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### Lesson31

Course: MA 11100, Spring 2011
School: Purdue
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Word Count: 262

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31 Section Lesson 6.2 Addition or Subtraction of Rational Expressions Remember: Fractions (rationals) can only be added or subtracted if they have a common 325 denominator. For example: + = 888 To add or subtract rational expressions with the same denominator: 1. Add or Subtract the numerators. 2. Keep the denominator. 3. Factor, if possible. 4. Simplify, if possible. A B A B = C C C Examples: 6 + 2x 8 1) + = x+7...

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31 Section Lesson 6.2 Addition or Subtraction of Rational Expressions Remember: Fractions (rationals) can only be added or subtracted if they have a common 325 denominator. For example: + = 888 To add or subtract rational expressions with the same denominator: 1. Add or Subtract the numerators. 2. Keep the denominator. 3. Factor, if possible. 4. Simplify, if possible. A B A B = C C C Examples: 6 + 2x 8 1) + = x+7 x+7 2) 5 7 + = 3a 3a 3) 4y + 2 y 3 = y2 y2 4) 3a 2 4a 7 2 = 2 a 25 a 25 1 When denominators are opposites, the denominators can be made the same polynomial by multiplying both numerator and denominator of one rational expression by 1 . Ex 5) Examine the following. x7 x 1 = 2 x 16 16 x 2 x 7 x 1 1 x 2 16 16 x 2 1 ( x 1) ( x 7) =2 x 16 16 x 2 ( ) ( x 7) + ( x 1) x 2 16 x 7 + x 1 2x 8 = =2 x 2 16 x 16 2( x 4) 2 = = ( x + 4)( x 4) x + 4 = When denominators are unlike, a common denominator must found be and the fractions are rewritten by multiplying numerator and denominator by the same nonzero quantity. To find the least common denominator (LCD): 1. Factor each denominator. 2. Find a product that contains each different factor the greatest number of times it occurs in any denominator. Examples: 6) , ( x + 2) 2 x( x + 2) 7) , ( x 3)( x + 1) ( x + 1)( x 5) 8) , 12 x 4 + 4 x 3 54 x 4 6 x 2 2 8.5) , , x 2 + 2 x x 2 ( x + 2)2 x 2 4 To add or subtract rational expressions with different denominators: 1. Find the LCD as outlined previously. 2. Multiply each numerator by the missing factor needed in order to write with the LCD. 3. Combine numerator terms together over the common denominator. 4. Factor and simplify, if possible. Examples: 9) a+3 a2 + = a 1 a + 4 10) 3+ 11) 7 9y + 2 +2 = 3y + y 4 3y 2 y 8 x+2 = x5 2 3 12) 6 xy x+ y = 2 x y x y 13) x 5 2 = x + 11x + 30 x + 9 x + 20 14) 2 5 a+3 + +2 = a+2 a2 a 4 2 2 4
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Purdue - MA - 11100
Lesson 32Section 6.4Rational EquationsRemember that a fraction cannot have a zero denominator. Because a rationalexpression cannot have a zero denominator, you must determine any values of x thatwould make a zero denominator when solving equations wi
Purdue - MA - 11100
Lesson 33, Section 6.5Application Problems Using Rational Equations1.2.3.4.1)Define a VariableDevelop A PlanWrite an EquationSolve and Answer the QuestionThe reciprocal of 5, plus the reciprocal of 7, is the reciprocal of what number?Let x = t
Purdue - MA - 11100
Lesson 34Section 6.8, VariationExamine this table:# hours workedPay1\$82\$163\$244\$326\$4910\$80When a relation between pairs of numbers is a constant ratio, such as above; it is called a8Direct Variation. The ratio above is and we say the p
Purdue - MA - 11100
