1. A line passes through the points (–3‚ –3) and (–1‚ 3). What is the slope of the line that passes through the two points? Hint X -3 -1/3 3 1/3 2. A line passes through the points (3‚ –4) and (7‚ 12). What is the y-intercept of the line? Hint X (0‚ 4) (4‚ 0) (0‚ –16) (–16‚ 0) 3. Consider the following system of equations. y = 8x - 8 y - 8x = 7 What can you conclude about the system of equations? Hint X The system of equations is inconsistent. The system
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Math Assessment Sample Items Section 1: Numerical Skills/Pre-algebra Placement Test Percentage of Items in Pool Content Areas Basic operations with integers Basic operations with fractions Basic operations with decimals Exponents Ratios and proportions Percentages Conversions between fractions and decimals Multiples and factors of integers Absolute values of numbers Averages (arithmetic means) Order concepts (greater than; less than) Estimation skills Number theory Counting problems and simple probability
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Summer 2010-3 CLASS NOTES CHAPTER 1 Section 1.1: Linear Equations Learning Objectives: 1. Solve a linear equation 2. Solve equations that lead to linear equations 3. Solve applied problems involving linear equations Examples: 1. [pic] [pic] 3. A total of $51‚000 is to be invested‚ some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3‚000‚ how much will be invested in each type
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CBSE TEST PAPER-01 MATHEMATICS (Class-10) Chapter 3 : Pair Linear Equations in Two Variables 1. 2. 3. 4. For which values of p does the pair of equations given below have unique solution? (2 marks) 4x + py + 8 = 0‚ 2x + 2y + 2 = 0 Solve graphically: 3x + 2y = 14x‚ x – 4y = 7 (3 marks) Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y -12 = 0. Represent this situation geometrically. (3 marks) a b c On comparing the ratio 1 ‚ 1 and 1 find out whether the lines representing the
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Course Syllabus MAT/116 Version 8 1 Course Syllabus Natasha Ramsay-Jordan College of Natural Sciences MAT/116 Version 8 Algebra 1A Copyright © 2012‚ 2010‚ 2009‚ 2007‚ 2006 by University of Phoenix. All rights reserved. Course Description This course introduces basic algebra concepts and assists in building skills for performing specific mathematical operations and problem solving. Students will solve equations‚ evaluate algebraic expressions‚ solve and graph linear equations and linear inequalities
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Elluminate Live! - LIVE LESSON 7.09 Jan 9‚ 2013 7:48:40 PM Welcome to Lesson 7.09 Page 1. Elluminate Live! - LIVE LESSON 7.09 Jan 9‚ 2013 7:48:40 PM 7.09 Room 1 - Attendance Page 2. Elluminate Live! - LIVE LESSON 7.09 Jan 9‚ 2013 7:48:40 PM 7.09 Room 1 - 7.09 Polynomials Activity Page 3. Elluminate Live! - LIVE LESSON 7.09 Jan 9‚ 2013 7:48:40 PM 7.09 Room 1 - Common Core Standards Covered in this Lesson: Page 4. Elluminate Live! - LIVE LESSON 7
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Aminata Kamara Week II Assignment 22 November 2012 This week assignment required to solve problem 68 on page 539 of Elementary and Intermediate Algebra. There are three part to this assignment and the first part is as follows; The accompanying graph shows all of the possibilities for the number of refrigerators and the number of TVs that will fit into an 18-wheeler. | | a) | Write an inequality to describe this region. | p = y1-y2 / X1-x2 = 330 – 0 / 0-110 = -3/1 the slope
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Review of Algebra 2 s REVIEW OF ALGEBRA Review of Algebra q q q q q q q q q q q q q q q Here we review the basic rules and procedures of algebra that you need to know in order to be successful in calculus. Arithmetic Operations The real numbers have the following properties: a b b a ab a b c a b ab c ab ac In particular‚ putting a b and so b c b c ba c (Commutative Law) (Associative Law) (Distributive law) ab c a bc 1 in the
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Algebra Problem Week 5 Joby Weatherwax Introduction to Algebra (MAT 221) Stacie Williams Apr 14‚ 2013 Algebra Problem Week 5 Buried treasure. Ahmed has half of a treasure map‚which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure‚ one must get to Castle Rock‚ walk x paces to the north‚ and then walk 2x + 4 paces to the east. If they share
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Bibliography: Published on U.S. 2007 Flanders‚ Harley and Price‚ Justin J.‚ Algebra Published on U.S. 2007 Hackworth‚ Robert‚ Focus on Elementary Algebra Published on U.S. 2008 Rowe‚ David E
