Quadratics and inequalities
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Quadratics and inequalities

Course Number: MAT 117, Spring 2010

College/University: University of Phoenix

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dug22241_ch10a.qxd 11/10/2004 18:29 Page 617 Quadratic Equations and Inequalities Is it possible to measure beauty? For thousands of years artists and philosophers have been challenged to answer this question. The seventeenth-century philosopher John Locke said, Beauty consists of a certain composition of color and gure causing delight in the beholder. Over the centuries many architects, sculptors, and...

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10 10.1 Factoring and Completing the Square 10.2 The Quadratic Formula 10.3 Graphing Parabolas 10.4 More on Quadratic Equations 10.5 Quadratic and Rational Inequalities Chapter Q uadratic Equations and Inequalities Is it possible to measure beauty? For thousands of years artists and philosophers have been challenged to answer this question. The seventeenth-century philoso- pher John Locke said, Beauty consists of a certain composition of color and figure causing delight in the beholder. Over the centuries many architects, sculptors, and painters have searched for beauty in their work by exploring numerical pat- terns in various art forms. Today many artists and architects still use the concepts of beauty given to us by the ancient Greeks. One principle, called the Golden Rectangle, concerns the most pleasing proportions of a rec- tangle. The Golden Rectangle appears in nature as well as in many cultures. Examples of it can be seen in Leonardo da Vincis Proportions of the Human Figure as well as in Indonesian temples and Chinese pagodas. Perhaps one of the best-known examples of the Golden Rectangle is in the faade and floor plan of the Parthenon, built in Athens in the fifth century B . C . In Exercise 91 of Section 10.4 we will see that the principle of the Golden Rectangle is based on a proportion that we can solve using the quadratic formula. L W W W W L 2 W dug22241_ch10a.qxd 11/10/2004 18:29 Page 617 618 Chapter 10 Quadratic Equations and Inequalities 10-2 In this Section Review of Factoring Review of the Even-Root Property Completing the Square Miscellaneous Equations Imaginary Solutions 10.1 Factoring and Completing the Square Factoring and the even-root property were used to solve quadratic equations in Chapters 5, 6, and 9. In this section we first review those methods. Then you will learn the method of completing the square, which can be used to solve any quadratic equation. Review of Factoring A quadratic equation has the form ax 2 bx c 0, where a , b , and c are real num- bers with a 0. In Section 5.6 we solved quadratic equations by factoring and then applying the zero factor property. Of course we can only use the factoring method when we can factor the quadratic poly- nomial. To solve a quadratic equation by factoring we use the following strategy. Zero Factor Property The equation ab 0 is equivalent to the compound equation a o r b 0. Strategy for Solving Quadratic Equations by Factoring 1. Write the equation with 0 on one side. 2. Factor the other side. 3. Use the zero factor property to set each factor equal to zero. 4. Solve the simpler equations. 5. Check the answers in the original equation. E X A M P L E 1 Solving a quadratic equation by factoring Solve 3 x 2 4 x 15 by factoring.

