around 250A.D. started some kind of research on some equations involving more than one variables which would take only integer values.These equations are famously known as “DIOPHANTINE EQUATION”‚named due to Diophantus.The simplest type of Diophantine equations that we shall consider is the Linear Diophantine equations in two variables: ax+by=c‚ where a‚b‚c are integers and a‚b are not both zero. We also have many kinds of Diophantine equations where our main goal is to find out its solutions
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Completing the Square: Quadratic Examples & Deriving the Quadratic Formula (page 2 of 2) Solve x2 + 6x + 10 = 0. Apply the same procedure as on the previous page: This is the original equation. x2 + 6x + 10 = 0 Move the loose number over to the other side. x2 + 6x = – 10 Take half of the coefficient on the x-term (that is‚ divide it by two‚ and keeping the sign)‚ and square it. Add this squares value to both sides of the equation. x^2 + 6x + 9 = –10 + 9 Convert the left-hand side to
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Algebra 2 Writing Assignment When solving a quadratic equation you are looking to get the roots/solutions/zeros or x-intercepts. There are many different methods. Those methods are‚ graphing using tables‚ factoring‚ square root method‚ completing the square‚ and quadratic formula. The two that I find the easiest are factoring and completing the square. This is how you would use these two methods. When using factoring to solve a quadratic equation you must set it to zero before you do anything
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01 Algebra 1 Review 01.02 Introduction to Functions 01.03 Module One Quiz 01.04 Graphing Linear Equations and Inequalities 01.05 Writing the Equation of a Line 01.06 Comparing Functions 01.07 Module One Review and Practice Test 01.08 Discussion-Based Assessment 01.09 Module One Test 02.00 Module Two Pretest 02.01 Rational Exponents 02.02 Properties of Rational Exponents 02.03 Solving Radical Equations 02.04 Module Two Quiz – EXEMPTED ITEM‚ Please skip 02.05 Complex Numbers 02.06 Operations of Complex
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To solve a system of equations by addition or subtraction (or elimination)‚ you must eliminate one of the variables so that you could solve for one of the variables. First‚ in this equation‚ you must look for a way to eliminate a variable (line the equations up vertically and look to see if there are any numbers that are equal to each other). If there is lets say a –2y on the top equation and a –2y on the bottom equation you could subtract them and they would eliminate themselves by equaling zero
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the quadratic formula? 2. What is it used for? 3. Provide an example‚ not found in the text. RESPONSE Many people may have heard of the quadratic formula‚ but are probably unfamiliar what it is or what it is used for. The actual quadratic formula is ‚ and its purpose is to solve quadratic equations and can only be applied to a quadratic equation that is in the standard form of (ax2+ bx +c = 0).It is important to differentiate between a quadratic formula and a quadratic equation‚ where
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Rational Equations Rational equations can be used to get a general idea about the rate at which a job can be completed. This can be really useful for business owners and other areas of daily life. Here is an example: Scenario: Sue can paint the garage in 4 hours and Joe has carpal tunnel so he is slower and can paint the same garage in 6 hours. How long (number of hours) will it take Sue and Joe to paint the garage if they work together? Solution: Sue can paint of the garage in 1 hour. Joe
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go back to the first signs of Algebra‚ we have to go back over 3700 years‚ to the Babylonian civilization. Babylonians were particularly proficient algebraists and in the ancient civilizations they could solve quadratic problems (Kleiner‚ 2007). Records show that in 1600 B.C equations and symbols were not used in these problems‚ rather they were written out and solved verbally (Corry‚ 2005). Corry’s (2005) study found that a typical example of a problem made by the Babylonians was‚ Method of
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MAPÚA INSTITUTE OF TECHNOLOGY Department of Mathematics VISION The Mapua Institute of Technology shall be a global center of excellence in education by providing instructions that are current in content and state-of-the-art in delivery; by engaging in cutting-edge‚ high impact research; and by aggressively taking on present-day global concerns. MISSION a. The Mapua Institute of Technology disseminates‚ generates‚ preserves and applies knowledge in various fields of study. b. The Institute
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6 Systems Represented by Differential and Difference Equations Recommended Problems P6.1 Suppose that y 1(t) and y 2(t) both satisfy the homogeneous linear constant-coeffi cient differential equation (LCCDE) dy(t) + ay(t) = 0 dt Show that y 3 (t) = ayi(t) + 3y2 (t)‚ where a and # are any two constants‚ is also a solution to the homogeneous LCCDE. P6.2 In this problem‚ we consider the homogeneous LCCDE d 2yt + 3 dy(t) + 2y(t) = 0 dt 2 dt (P6.2-1) (a) Assume that a solution to
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