Lesson 36Section 7.212What is a value for 9 ?Consider This.121211+229 9 = 9= 91 = 9 using the product rule of exponents.Now, Think!What other number times itself equals 9? 3 3 = 912Since both products equal 9, we can conclude that 9 = 3
Purdue - MA - 11100
Lesson 37Examine the following:4 9 = 23 = 6Sections 7.3 &amp; 7.4Since both equal 6, the expressions are equal.4 9 = 36 = 6Conclusion: 4 9 = 4 9Likewise:16=44=22Since both equal 2, the expressions are equal.16= 4=24Conclusion:164=164Th
Purdue - MA - 11100
Lesson 38Sections 7.5When two radicals have the same indices (plural of index) and same radicands, they aresaid to be 'like radicals'. They can be combined the same as 'like terms'.Like Radicals: 3 r , r,2 3 5m ,4r 3 x 3 5m , 12 3 5m5 4 5, 10 4 5
Purdue - MA - 11100
Lesson 39 Sections 7.6 and 8.1Solving Radical EquationsUsing the Principle of Square Roots to Solve an Equationx=3You know you can add, subtract, multiply, or divide (by nonnegative number) and get atrue equation. Let's see if both sides can be raise
Purdue - MA - 11100
Lesson 40Section 8.2Quadratic Formula:If ax 2 + bx + c = 0 , then the value(s) of x can be found by x =Note: b mean the opposite of b 4ac means (-4)(a)(c) b b 2 4ac.2ab 2 is always positiveUse the quadratic formula to solve the following quadrat
Purdue - MA - 11100
Linear ConnectionsAny two points ofthe line-pt. 1:( x1 , y1 )pt. 2: ( x 2 , y 2 )Slope Formulahorizontalline:y = y1m=y 2 y1 r=x 2 x1 sverticalline:x = x1Point-Slope Form of Liney y1 = m( x x1 )Standard Form ofLineA, B, &amp; C areintegers
Purdue - MA - 11100
MA 11100 and MA 15200 Spring 2011Information Needed to Register for Online HomeworkAddress: www.coursecompass.comPurdue Zip Code: 47907Adobe FlashPlayer is all that is needed on a computer.For your UserName: Use your Purdue email address (with the @p
Purdue - MA - 11100
E-mail messages Spring 2011message 1Hello!You are enrolled in MA 11100 for this fall semester. The class begin on Monday,January 10th and the class meets Monday, Wednesday, and Friday for most weeks.Vacation days are Martin Luther King Day (January 1
Purdue - MA - 11100
E-mail messages, spring 2011Message 2Hello!I recommend you buy your textbook as soon as you are able. It is advantageous to have yourtextbook and MyMathLab kit by Wednesday, January 12. Students will be asked to bringthe MyMathLab student access kit
Purdue - MA - 11100
E-Mail messages, spring 2011Message 3Hello!Today, I have attached some general comments about the class that I used tocommunicate to students the first day. However, since there are so many announcementsplus a lesson on the first day, I decided to se
Purdue - MA - 11100
E-mail Messages, spring 2011Message 4Hello!The course web page has all of the information for this course. It includes courseinformation, resources, exam information, instructor information, lesson notes, onlinehomework information, etc.Address:www
Purdue - MA - 11100
Purdue - MA - 11100
MA 11100, Intermediate Algebra, Spring 2011Memo: To MA 11100 studentsFrom: Charlotte Bailey, Course CoordinatorConcerning Classes/LessonsBefore each class, read the appropriate pages form the textbook for that lesson.ATTEND CLASS!Have the large majo
Purdue - MA - 11100
Outline for Linear Equations and Inequalities of 2 variablesAGraphing a line by Plotting Points1.2.BSubstitute any value for x in the equation and solve for y. This results ina point (x, y). ORSubstitute any value for y in the equation and solve f
Purdue - MA - 11100