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University of Phoenix - MAT - 117
Axia College MaterialAppendix C PolynomialsRetail companies need to keep close track of their operations in order to maintain profitability. Often, the sales data of each individual product is analyzed separately, which can be used to help set pricing a
University of Phoenix - MAT - 117
Gregory MannMAT 117Post a 50 word response to the following: How do you determine if a polynomial is the difference of two squares?When solving for polynomials remember that only one term of the binomial can be negative and that the powers on all the v
University of Phoenix - MAT - 117
Axia College MaterialAppendix D The EnvironmentEnvironmental and wildlife preservation ensures future generations will have available resources and can enjoy the beauty of Earth. On the other hand, some of the damage humans have already done to the envi
University of Phoenix - MAT - 117
#24=When finding even Nth roots absolute values are necessary=#23=Isolate radical then square both sides and simplify#2225 =using laws of exponents and fractional exponents#215 = using laws of exponents and fractional exponents =#12=Using ru
University of Phoenix - MAT - 117
Week 6 Concept Check MAT 117 The Pythagorean Theorem is a mathematical rule that gives the relationship and lengths between the sides of a right triangle. When we deal with the lengths of the sides to a right triangle, the Pythagorean Theorem can be used
University of Phoenix - MAT - 117
Axia College MaterialAppendix F Ticket SalesLiving in or near a metropolitan area has some advantages. Entertainment opportunities are almost endless in a major city. Events occur almost every night, from sporting events to the symphony. Tickets to thes
University of Phoenix - MAT - 117
Week 8 Concept Check Gregory MannIn order to determine where to find the solutions when looking at a graph of a quadratic equation, we must locate the x-coordinates of the points where a graph touches or crosses the xaxis. The solutions are located at th
University of Phoenix - HUM - 130
Elements Matrix1Axia College MaterialAppendix G Eastern Religion Elements MatrixHINDUISM INDIA COUNTRIES OF ORIGIN BUDDHISM DEVELOPED IN INDIA AND SPREAD TO EAST ASIA. CONFUCIANISM DEVELOPED IN EAST ASIA, GREW IN CHINA, AND LATER SPREAD TO JAPAN AND K
University of Phoenix - HUM - 130
Axia College MaterialAppendix G Eastern Religion Elements MatrixHINDUISMINDIA INDIABUDDHISMCONFUCIANISMFIRST DOCUMENTED IN CHINA DEVELOPING FURTHER IN EAST ASIA, AND GREW INTO JAPAN AND KOREA.DAOISMFIRST DOCUMENTED IN CHINA DEVELOPING IN EAST ASIA
University of Phoenix - HUM - 130
Axia College MaterialAppendix G Eastern Religion Elements MatrixHINDUISM BUDDHISM CONFUCIANISM DAOISMIndiaCOUNTRIES OF ORIGINIndiaF irst documented in First documented in China developing China developing further in east in east asia, and asia, and
University of Phoenix - HUM - 130
MY FILE WAS UPLOADING AND TAKING A LONG TIME AND DIDNT WANT TO BE ANOTHER DAY LATE AND ATTEMPTED TO OPEN NEW WINDOW AND SEND FILE AGAINIF I MAY ASK FOR A 1 MINUTE BUFFER BEING 12:01 WHEN FINALLY UPLOADEDTHANKS AND THIS VERSION SHOULD BE EASIER TO READ.Ax
University of Phoenix - HUM - 130
MY FILE WAS UPLOADING AND TAKING A LONG TIME AND DIDNT WANT TO BE ANOTHER DAY LATE AND ATTEMPTED TO OPEN NEW WINDOW AND SEND FILE AGAINIF I MAY ASK FOR A 1 MINUTE BUFFER BEING 12:01 WHEN FINALLY UPLOADEDTHANKS AND THIS VERSION SHOULD BE EASIER TO READ.Ax
University of Phoenix - HUM - 130
Week 9 Capstone CheckPoint 1Check Point: Capstone Gregory Mann Axia College of University of PhoenixWeek 9 Capstone CheckPoint 2Learning about world religions has influenced and educated me in reference to some of the waysof life of different cultures
University of Phoenix - HUM - 130
