...Simplifying Expressions Christy Bailey MATT 221: Introduction to Algebra Instructor: Stacie Williams October 13, 2013 Simplifying Expression Include in this paper I have demonstrated the following solutions for the three problems listed below. Using th given vocabulary words I have broken down each problem using the proper steps in solving the algebraic expressions. Also shown will be what is important about real numbers and in what way they are useful in using real numbers in solving algebraic expressions. By breaking down the equation you can simplify the equation down to lowest terms. Gathering the like terms in the equation is a step in breaking down the expression correctly. Take the coefficient and multiply it by the variable. The distributive property in the expression is the letters in the expression. When solving a algebraic expression you always remove the parenthesis first. A.)2a(-5 + a) + 4(a + -5) Simplify the terms (-5 * 2a + a * 2a) + 4(a + -5) (-10a + 2a2) + 4(a + -5) -10a + 2a2 + 4(-5 + a) Reorder the terms -10a + 2a2 + (-5 * 4 + a * 4) -10a + 2a2 + (-20 + 4a) -10a + 4a = -6a -20 + -6a + 2a2 Combine the like terms : -20 + -6a + 2a2 a = 5 This is...
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...Mathematical Operations of Numbers and Simplifying Algebraic Expressions Section A.: Mathematical Operations of Numbers 1.) 8+((12+5) x 4)/2= 8+(17x4)/2= 8+68/2= 8+34= 42 2.) ((3+4)²+4)-2= (7²+4)-2= (49+4)-2= 53-2= 51 3.) ((12+7)+(8/4)²) (19)+(2)² 19+4 23 4.) ½ + ¼ - ⅓= 6/12+3/12-4/12= 9/12-4/12= 5/12 5.) 2/3 x 3/5 = Multiply straight across 2/3 x 3/5 = 6/15 Find common denominator Reduce to lowest term 6/15 ÷ 3/3 = 2/5 6.) ⅓ ÷ ½ = Multiply by reciprocal ⅓ x 2/1= 2/3 7.) 3/2 ÷ ( 1/5 + 6/10) = 3/2 ÷ (2/10 + 6/10) = 3/2 ÷ 8/10 = Multiply by reciprocal 3/2 x 10/8 = 30/16 = 15/8 = 1 7/8 Section B.: Simplifying Algebraic Expressions 1.) 2x + 3x - 5x + x = 5x - 5x + x = 0 + x = x 2.) 2(6x + 5) = 2(6x) + (2x5) = 12x + 10 = 3.) (14x - 7) /7 = 14x - 7 ÷ 7 = 14x ÷ 7 = 2x -7 ÷ 7 = -1 2x - 1 4.) -(-15x) - 3x = 15x - 3x = 12x 5.) 5(3x+4) - 4 = 15x + 20 - 4 = 15x + 16 = 6.) 5(3x-2)+12x = 15x -10+12x = 27x - 10 = 7.) 4(2y-6)+3(5y+10) = 8y-24+15y+30 = 23y-24+30 = 23y+6= 8.) (x+1) (x-2) = Multiply the first 2, outside 2, inside 2, last 2 xx - 2x + 1x - 2 = xx - 2x + x - 2...
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...Comparison of key skills specifications 2000/2002 with 2004 standardsX015461July 2004Issue 1 GCE Mathematics (6663/01) General Principal for Pure Mathematics Marking (But note that specific mark schemes may sometimes override these general principles). Method mark for solving 3 term quadratic: 1. Factorisation [pic], leading to x = … [pic], leading to x = … 2. Formula Attempt to use correct formula (with values for a, b and c). 3. Completing the square Solving [pic]: [pic], leading to x = … Method marks for differentiation and integration: 1. Differentiation Power of at least one term decreased by 1. ([pic]) 2. Integration Power of at least one term increased by 1. ([pic]) Use of a formula Where a method involves using a formula that has been learnt, the advice given in recent examiners’ reports is that the formula should be quoted first. Normal marking procedure is as follows: Method mark for quoting a correct formula and attempting to use it, even if there are mistakes in the substitution of values. Where the formula is not quoted, the method mark can be gained by implication from correct working with values, but may be lost if there is any mistake in the working. Exact answers Examiners’ reports have emphasised that where, for example, an exact answer is asked...
