ( n + 5) 4 ( n + 8) 5. ( x + 5) x + 3( x 6)
More informationBeauchamp College Year 11/12 - A- Level Transition Work. Physics.
Beauchamp College Year 11/1 - A- Level Transition Work Physics Gareth.butcher@beauchamp.org.uk Using S.I. units Specification references.1. a) b) c) d) M0.1 Recognise and make use of appropriate units
More information2-7 Solving Absolute-Value Inequalities
Warm Up Solve each inequality and graph the solution. 1. x + 7 < 4 2. 14x 28 3. 5 + 2x > 1 When an inequality contains an absolute-value expression, it can be written as a compound inequality. The inequality
More information6.5 Work and Fluid Forces
6.5 Work and Fluid Forces Work Work=Force Distance Work Work=Force Distance Units Force Distance Work Newton meter Joule (J) pound foot foot-pound (ft lb) Work Work=Force Distance Units Force Distance
More informationWords to Review. Give an example of the vocabulary word. Numerical expression. Variable. Variable expression. Evaluate a variable expression
1 Words to Review Give an example of the vocabulary word. Numerical expression 5 1 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression
More informationSolving Physics Problems
Solving Physics Problems Vectors Characteristic Displacement, velocity, acceleration, forces, momentum, impulse, electric field, magnetic field Break each vector into x and y components Add up x components
More informationHow High Can You Jump On Mars? (A Lesson In High School Algebra)
How High Can You Jump On Mars? (A Lesson In High School Algebra) by Tom Atwood October 11, 016 Phun with Physics This article uses nothing more than high school algebra to show some of the astounding bits
More informationPurpose of the experiment
Work and Energy PES 1160 General Physics Lab I Purpose of the experiment What is Work and how is related to Force? To understand the work done by a constant force and a variable force. To see how gravitational
More information1Add and subtract 2Multiply radical
Then You simplified radical expressions. (Lesson 10-2) Now 1Add and subtract radical expressions. 2Multiply radical expressions. Operations with Radical Expressions Why? Conchita is going to run in her
More informationObjects usually are charged up through the transfer of electrons from one object to the other.
1 Part 1: Electric Force Review of Vectors Review your vectors! You should know how to convert from polar form to component form and vice versa add and subtract vectors multiply vectors by scalars Find
More informationArkansas Tech University MATH 2924: Calculus II Dr. Marcel B. Finan. Solutions to Assignment 7.6. sin. sin
Arkansas Tech University MATH 94: Calculus II Dr. Marcel B. Finan Solutions to Assignment 7.6 Exercise We have [ 5x dx = 5 ] = 4.5 ft lb x Exercise We have ( π cos x dx = [ ( π ] sin π x = J. From x =
More informationCourse Name: MAT 135 Spring 2017 Master Course Code: N/A. ALEKS Course: Intermediate Algebra Instructor: Master Templates
Course Name: MAT 135 Spring 2017 Master Course Code: N/A ALEKS Course: Intermediate Algebra Instructor: Master Templates Course Dates: Begin: 01/15/2017 End: 05/31/2017 Course Content: 279 Topics (207
More informationTest 4 also includes review problems from earlier sections so study test reviews 1, 2, and 3 also.
MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 4 (1.1-10.1, not including 8.2) Test 4 also includes review problems from earlier sections so study test reviews 1, 2, and 3 also. 1. Factor completely: a 2
More informationThe trick is to multiply the numerator and denominator of the big fraction by the least common denominator of every little fraction.