Mormonism1Mormonism Gregory Mann Axia College University of PhoenixMormonismMormonismIn 1827, a man named Joseph Smith had seen visions of an angel named Moroni, which told him not to join any church or any denomination. This same angel came to Smith
University of Phoenix - HUM - 130
M ike Ansley Final Paper G reek Philosophy Professor Michaud December 9, 2010 The Creation of Western PhilosophyGreek life impacted the creation of western philosophy. The culture, historical events, technology, and politics of the Bronze Age , Dark Age
University of Phoenix - HUM - 130
Five Pillars of Islam1Five Pillars of Islam Gregory Mann University of PhoenixHUM130Five Pillars of Islam2Five Pillars of IslamThe Five Pillars of Islam are considered the foundation in shaping Muslim beliefs and are the core religious practices pe
University of Phoenix - HUM - 130
Hinduism1Hinduism Gregory Mann Axia College of University of PhoenixHUM 130Hinduism2There are many misconceptions surrounding the religion of Hinduism in most countries and amongst the various populations of the world. Difficulties have also existed
University of Phoenix - HUM - 130
Axia College MaterialAppendix B 7 Question Final Project PlanWhat religion would you like to consider for your final project? Describe the place of worship you will visit. What do you already know about this topic?II am choosing the Islamic religionI
University of Phoenix - HUM - 130
Axia College MaterialAppendix E Hindu Terms MapWord What is your personal understanding of each of these terms? I believe Karma can either be good or bad; the action of a person in one life will determine what happens in the next life or as some believe
University of Phoenix - HUM - 130
Axia College MaterialAppendix G Eastern Religion Elements MatrixHinduism India Countries of origin India Buddhism Confucianism China China DaoismHistorical figures and eventsHinduism has no known founder or leader. This religion dates back to the Vedi
University of Phoenix - HUM - 130
Axia College MaterialAppendix C HUM 130 Week 1 Vocabulary QuizDefine these terms in your own words. 1. Immanent 2. Religion 3. Theistic 4. Monotheistic 5. Profane 6. Polytheistic 7. Monistic 8. Dogma 9. Nontheistic 10. Transcendent 11. Incarnations 12.
University of Phoenix - HUM - 130
Axia College MaterialAppendix C HUM 130 Week 1 Vocabulary QuizDefine these terms in your own words. 1. Immanent 2. Religion 3. Theistic 4. Monotheistic 5. Profane 6. Polytheistic 7. Monistic 8. Dogma 9. Nontheistic 10. Transcendent 11. Incarnations 12.
University of Phoenix - HUM - 130
Axia College MaterialAppendix H Monotheistic Religion Elements MatrixJudaism Israel Countries of origin Abraham, The holy covenant between God and Abraham. Other figures include Jacob, Isaac and Moses. Jesus Christ of Nazareth, The Last Supper and Chris
University of Phoenix - HUM - 130
HUM/130: Week 2 Discussion Question 1Find two Web sites dealing with indigenous cultures or religions. Discuss how modern civilization has affected the spiritual lives of the indigenous peoples you explored. Are indigenous religions still practiced today
University of Phoenix - HUM - 130
HUM130Organized religion has had some very important events throughout the history of mankind. From early Roman Catholicism and the Roman Empire, to the current events of the pastor in Florida; who organized the intentional burning of the Quran. Religion
University of Phoenix - HUM - 130
Jesus and Mohammed1Jesus and Mohammed Gregory Mann Axia College of University of PhoenixHUM 130Jesus and Mohammed2Two of the most dominant figures who influence modern religions are Jesus and the prophet Mohammed. Although both religious figures hav
University of Phoenix - HUM - 130
Jesus and Mohammedo o o o Trace the lives of Jesus and Mohammed historically. Compare what impact the death of each person had on his respective religion. Describe the ways each individual was or is worshipped. Explain how their messages are being carrie
University of Phoenix - HUM - 130