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...A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. The simplest polynomials have one variable but they can have two three or more variables. Knowing the formula and how to use and brake down polynomial can help us in our everyday lives. It can help you figure out how much interest you can accrue from a deposit or investment that you made with a given interest rate. Let’s take a closer look at an equation that deals with polynomials. “P dollars is invested at annual interest rate r for 1 year. If the interest is compounded annually then the polynomial P(1 + r)2 represents the value of the investment after 1year” (Dugopolski, 2012). P(1 + r/2)2 Original expression P(1 + r/2)(1 + r/2) Simplify the expression by using foil this means multiply first outer, Inner, last P(1+ r/2 + r/2 + r2/4) Combine the like terms P(1 + 2(r/2) + r2/4) Distribute P across the trinomial P + Pr + Pr2/4 Put all variables in descending order Now let’s try our formula with a given set of numerical information P=200 r =10% interest rate .10 as a decimal. P + Pr + Pr2/4 expanded formula 200 + 2/4(200)(.10) + 200(.10)2 substitute values into formula 200 + 10 + 200(.01) multiply 200 + 10 + 2 ...
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...strands (problem solving, communication, connections, reasoning and proof, and representation) are included in the strategies. The purpose of the suggested teaching strategies is to assist school districts and teachers in the development of possible methods of organizing the competencies and objectives to be taught. Since the competencies and objectives require multiple assessment methods, some assessment ideas may be included in the strategy. October 2007 2007 Mississippi Mathematics Framework Revised Strategies Comp. 1 2 Obj. a g Suggested Teaching Strategies Give students an algebraic expression such as 3x + 2y2. Ask them to create as many different algebraic expressions that can be simplified to the given expression. Some possible expressions might be: 1) 2x + 2(x + y2) – x; 2) 4(x – ay) + 2y(2a + y) – x; or 3) 3(x + y2) – y2. Have students share their expressions as others check to be sure that it can be simplified...
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...impressed is the artwork named ‘a presage of happiness’ made from Park Yoonhee. This artwork is huge stacked of isomorphic cubes. And on the top of this artwork, arrangement for cube looks like stair. Material for cube looks like hard and somewhat opaque. When I was in front of those, I could just see the contour of my body. And there are not any additional shapes or patterns or colors. Actually when I saw this artwork, I just thought ‘what is this?’ In other words, I didn’t know what this means. It looks like some figures which I can see in math course-book in middle school. In addition to this feeling, after looking the title, I was curious how the name and this artwork can be matched. Usually when we thought about the happiness, the expression for this feeling is something bright. After reading brochure and talking with Prof. LEE, I realized that the artist wanted to criticize our way of living. When I did first online session and project for creative practitioner, creativity is related with changing perspective within understandable context. The artist broke ‘normal’ image for happiness in our mind and looked the way in which modern people live in critical manner. I think this artist is also creative practitioner in these contexts. It means this perspective is somewhat different for usual notion of happiness and in the way that criticism, it is understandable by expressing it in stacked of same pattern cubes. In this museum, I think there are not many artworks, but each...
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...WEEK 1 ASSIGNMENT: Solving Proportion MAT222: Intermediate Algebra Page 437 #56.) Bear Population: To estimate the size of the bear population on the Keweenaw Peninsula, conservationist captured, tagged, and released 500 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist’s estimate of the size of the bear population? x500=1002 2x2=500002 x=25000 In this problem we are seeking to find a total amount. We must use the information we have to locate this amount. To solve we utilize the proportions formula. For this formula we use the total amount divided by the known tagged amount. Once we plug in the given amounts along with the “x” variable, we can begin to solve. First we cross multiply then finally we divide. The outcome is the total amount. Page 444 #10.) Simplify: y-1x+3=-13 3y-1=-1x+3 3y-3=-x-3 y=-x3 In this problem we have two fractional equations better known as a proportion. Next we cross using the extreme means property. The next step is to appropriately distribute on both sides. In order to solve for “y” we must move everything away from “y”. We start by subtracting, and then we divide. The final results are the equivalence of “y”. Upon going back to the top of problem#10 to check to see whether the solution is correct. I was unable to obtain a clear defined solution due to the negative fraction. However it is also unclear as to whether the problem is extraneous. One observation...