Complex Fractions A complex fraction is an expression that features fractions within fractions. To simplify complex fractions, we only need to master one very simple method. Simplify 7 6 +3 8 4 3 4 The
More informationCorrelation: California State Curriculum Standards of Mathematics for Grade 6 SUCCESS IN MATH: BASIC ALGEBRA
Correlation: California State Curriculum Standards of Mathematics for Grade 6 To SUCCESS IN MATH: BASIC ALGEBRA 1 ALGEBRA AND FUNCTIONS 1.0 Students write verbal expressions and sentences as algebraic
More information( )( ) Algebra I / Technical Algebra. (This can be read: given n elements, choose r, 5! 5 4 3! ! ( 5 3 )! 3!(2) 2
470 Algebra I / Technical Algebra Absolute Value: A number s distance from zero on a number line. A number s absolute value is nonnegative. 4 = 4 = 4 Algebraic Expressions: A mathematical phrase that can
More informationMATH98 Intermediate Algebra Practice Test Form A
MATH98 Intermediate Algebra Practice Test Form A MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y - 4) - (y + ) = 3y 1) A)
More information2009 Assessment Report Physics GA 1: Written examination 1
2009 Physics GA 1: Written examination 1 GENERAL COMMENTS The number of students who sat for the 2009 Physics examination 1 was 6868. With a mean score of 68 per cent, students generally found the paper
More informationChapter 2 Linear Equations and Inequalities in One Variable
Chapter 2 Linear Equations and Inequalities in One Variable Section 2.1: Linear Equations in One Variable Section 2.3: Solving Formulas Section 2.5: Linear Inequalities in One Variable Section 2.6: Compound
More informationAP Physics C Mechanics Summer Assignment
AP Physics C Mechanics Summer Assignment 2018 2019 School Year Welcome to AP Physics C, an exciting and intensive introductory college physics course for students majoring in the physical sciences or engineering.
More informationNorth Dakota Mathematics Content Standards Grade 6 Prioritized Standards Northeast Education Services Cooperative (NESC)
North Dakota Mathematics Content Standards Grade 6 Prioritized Standards Northeast Education Services Cooperative (NESC) - 2017 How to Read This Document Example: 6.RP.1 6.RP.1 references the grade level
More information1
Plg4: lgebra and Functions 1 4.1 Writing and Evaluating lgebraic Expressions MULTIPLE HOIE 1. Write the following as an algebraic expression: a number increased by 16 a. 16 c. n 16 b. n 16 d. n 16 NS:
More information2.2. Formulas and Percent. Objectives. Solve a formula for a specified variable. Solve applied problems by using formulas. Solve percent problems.
Chapter 2 Section 2 2.2 Formulas and Percent Objectives 1 2 3 4 Solve a formula for a specified variable. Solve applied problems by using formulas. Solve percent problems. Solve problems involving percent
More information2-5 Solving for a Variable
Warm Up Solve each equation. 1. 5 + x = 2 2. 8m = 43 3. 4. 0.3s + 0.6 = 1.5 5. 10k 6 = 9k + 2 Learning Goals 1. Students will use formulas to solve application problems 2-3. Students will solve a formulas
More informationMath 7.2, Period. Using Set notation: 4, 4 is the set containing 4 and 4 and is the solution set to the equation listed above.
Solutions to Equations and Inequalities Study Guide SOLUTIONS TO EQUATIONS Solutions to Equations are expressed in 3 ways: In Words: the equation x! = 16 has solutions of 4 and 4. Or, x! = 16 is a true
More informationALGEBRA GRADE 7. Do not open this booklet until instructed to do so. Mark your answer on the answer sheet by FILLING in the oval.
Kansas City Area Teachers of Mathematics 2014 KCATM Math Competition ALGEBRA GRADE 7 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may NOT use calculators.