Jesus and Mohammed 1Jesus and Mohammed Gregory Mann Axia College of University of PhoenixHUM 130Jesus and Mohammed 2Both Christianity and Islam are the defiant cousins of Judah and two of the most dominant figuresin these religions respectively, are
University of Phoenix - HUM - 130
Judaism JudaismGregory Mann HUM 130RelationshipWithGod/Torah HistoryofKeySacredTexts TenCommandments Jerusalem TheNationofIsrael TheHolocaustDifferentSectsofJudaism SacredPracticesandHolidays JudaismTodayOverview OverviewRelationshipWithGod/Torah Rel
University of Phoenix - HUM - 130
The Book of Mormon Will Change Your Life John Hilton III, BYU Education Week 2005 The Book of Mormon is the Keystone of our Religion The Book of Mormon is the keystone of our religion. This was the Prophet Joseph Smiths statement. He testified tha
University of Phoenix - HUM - 130
Central Planning and Transition in the American Desert: Latter-day Saints in Present-Day Sight.1 By Gregory Grossman, University of California, Berkeley. All rights reserved. From 1847 to 1896 the Mormons ran a distinctive economic system in the western
University of Phoenix - HUM - 130
o o o o oIntroduction of the religion Name, location and review of the site. Interview summary Comparing and contrasting with another religion ConclusionMy report is on Mormonism and the Church of Jesus Christ of Latter Day Saints, and my interview will
University of Phoenix - HUM - 130
Mormonism1Mormonism Gregory Mann Axia College University of PhoenixMormonismMormonism In 1827, a man named Joseph Smith had seen visions of an angel named Moroni, which told him not to join any church or any denomination. This same angel came to Smith
University of Phoenix - HUM - 130
Axia College MaterialAppendix D Indigenous Culture Web Site Review TemplateQuestion Web site 1 URL: Name of Indigenous culture/religio n presented in Web site Consider the examples of roles and observances held sacred by these people. Is this practice b
University of Phoenix - FIN - 200
FIN200 Week 1 Assignment Cash Flow PreparationCrosby Corporation Statement of Cash Flows For the Year Ended December 31, 2008 Operating activities: Net Income Add items not requiring an outlay of cash: Depreciation Cash flow from operations Increase in a
University of Phoenix - FIN - 200
Financial management is the overall management of funds and includes, investment decision, financing decisions and dividend decisions of an organization. There are two main goals of the financial management mainly:a) Profit maximization b) Wealth maximiz
University of Phoenix - FIN - 200
FIN200 Week 2 CheckPoint Financial RatiosGoodyear Calendar Company Income Statement For the Year Ending December 31, 2004 Sales (on credit). $2,000,000 Less: Cost of goods sold. 1,300,000 Gross profit. 700,000 Less: Selling and administrative expenses. 4
University of Phoenix - FIN - 200
1) Firms exposed to the risk of interest rate changes may reduce that risk by A. pledging or factoring accounts receivable. B. hedging in the financial futures market. C. hedging in the commodities market. D. obtaining a Eurodollar loan.2) LIBOR is A. th
University of Phoenix - FIN - 200
Youareconsideringinvestinginacompany.Whichfinancialratioswouldyoufindmost useful? Thesignificanceofallfinancialratiosisvitalindeterminingwhichcompanytoinvestit.Thereare,however,certainfinancialratiosthataremorerelevantthanothers. Inordertodeterminewhich
University of Phoenix - FIN - 200
You are an upper-level manager in a company. Which financial ratios would you consider most useful? Would these ratios be different than the ones you would consider useful as an investor? Why or why not? If I were an upper-level manager, I would certainly
University of Phoenix - FIN - 200
Sheet1The Landis Corporation had 2008 sales of $100 million. The balance sheet items that vary directly with sales and th Percent Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5% Accounts receivable. . . . . . . . . . . . . . . .