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... - ‘What the French call ‘laïcité’ is a matter which concerns the separation of religion and state. In England, this issue is not taken as seriously as in France.’ a good deal of… (beaucoup) ALTERNATIVE EXPRESSIONS - a large amount of - a considerable number of - a significant amount of - a great deal of (more emphatic) NB- You can mix the phrases: ‘a large number of’/ ‘a considerable amount’/ a good amount of Fierce (féroce/passionné) heated lively vivid to give a series of… (donner plusieurs/une serie de) - Professor Clark will give a series of lectures - The Cinematheque plans to show a series of films by the Lumiere brothers - The police made a series of arrests in connection with a drugs cartel - The government has announced a series of initiatives to encourage reading among 6-12 year-olds NB- Dans les phrases en-dessus, le verbe ‘give’ est remplace par un autre verbe ‘show’/ ‘make’/ ‘announce’ selon l’action- verifies toujours le meilleur verbe pour l’action. ALTERNATIVE EXPRESSIONS to give a number of to give a succession of Strategy… Indefensible… ‘The policy of taxing poor people more than rich people is indefensible.’ ‘The policy of making children under the age of 16 work full-time is indefensible.’ ALTERNATIVE EXPRESSIONS unacceptable- unjustifiable- ‘Paying workers less than they need to survive is unjustifiable’ cannot be justified- off the charts- (really high/ unprecedented) -‘The level of...
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...between man and man. Every work of art causes the receiver to enter into a certain kind of relationship both with him who produced, or is producing, the art, and with all those who, simultaneously, previously, or subsequently, receive the same artistic impression. Speech, transmitting the thoughts and experiences of men, serves as a means of union among them, and art acts in a similar manner. The peculiarity of this latter means of intercourse, distinguishing it from intercourse by means of words, consists in this, that whereas by words a man transmits his thoughts to another, by means of art he transmits his feelings. The activity of art is based on the fact that a man, receiving through his sense of hearing or sight another man’s expression of feeling, is capable of experiencing the emotion which moved the man who expressed it. To take the simplest example; one man laughs, and another who hears becomes merry; or a man weeps, and another who hears feels sorrow. A man is excited or irritated, and another man seeing him comes to a similar state of mind. By his movements or by the sounds of his voice, a man expresses courage and determination or sadness and calmness, and this state of mind passes on to others. A man suffers, expressing his sufferings by groans and spasms, and this suffering transmits itself to other people; a man expresses his feeling of admiration, devotion, fear, respect, or love to certain objects, persons, or phenomena, and others are infected by the same...
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...arguing the idea that hip-hop is mostly about the music, the sound surrounding the lyrics (I mean, he also spends much of the book expressing the same ideas over and over and over again, but I won’t get into that). Bradley expresses the idea that the music comes first, and the content comes second, and I found myself strongly disagreeing with the notion. To put it simply, hip-hop is indeed art. In order to make this assertion, however, you have to take a step back and ask: what is art? Is it taking some Crayola crayons and rubbing them on a piece of paper, soon to be hung up on the fridge? Is it a statue of some random naked muscular man? I believe that art simply describes a method of expression. It could be a painting—Picasso’s Guernica, for example—which is a form of visual expression. A painter wants to express a feeling about, say, a...
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...Algebra I Quarter 3 Exam Name/Student Number:__________________________ Score:_______/________ Directions: For each question show all work that is required to arrive at the solution. Save this document with your answers and submit as an attachment to be graded. Simplify each expression. Use positive exponents. 1. m3n–6p0 2. a 4 b 3 ab 2 3. (x–2y–4x3) –2 4. Write the explicit formula that represents the geometric sequence -2, 8, -32, 128 5. Evaluate the function f (x) 4 • 7x for x 1 and x = 2. Show your work. 6. Simplify the quotient 4.5 x 103 9 x 107 . Write your answer in scientific notation. Show your work. Simplify the expressions. Show your work. 7. 3x(4x4 – 5x) 8. (5x4 – 3x3 + 6x) – ( 3x3 + 11x2 – 8x) 9. (x – 2) (3x-4) 10. (x + 6)2 Factor each expression. Show your work. 11. r2 + 12r + 27 12. g2 – 9 13. 2p3 + 6p2 + 3p + 9 Solve each quadratic equation. Show your work. 14. (2x – 1)(x + 7) = 0 15. x2 + 3x = 10 16. 4x2 = 100 17. Find the roots of the quadratic equation x2 – 8x = 9 by completing the square. Show your work. 18. Use the discriminant to find the number of real solutions of the equation 3x2 – 5x + 4 = 0. Show your work. A water balloon is tossed into the air with an upward velocity of 25 ft/s. Its height h(t) in ft after t seconds is given by the function h(t) = − 16t2 + 25t + 3. Show your work. 19. After how many seconds will the balloon hit the ground? (hint: Use the...