SOLUTION IS.1 ordered pair infinite ordered pairsno ordered pair
Purdue - MA - 11100
3 Methods for Solving a Linear or other Systems of EquationsMethodGraphicalSubstitutionEliminationStrengths1. Solution(s) is easilyvisible2. Can be used with anysystem that can begraphed1.2.1. Yields exact solution(s)2. Easy to use when ava
Purdue - MA - 15300
Purdue - MA - 15300
Purdue - MA - 15300
Purdue - MA - 15300
MA 15300Exam 1 InformationThursday, February 36:30 pmSee your instructor for Exam locationYou will need to sit with your instructor's section.Lessons 1-9 (including lesson 1 and 9)BRING YOUR STUDENT ID TO THE EXAM WITH YOU.15 multiple-choice, mach
Shelton State Community College - SPCH - 101
Topics for Persuasive SpeechHyeok LeeSPH 1061. Internet Filtering in college or public library .There still is controversy about whether filtering internet in public library and inschool is violation of the first amendment or not.2. It is about time
Purdue - MA - 15300
Exam 1Question #Orange FormAnswerSpring 201112AD3B45CE3a 2 b 52x + 3x 105 xy5 xy 267DDx 3x + 4 y x 4 x 4 y + 16 y 28Ax 3x + 5x ( x 3)9C1011AEx +1x+7x is less than 10.All real numbers x are solutionsx2 yx18 y12645
Purdue - MA - 15300
MA 15300Exam 2 InformationThursday, March 38:00 pmSee your instructor for Exam locationYou will need to sit with your instructor's section.Lessons 10-20BRING YOUR STUDENT ID TO THE EXAM WITH YOU.15 multiple-choice, machine graded problemsOnly you
Purdue - MA - 15300
Exam 2Question #Orange FormAnswerSpring 20111234EEDDNone of the above (-3/2, 3)5A3 4 2 i6789BDDB10E11C12CNone of the above (-1)[-5, 1]3 , 3] , )2(12 5iOne positive solution.57 3, 2 ) ( 2 , )( x 2 ) + ( y + 3)2-6
Purdue - MA - 15300
MA 15300Exam 3 InformationTuesday, April 126:30 pmSee your instructor for Exam locationWe are sitting in every other seat.Lessons 21-33 inclusive.BRING YOUR STUDENT ID TO THE EXAM WITH YOU.15 multiple-choice, machine graded problemsOnly your answ
Purdue - MA - 15300
Exam 3Question #Orange FormAnswerSpring 2011171234ACAC56CD7C8910DCE11By = 4x +132y = ( x + 2) 12 3, 1] [3, )12Dy = 2 ( x 2) 91314BB375 feet15Ex 13 x + 4021 , 4)2y = 5, y = 474 2, 1] 1, 2]2d ( t ) = 36t
Purdue - MA - 15300
MA 15300Final Exam InformationTuesday, May 33:20 pm (2 hour final)STEW 183 (Loeb Playhouse).Pick up a scantron from your instructor upon entering for yourassigned seat.200 pointsAccumulative (covers the entire semester)BRING YOUR STUDENT ID TO TH
Purdue - MA - 15300
Purdue - MA - 15300
MA 153Lesson 1 OutlineLesson 1 Section 1.1Example:If x&gt;0 and y&lt;0, find the resulting sign of:(a) xy(b)x yyExample:Express as an inequality:(a) y is nonpositive(b) The reciprocal of w is at least 9.Example:5 36Section 1.2 Exponentsx n ; x i
Purdue - MA - 15300
MA 153Lesson 2 OutlineAnswering of homework questions over lesson 1.Lesson 2 Section 1.2 (cont) RadicalsnaExample:(a) 0 =16 =(b)(c)38 =(d)416 =Laws(1) n ab = n a n bExample:36 x 2 y(2)na na=b nbExample:3278Example12 x 8 y 7 z
Purdue - MA - 15300
MA 153Lesson 3 OutlineAnswering of homework questions over lesson 2.Lesson 3 Section 1.3 PolynomialsExample:9 x 6 + 4 x 5 + x 2 21Degree =Leading coefficient=Adding and subtracting polynomialsExample:(6x3 2 x2 + x 2) ( x2 x + 2)Multiplying an
Purdue - MA - 15300
MA 153Lesson 4 OutlineQuiz Solutions (Practice problems for distance learning students)1. Evaluate: 4 5 ( 2 ) + 3= 4 7 = 4 ( 7 )= 282. Simplify. Do not leave negative exponents in your answer.3x 5 y 46 x3 y 7=3 y46 x3 x5 y 7=12 x8 y 33. Si