More informationNew Rochelle High School Geometry Summer Assignment
NAME - New Rochelle High School Geometry Summer Assignment To all Geometry students, This assignment will help you refresh some of the necessary math skills you will need to be successful in Geometry and
More informationSolving Equations. A: Solving One-Variable Equations. One Step x + 6 = 9-3y = 15. Two Step 2a 3 6. Algebra 2 Chapter 1 Notes 1.4 Solving Equations
Algebra 2 Chapter 1 Notes 1.4 Solving Equations 1.4 Solving Equations Topics: Solving Equations Translating Words into Algebra Solving Word Problems A: Solving One-Variable Equations The equations below
More information16.3 Conservative Vector Fields
16.3 Conservative Vector Fields Lukas Geyer Montana State University M273, Fall 2011 Lukas Geyer (MSU) 16.3 Conservative Vector Fields M273, Fall 2011 1 / 23 Fundamental Theorem for Conservative Vector
More informationCheck boxes of Edited Copy of Sp Topics (was 261-pilot)
Check boxes of Edited Copy of 10023 Sp 11 253 Topics (was 261-pilot) Intermediate Algebra (2011), 3rd Ed. [open all close all] R-Review of Basic Algebraic Concepts Section R.2 Ordering integers Plotting
More informationWhich one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x ) A) x = 5 B) x = -6 C) x = -5 D) x = 6
Review for Final Exam Math 124A (Flatley) Name Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x - 14 1) A) x = 5 B) x = -6 C) x = -5 D) x = 6 Solve the linear equation.
More informationLESSON 9.1 ROOTS AND RADICALS
LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS 67 OVERVIEW Here s what you ll learn in this lesson: Square Roots and Cube Roots a. Definition of square root and cube root b. Radicand, radical
More informationApplication Force Planck has two bars. Application Force Planck two rods (or two bars)
Application Force Planck has two bars Application Force Planck two rods (or two bars) Planck force that we know is a force that can represented a gravitational force between two spherical masses, but you
More informationLinear Equations - Two-Step Equations
1.2 Linear Equations - Two-Step Equations Objective: Solve two-step equations by balancing and using inverse opperations. After mastering the technique for solving equations that are simple one-step equations,
More information8/15/2018, 8:31 PM. Assignment: Math 0410 Homework150bbbbtsiallnew123. Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 2018
of 3 8/15/018, 8:31 PM Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 018 Assignment: Math 0410 Homework150bbbbtsiallnew13 1. Evaluate x y for the given replacement values. x=4and
More informationMath 9 Practice Final Exam #1
Class: Date: Math Practice Final Exam #1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the value of 0.64. a. 0.8 b. 0.08 0.4 d. 0.1 2. Which
More informationForce versus distance graph
Force versus distance graph Objectives Investigate examples of kinetic and potential energy and their transformations. Calculate work from the area under the force vs. distance graph. Relate the net work
More information2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY
2017 SUMMER REVIEW FOR STUDENTS ENTERING GEOMETRY The following are topics that you will use in Geometry and should be retained throughout the summer. Please use this practice to review the topics you
More informationOrbiting Satellites and Free-Fall Elevators
Orbiting Satellites and Free-Fall Elevators Paul Robinson San Mateo High School pablo@laserpablo.com www.laserpablo.com Dig deep... Suppose you could bore a tunnel through the center of the earth. Further
More informationReview of Exponential Change Model and Forces
Physics 7B-1 (A/B) Professor Cebra Winter 2010 Lecture 5 Review of Exponential Change Model and Forces Slide 1 of 37 Exponential Growth Slide 2 of 37 Slide 3 of 37 Exponential decay Slide 4 of 37 The half
More informationALGEBRA 1. Interactive Notebook Chapter 2: Linear Equations
ALGEBRA 1 Interactive Notebook Chapter 2: Linear Equations 1 TO WRITE AN EQUATION: 1. Identify the unknown (the variable which you are looking to find) 2. Write the sentence as an equation 3. Look for
More informationShape Perimeter Area. + s 3. + s 2. side 3 (s 3 ) base (b) and side 1 (s 1
Geometric Formulas Reteaching 91 Math Course 1, Lesson 91 Shape Perimeter Area Square P = 4s A = s 2 Rectangle P = 2l + 2w A = lw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1 2 bh
More informationd = k where k is a constant of proportionality equal to the gradient.
VARIATION In Physics and Chemistry there are many laws where one quantity varies in some way with another quantity. We will be studying three types of variation direct, inverse and joint.. DIRECT VARIATION
More informationC. Incorrect! This symbol means greater than or equal to or at least. D. Correct! This symbol means at most or less than or equal to.