University of Phoenix - FIN - 200
The predominant reasons why companies need financial forecasts is normally when they need to take out business loans or are planning to grow their business. For example, a financial forecast for a new company is necessary so that the company can properly
University of Phoenix - FIN - 200
Need a financial expert for this example. Show Calculations Lear, Inc., has $800,000 in current assets, $350,000 of which are considered permanent current assets. In addition, the firm has $600,000 invested in fixed assets. a. Lear wishes to finance all f
University of Phoenix - FIN - 200
Write a 200- to 300-word paper comparing long- and short-term financing. Describe situations in which each type of financing would be used. Word count: 296 Both new and established businesses will find it necessary to incur debts during the course of busi
University of Phoenix - FIN - 200
Healthy Foods, Inc., sells 50- pound bags of grapes to the military for $10 a bag. The fixed costs of this operation are $80,000, while the variable costs of the grapes are $.10 per pound. a. what is the break-even point in bags b. calculate the profit of
University of Phoenix - FIN - 200
1) A rapid rate of growth in sales may require A. increased borrowing by the firm to support the sales increase. B. higher dividend payments to shareholders. C. the firm to be more lenient with credit customers. D. sales forecasts to be made less frequent
University of Phoenix - FIN - 200
A company would want to use leverage to acquiring a company. This is called leverage buyout. In leverage buyout, company is acquired using the assets and cash flow of acquired company to finance the purchase. Debt has low cost so cost of capital is low. A
Boise State - HIST - 101
Chapman The Unfinished Nation Part II, episodes 43-44: These episodes were about the lat 1940s, the war was over and the people had something to look forward to. Unfortunately at this same time Russia decided that they needed an Atom Bomb, this was the s
Boise State - HIST - 101
Chapman `The Unfinished Nation Part II, episodes 41-42: Episodes 41 and 42 were about World War II and the after math of the war. During the war something happened in America, we got some common sense. It did not last long but it was there. Women began i
Boise State - HIST - 101
Chapman The Unfinished Nation Part II, episodes 39-40: These episodes were about the events in the economy and internationally that lead to WWII. The U.S. was bound and determined to stay out of the war this time, unfortunately the world needed us to int
Boise State - HIST - 101
Chapman 13. Discuss the culture of the Plains Indians and the reasons for Indian conflict with white America. Why was violence so common? Was a peaceful resolution possible? Why or why not? The Plains Indians had evolved in comparison to the earlier gene
Boise State - HIST - 101
Chapman 110. Why wasnt World War I the War to end all Wars? World War I was the largest war in recorded history at the time . Fifteen million people were killed as a result of the war, and millions others were injured. This war was supposed to be the fin
Boise State - HIST - 101
Chapman 1The Unfinished Nation Part 1: Episodes 37 and 38 The videos are easing out of the progressive era and moving into the depression. The war is now over and there is a price to pay. I know some people say that war is good for the economy but I woul
Boise State - HIST - 101
Chapman 1The Unfinished Nation Part 1: Episodes 35 and 36 These episodes were mainly about World War I. Towards the end of the progressive era tensions ran at an all time high between the U.S. and several other nations. Once the Archduke of Austria was a
Boise State - HIST - 101
Chapman 1The Unfinished Nation Part 1: Episodes 33 and 34 The progressive era as a time of reformation and everything from politics down was changing. I have broken the video and the progressive era in fact into two main categories. The way I see it, Wom
Boise State - HIST - 101
Chapman XThe Unfinished Nation Part 1, episodes 19-20: Watching these episodes just confirms my opinion about the greed in Americans. From 1849 on California underwent drastic change in culture. Americans went there to seek out fortune, the Mexicans that
Boise State - HIST - 101
Chapman hThe Unfinished Nation Part 1, episodes 17-18: Social order in the 19th century according to the video is the basis of social order now. The idea of women spending their time at home and men working in the Capitalistic market to bring in the mone
Boise State - HIST - 101
Chapman The Unfinished Nation Part 1, episodes 15-16: There is one thing in particular that really stood out tome when I watched these episodes. The Native Americans got screwed. How could we just pretend that they are not humans. They had no rights and
Boise State - HIST - 101
Chapman PThe Unfinished Nation Part 1, episodes 13 and 14: During the early 19th century the U.S. economy was not in good shape. Even though the era was the era of good feelings things were not looking up. After the War of 1812 the U.S. owed a substantia
Boise State - HIST - 101
Chapman cfw_The Unfinished Nation Part 1, Episodes 11 and 12: The only thing that really caught my attention in episodes 11 and 12 was the section about the War of 1812. During this war thousands of people died on both sides. The British received the sup
Boise State - HIST - 101
Chapman 12. Compare French America and British America. Discuss reasons for settlement,attitudes toward Indians, forms of labor, major economies, role of religion, and systems of government. The British and the French have been enemies for centuries, bu