Purdue - MA - 15300
MA 153Lesson 5 OutlineQuiz Solutions (Practice problems for distance learning students)1. Subtract and express as a polynomial.( 3x4+ 2 x 2 4 x + 1) ( x 4 5 x 2 + 7 )= 3x 4 + 2 x 2 4 x + 1 x 4 + 5 x 2 7= 2 x4 + 7 x2 4 x 62. Multiply. Express your
Purdue - MA - 15300
MA 153Lesson 6 OutlineQuiz Solutions (Practice problems for distance learning students)1. Factor each of the following as much as possible:(a) 3 x 2 + 1 0 x 8(b) 1 6 x 4 1= ( 3x 2 ) ( x + 4 )= (4 x 2 + 1)(4 x 2 1)= ( 4 x 2 + 1) ( 2 x + 1) ( 2 x 1)
Purdue - MA - 15300
MA 153Lesson 7 OutlineAnswering of homework questions over lesson 6.Lesson 7 Section 2.1 Equations(I) Linear EquationsExample:4 ( 2 y + 5) 3( 4 y ) = 0(II) Rational Equations(a) Example (Method 1):538 = 2+xx(a) Example (Method 2):538 = 2+
Purdue - MA - 15300
MA 153Lesson 8 OutlineAnswering of homework questions over lesson 7.Lesson 8 Section 2.2 ApplicationsExample:Kathy invested \$50,000 into two different accounts. One account earns 7% simpleinterest and the other pays 5% simple interest. How much is i
Purdue - MA - 15300
MA 153Lesson 9 OutlineQuiz Solutions (Practice problems for distance learning students)1. Solve for x:7 ( 2 x 1) 3 ( 4 x ) + 2 = 814 x 7 12 x = 62 x = 13x=1322. The following equation is an identity in which 0=0. What is the solution for x?32
Purdue - MA - 15300
MA 153Lesson 10 OutlineAnswering of homework questions over lesson 9.Lesson 10 Section 2.3 Solving Quadratic Equationsax 2 + bx + c = 0Solving:(1) By factoring: If ab = 0 , then a=0 or b=0.Example:x ( 3x + 10 ) = 77Example:5x36+ +2=x2 xx (
Purdue - MA - 15300
MA 153Lesson 11 OutlinePractice Quiz Solution (Practice problems for distance learning students)1. If Jon and Kathy work together, they can do a job in 35 minutes. If Jon works alone,he can do the same job in 55 minutes. How long would it take Kathy t
Purdue - MA - 15300
MA 153Lesson 12 OutlinePractice Quiz Solution (Practice problems for distance learning students)1. Solve for x:x ( 3x + 7 ) = 23x 2 + 7 x + 2 = 0(3 x + 1)( x + 2) = 03 x + 1 = 0, x + 2 = 01x = , x = 232. Solve for x:( x 4)2=5x4= 5x = 4 5A
Purdue - MA - 15300
MA 153Lesson 13 OutlinePractice Quiz Solution (Practice problems for distance learning students)1. A ball is thrown upward with an initial velocity of 48 ft./sec. The number of feet, s,above the ground after t seconds is given by s ( t ) = 16t 2 + 48t
Purdue - MA - 15300
MA 153Lesson 14 OutlineAnswering of homework questions over lesson 13.Lesson 14 Section 2.5 Other Types of EquationsAbsolute ValueExample:(a) x = 4(b) 4 x + 1 3 = 9Example:x=3Square both sides:x2 = 9Solve for x:x = 3, x = 3x = 3 is called an
Purdue - MA - 15300
MA 153Lesson 15 OutlineAnswering of homework questions over lesson 14.Lesson 15 Section 2.6 InequalitiesNotationInequalityInterval NotationGraph(a) 2 &lt; x 1(b) x 2(c) x 4 or x &gt; 2If you do not include an end value, use parantheses.If you do inc
Purdue - MA - 15300
MA 153Lesson 16 OutlineAnswering of homework questions over lesson 15.Lesson 16 Section 3.1 Rectangular Coordinate SystemyQ IIQIxQ IVQ IIIExample:Plot the point ( 2, 4 ) on the above axesDistance FormulaIf A ( x1 , y1 ) and B ( x2 , y2 ) , th
Purdue - MA - 15300
MA 153Lesson 17 OutlineReivew of lesson 16 formulas:Distance formula: d ( A, B ) =( x2 x1 ) + ( y2 y1 )22x +x y +y Midpoint formula: 1 2 , 1 2 22Answering of homework questions over lesson 16.Lesson 17 Section 3.2 GraphsExample:Graph y = x 2