SAT Math - Problem Drill 10: Inequalities No. 1 of 10 1. Choose the inequality symbol that means at most. (A) > (B) < (C) (D) (E) This symbol means greater than. This symbol means less than. This symbol
More informationSection 1.1 Notes. Real Numbers
Section 1.1 Notes Real Numbers 1 Types of Real Numbers The Natural Numbers 1,,, 4, 5, 6,... These are also sometimes called counting numbers. Denoted by the symbol N Integers..., 6, 5, 4,,, 1, 0, 1,,,
More informationLHS Algebra Pre-Test
Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well
More informationCheck boxes of Edited Copy of Sp Topics (was 217-pilot)
Check boxes of Edited Copy of 10024 Sp 11 213 Topics (was 217-pilot) College Algebra, 9th Ed. [open all close all] R-Basic Algebra Operations Section R.1 Integers and rational numbers Rational and irrational
More informationCore Mathematics 3 Algebra
http://kumarmathsweeblycom/ Core Mathematics 3 Algebra Edited by K V Kumaran Core Maths 3 Algebra Page Algebra fractions C3 The specifications suggest that you should be able to do the following: Simplify
More informationA. Incorrect! Perform inverse operations to find the solution. B. Correct! Add 1 to both sides of the equation then divide by 2 to get x = 5.
Test-Prep Math - Problem Drill 07: The Multi-Step Equations Question No. 1 of 10 1. Solve: 2x 1 = 9 Question #01 (A) 4 (B) 5 (C) 1/5 (D) -5 (E) 0 B. Correct! Add 1 to both sides of the equation then divide
More informationReady To Go On? Skills Intervention 7-1 Integer Exponents
7A Evaluating Expressions with Zero and Negative Exponents Zero Exponent: Any nonzero number raised to the zero power is. 4 0 Ready To Go On? Skills Intervention 7-1 Integer Exponents Negative Exponent:
More informationMath 20-1 Functions and Equations Multiple Choice Questions
Math 0-1 Functions and Equations Multiple Choice Questions 1 7 18 simplifies to: A. 9 B. 10 C. 90 D. 4 ( x)(4 x) simplifies to: A. 1 x B. 1x 1 4 C. 1x D. 1 x 18 4 simplifies to: 6 A. 9 B. 4 C. D. 7 4 The
More information2-6 Nonlinear Inequalities
31. Find the domain of each expression. For the expression to be defined, x 2 3x 40 0. Let f (x) = x 2 3x 40. A factored form of f (x) is f (x) = (x 8)(x + 5). f (x) has real zeros at x = 8 and x = 5.
More informationMath 155 Prerequisite Review Handout
Math 155 Prerequisite Review Handout August 23, 2010 Contents 1 Basic Mathematical Operations 2 1.1 Examples...................................... 2 1.2 Exercises.......................................
More informationEQUATIONS. Equations PASSPORT
EQUATIONS PASSPORT www.mathletics.com.au This booklet shows you how to apply algebraic skills in the solution of simple equations and problems. These words appear a lot in this unit. Investigate and write
More informationCheck boxes of Edited Copy of Sp Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and
Check boxes of Edited Copy of 10021 Sp 11 152 Topics (was 145 for pilot) Beginning Algebra, 3rd Ed. [open all close all] Course Readiness and Additional Topics Appendix Course Readiness Multiplication
More informationSolving Two-Step Equations
Solving Two-Step Equations Warm Up Problem of the Day Lesson Presentation 3 Warm Up Solve. 1. x + 12 = 35 2. 8x = 120 y 9 3. = 7 4. 34 = y + 56 x = 23 x = 15 y = 63 y = 90 Learn to solve two-step equations.