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...freely to express everything necessary to what he wants to talk about. © 3. ( E) The word captured is referred to the meaning taking something in your possession controlled by force. The girl was angry and frustrated, instead of taking the frustration else where it was already lead on. 4. (P) The word Gestapo is being identified as a word much more than an actual person, defining what is acceptable and what is not. 5. Cussing make one better by growing up with the idea of the cussing instead of “soap licking” witch was mentioned in the text. You have to be a certain legal age to be engaged in “cuss time”. 6. (T) No, cussing is not the only way we can express individuality, by limiting or denying freedom of speech and expression people take away a lot of potential of what they do have. 7. (B) The family’s feelings described in the last sentence was just very blunt and realistic about the situation, expressing your feelings in a fiction novel calls for using your freedom and using it wisely. 8. (H) It adds to the understatement of freedom because why be embarrassed, because having freedom is not being scared to hold back or withdraw information that’s suitable to be put to use. 9. (K) When you have so many ways about going with your words and actions, it leads to many options and sometimes we are overwhelmed by it all. 10. (D) The impact of the boys statement was angry, and frustration occurred but she didn’t come off in that...
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...Assessment and Text Evaluation in the Content Area Classroom My content area text book that I chose was an Algebra 1 textbook. Algebra 1 is usually taken in either the 8th or 9th grade. To get estimated grade level I used Fry's Readability Formula. To get this estimation, I randomly selected three passages from the textbook of one hundred words each. For each section of one hundred words, I counted the number of sentences and the number of syllables. For the first one hundred word sample, the number of sentences was roughly 4.9 with 180 syllables, the second sample was roughly 3 sentences with 131 syllables, and the last sample was roughly 5.3 sentences with 156 syllables. This averages out to roughly 4.4 sentences with 155.67 syllables. According to the Fry's Readability Formula, this textbook was estimated to be between the 10th and 11th grade reading level, which is a little bit higher than it should be. After determining the reading level of the Algebra 1 textbook, I then took another passage, from the same textbook, and performed a cloze procedure. To do this, I took another random one hundred word sample and deleted a random word from the second sentence and from there after deleted every five words. The test was then given to two different students. Here is the cloze test I created: Cloze Test: The process of designing an experiment begins with determining what type of data is needed and how it should be obtained. The best way to test a _______ would...
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...an equation has no solution? Assignment: Expressions and Equations Complete Appendix C to apply the skills learned in Ch. 1 and sections 2.1–2.6 of Ch. 2 to a real-life situation. Use Equation Editor® to write mathematical equations and expressions in Appendix C. Week 4: Exercise: Week Four Concept Check Post your 50-word response to the following: Explain in your own words why the line x = 4 is a vertical line. Assignment: Solving Inequalities and Graphing Equations Complete Appendix D to apply skills learned in Ch. 2 & 3 to a real-life situation. Use Equation Editor® to write mathematical equations and expression in Appendix D. Week 6: Exercise: Week Six Concept Check Post your 50-word response to the following: How can you determine if two lines are perpendicular? Assignment: Functions and Their Graphs Complete Appendix E to apply the skills learned in Ch. 7 to a real-life situation. Use Equation Editor® to write mathematical expressions and equations in Appendix E. MAT 116 COMPLETE CLASS To purchase this visit here: http://www.activitymode.com/product/mat-116-complete-class/ Contact us at: SUPPORT@ACTIVITYMODE.COM MAT 116 COMPLETE CLASS MAT 116 FINAL EXAM Week 2: Exercise: Week Two Concept Check Post your 50-word response to the following: How do you know when an equation has infinitely many solutions? How do you know when an equation has no solution? Assignment: Expressions and Equations Complete Appendix C to apply...
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...Equations and Inequalities Unit Overview Investigating patterns is a good foundation for studying Algebra 1. You will begin this unit by analyzing, describing, and generalizing patterns using tables, expressions, graphs, and words. You will then write and solve equations and inequalities in mathematical and real-world problems. Key Terms As you study this unit, add these and other terms to your math notebook. Include in your notes your prior knowledge of each word, as well as your experiences in using the word in different mathematical examples. If needed, ask for help in pronouncing new words and add information on pronunciation to your math notebook. It is important that you learn new terms and use them correctly in your class discussions and in your problem solutions. © 2014 College Board. All rights reserved. Academic Vocabulary • consecutive Math Terms • sequence • common difference • expression • variable • equilateral • equation • solution • formula • literal equation • compound inequality • conjunction • disjunction • absolute value • absolute value notation • absolute value equation • absolute value inequality ESSENTIAL QUESTIONS How can you represent patterns from everyday life by using tables, expressions, and graphs? How can you write and solve equations and inequalities? EMBEDDED ASSESSMENTS These assessments, following Activities 2 and 4, will give you an opportunity to demonstrate what you have learned...
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