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Tatenda Shumba Shane Johnson Per 4 Is algebra necessary? Algebra is important to learn. But it is not necessary. Life existed before algebra was invented and could still continue without it. There are many applications of Algebra in real life situations. It is important to learn the basics‚ especially when it comes to money and finance. Many adults use the basics but not anything beyond‚ like if you were to go around and ask what is the quadratic equation not most adults would get it
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INTRODUCTION Abstract Algebra is more rightly considered meta-mathematics than mathematics proper‚ because it can be used to describe the structures that exist within mathematics from a general standpoint. The basic notions of Groups‚ Rings‚ Fields‚ and Algebraic Extensions provide a framework from which to examine almost all of mathematics. These notions serve as unifying concepts that interlace such seemingly disparate subjects as geometry‚ analysis‚ number theory‚ topology and even applied
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Oklahoma Algebra II End-of-Instruction Test Preparation and Practice Teacher’s Guide Help for the Oklahoma ACE Algebra II Test i-viii_OK_A2_TE_FM.indd i 7/11/09 12:38:29 AM Copyright © by Houghton Mifﬂin Harcourt Publishing Company. All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means‚ electronic or mechanical‚ including photocopying or recording‚ or by any information storage or retrieval system‚ without the prior written permission of
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Name: __________________________________________ Algebra Keystone Exam Review 1) Simplify the expression: √ √ √ √ A) √ B) √ C) √ D) A right triangle has one leg that is twice the length of the other leg. If the hypotenuse is √ ‚ find the length of the longer leg. 2) A) 8 B) 16 C) 4 D) 32 3) Which statement has the largest value of x? A) √ B) √ C) √ √ D) √ √ 4) Simplify: ( √ ) A) B) C)
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Chapter’s 1 & 2 Test Review 1) Write the expression in standard form a+bi (2-2i)(9+i) (-7+5i) - (6-8i) (3+i)^2 2) Solve the following equation by factoring x^2 - 6x = 0 3) A bank loaned $17‚000‚ part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled at $2‚000‚ how much was loaned at 8%? 4) Find the real solutions of the equation √2x-7 = 0 5) Solve the inequality 5 < 7 - ½x < 9 6) Decide whether the following
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Quadratic equation In elementary algebra‚ a quadratic equation (from the Latin quadratus for "square") is any equation having the form where x represents an unknown‚ and a‚ b‚ and c represent known numbers such that a is not equal to 0. If a = 0‚ then the equation is linear‚ not quadratic. The numbers a‚ b‚ and c are the coefficients of the equation‚ and may be distinguished by calling them‚ the quadratic coefficient‚ the linear coefficient and the constant or free
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The History of Algebra The history of algebra has been around for several decades‚ this method of mathematics has been used during the beginning of time. The development of algebraic notation progressed through out three stages: the rhetorical stage‚ the syncopated stage‚ and the symbolic stage with which we are use to using in our daily usage of algebra. In ancient civilization math was used to help leaders to strategically form how their troops should be lined up for battle and help decide
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Quadratic Equations ax2 + bx + c = 0 Examples of Quadratic equations 1. x2 +2x – 8 = 0 2. x2 – 10x + 25 = 0 3. 3x2 + x - 2 = 0 Quadratic Formula If [pic] a x2 + b x + c = 0‚ then [pic] Finding the zeros of the quadratic functions - The zeros of a function are the input values which result in an output value of zero. One way of solving quadratic equations is using factoring Examples are the following: 1) x2 + 5x + 6 = 0 Set this equal to zero:
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HISTORY OF ALGEBRA M AT H 1 WHAT IS ALGEBRA? • Denotes various kinds of mathematical ideas and techniques • more or less directly associated with formal manipulation of abstract symbols and/or with finding the solutions of an equation. HISTORICAL OBJECTIVES 1. attempts to deal with problems devoted to finding the values of one or more unknown quantities. 2. the evolution of the notion of number 3. the gradual refinement of a symbolic language THE SEARCH OF “EQUATION” • Egyptian Mathematics
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Algebra Algebra was invented by the Muslim mathematician Al-Khwarizmi in the book he wrote in 820. Algebra is the Arabic word (aljabr) for "equation"‚ and the word "algorithm" comes from the author’s name‚ Al-Khwarizmi. He is rightly known as "the father of Algebra The roots of algebra can be traced to the ancient Babylonians‚ who developed an advanced arithmetical system with which they were able to do calculations in analgorithmic fashion. The Babylonians developed formulas to calculate solutions
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