More informationMath 154 :: Elementary Algebra
Math 4 :: Elementary Algebra Section. Additive Property of Equality Section. Multiplicative Property of Equality Section.3 Linear Equations in One-Variable Section.4 Linear Equations in One-Variable with
More informationRecall that when you multiply or divide both sides of an inequality by a negative number, you must
Unit 3, Lesson 5.3 Creating Rational Inequalities Recall that a rational equation is an equation that includes the ratio of two rational epressions, in which a variable appears in the denominator of at
More informationThe Law of Averages. MARK FLANAGAN School of Electrical, Electronic and Communications Engineering University College Dublin
The Law of Averages MARK FLANAGAN School of Electrical, Electronic and Communications Engineering University College Dublin Basic Principle of Inequalities: For any real number x, we have 3 x 2 0, with
More informationGravitational Fields
Gravitational Fields Examples 00 Currently, the space probe, Cassini, is between Jupiter and Saturn. Cassini s mission is to deliver a probe to one of Saturn s moons, Titan, and then orbit Saturn collecting
More informationPrep for College Algebra
Prep for College Algebra This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (219 topics + 85 additional topics)
More informationElectricity Final Unit Final Assessment
Electricity Final Unit Final Assessment Name k = 1/ (4pe 0 ) = 9.0 10 9 N m 2 C -2 mass of an electron = 9.11 10-31 kg mass of a proton = 1.67 10-27 kg G = 6.67 10-11 N m 2 kg -2 C = 3 x10 8 m/s Show all
More informationPhys 207. Announcements. Hwk 6 is posted online; submission deadline = April 4 Exam 2 on Friday, April 8th. Today s Agenda
Phs 07 Announcements Hwk 6 is posted online; submission deadline = April 4 Exam on Frida, April 8th Toda s Agenda Freshman Interim Grades eview Work done b variable force in 3-D Newton s gravitational
More informationSolving for a Variable
2- Solving for a Variable Objectives Solve a formula for a given variable. Solve an equation in two or more variables for one of the variables. Vocabulary formula literal equation Who uses this? Athletes
More informationEXAM I. Phys 172H fall 2006, Purdue University
EXAM I Phys 17H fall 006, Purdue University PRINT YOUR NAME: Lab section: Do not use other paper. Write on the back of this test if needed. All problems except the last one are multiple choice and only
More informationIn #1 and 2, use inverse operations to solve each equation. 2.
In #1 and 2, use inverse operations to solve each equation. 1. 3x + 12 + 5x = 7 2. 1 (4x + 10) = x 5 2 3. Alex and Alyssa both have savings accounts. Alex has $515 and saves $23 per month. Alyssa has $725
More informationPrep for College Algebra with Trigonometry
Prep for College Algebra with Trigonometry This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (246 topics +
More informationStepping stones for Number systems. 1) Concept of a number line : Marking using sticks on the floor. (1 stick length = 1 unit)
Quality for Equality Stepping stones for Number systems 1) Concept of a number line : Marking using sticks on the floor. (1 stick length = 1 unit) 2) Counting numbers: 1,2,3,... Natural numbers Represent
More informationMath 75B Practice Midterm III Solutions Chapter 6 (Stewart) Multiple Choice. Circle the letter of the best answer.
Math 75B Practice Midterm III Solutions Chapter 6 Stewart) English system formulas: Metric system formulas: ft. = in. F = m a 58 ft. = mi. g = 9.8 m/s 6 oz. = lb. cm = m Weight of water: ω = 6.5 lb./ft.
More informationREAL WORLD SCENARIOS: PART IV {mostly for those wanting 114 or higher} 1. If 4x + y = 110 where 10 < x < 20, what is the least possible value of y?
REAL WORLD SCENARIOS: PART IV {mostly for those wanting 114 or higher} REAL WORLD SCENARIOS 1. If 4x + y = 110 where 10 < x < 0, what is the least possible value of y? WORK AND ANSWER SECTION. Evaluate
More informationExponents. Reteach. Write each expression in exponential form (0.4)
9-1 Exponents You can write a number in exponential form to show repeated multiplication. A number written in exponential form has a base and an exponent. The exponent tells you how many times a number,
More information