Purdue - MA - 15300
MA 153Lesson 18 OutlineAnswering of homework questions over lesson 17.Lesson 18 Section 3.3 LinesExample: A ( 2, 3) and B ( 1, 2 )ySlope (m)m=rise y2 y1=run x2 x1xExample: x = 2Example: y = 3yyxxEquations of lines(1) Point-slope formy
Purdue - MA - 15300
MA 153Lesson 19 OutlineQuiz Solutions (Practice problems for distance learning students)1. Find the x intercept for the following equation:y = x 30 = x 33= xx = 9;( 9, 0 )2. Find the center and the radius of the circle given by the equation:x2 +
Purdue - MA - 15300
MA 153Lesson 20 OutlineQuiz Solutions (Practice problems for distance learning students)21. Find the slope of the line perpendicular to the line y = x + 1 .32Slope of given line = 3Slope of line perpendicular is negative reciprocal or322. Find
Purdue - MA - 15300
MA 153Lesson 21 OutlineLesson 21 Section 3.4 (cont) FunctionsGraphing Functions(1) IncreasingyAs x gets bigger, y gets bigger also.What values of x make the ys larger?5Increasing on [1, 4]21x4(2) DecreasingAs x gets bigger, y gets smaller.
Purdue - MA - 15300
MA 153Lesson 22 OutlineQuiz Solution (Practice problems for distance learning students)1. Given the graph below, find the following:(a) DomainDomain is the smallest x to the largest x, so D : [ 0, 4](b) RangeRange is the smallest y to the largest y
Purdue - MA - 15300
MA 153Lesson 23 OutlineReview of Changes in GraphsA vertical change is something being done to the function and changes the y-values.A horizontal change is something being done within the function and changes the xvalues.Start with graph of y = f ( x
Purdue - MA - 15300
MA 153Lesson 24 OutlineAnswering of homework questions over lesson 23.Lesson 24 Section 3.5 (cont) Piecewise FunctionsExample:x + 3f ( x) = 4i f x 1if x &gt; 1Find:(a) f ( 4 )(b) f ( 1)(c) f ( 2 )(d) f (100 )GraphingExample (same as above):x
Purdue - MA - 15300
MA 153Lesson 25 OutlineQuiz Solutions (Practice problems for distance learning students)1. Given a function y = f ( x ) whose graph contains the following points:( 3, 4 ) , ( 2, 6 ) , ( 1, 3)Find the points of the function y = f ( x 2 ) + 5(You do n
Purdue - MA - 15300
MA 153Lesson 26 OutlineReview from last lesson:Parabolas:1. Standard Equation : y = a( x h) 2 + kVertex: ( h, k )2. Quadratic form: y = ax 2 + bx + cVertex can be found one of two ways:b. Substitute the x-coordinate (once2aknown) into the equat
Purdue - MA - 15300
MA 153Lesson 27 OutlineAnswering of homework questions over lesson 26.Lesson 27 Section 3.7 Operations on FunctionsLet f(x) and g(x) be two functions:(1)( f + g )( x) = f ( x) + g ( x)(2) ( f g ) ( x ) = f ( x ) g ( x )( 3) ( fg ) ( x ) = f ( x )
Purdue - MA - 15300
MA 153Lesson 28 OutlineQuiz Solutions (Practice problems for distance learning students)1. Find the maximum or minimum value (specify whether it is a max or a min):2y = 2 ( x 3) 5Min value = -5(It is a min because a is positive so parabola opens up
Purdue - MA - 15300
MA 153Lesson 29 OutlineAnswering of homework questions over lesson 28.Lesson 29 Section 4.1 Polynomials with degree greater than 2Degree 1: y = 7 x + 3 is a lineDegree 2: y = 3 x 2 2 x + 1 is a parabolaDegree 3: ?Example:Given the sign chart below
Purdue - MA - 15300
MA 153RLesson 30 OutlineQuiz Solutions (Practice problems for distance learning students)1. Find all the values that would be included on the top of the sign chart for:( x + 2 ) ( x 1) 0Would needx = 2,1, and 5 on thetop of the sign chartx+5(Do N