1. Every point on the number line can be represented as a unique __________. a. b. c. d. Integer Real number Natural number Fraction √ √ √ √ the answer is 2. When you add a. b. c. d. √ √ √ √ √ √ √ √ 3. The degree of polynomial √ a. b. c. d. √ 2 1 It is not a polynomial is : 4. The remainder when a. 1 b. c. d. is divided by is 5. Two sides of a triangle are of lengths 7 cm and 3.5 cm. The length of the 3rd side cannot be a. 4.1 cm b. 3.4 cm c. 3.8 cm d. 3.6 cm Copyright ©
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Structure of Mathematics Courses for the UG Program Sem Name of the courses to be offered by the Department of mathematics 1 Analysis and Linear Algebra 2 Analysis and Linear Algebra 3 Probability and Statistics 4 Multivariable Calculus and Complex Variable Elementary Algebra and Number Theory Elective Elective 5 Algebra I Linear Algebra Analysis I Topology I 6 Analysis II Complex Analysis ODE Elective 7 Algebraic Topology
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(2) are given by the well-known quadratic formula x= −b ± b2 − 4ac ‚ 2a a=0 in terms of a‚ b and c. Nicomedes Alonso III Abstract Algebra 3 of 29 SOLVABILITY BY RADICALS - Cubic Equation For the general cubic polynomial equation 3 2 ax + bx + cx + d = 0‚ (3) the roots are given by Cardan’s formulas p = q = R = c a d p3 27 P = Q = 3 3a2 bc − a 3 b2 − 3a2 − 2b3 27a3 q2 + −
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MULTIPLE REGRESSION After completing this chapter‚ you should be able to: understand model building using multiple regression analysis apply multiple regression analysis to business decision-making situations analyze and interpret the computer output for a multiple regression model test the significance of the independent variables in a multiple regression model use variable transformations to model nonlinear relationships recognize potential problems in multiple
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class P Decision problems vs. Optimization problems Class NP Reductions NP-complete class 2 3 4 5 Pham Quang Dung () Algorithm Analysis and Design NP-Completeness Hanoi‚ 2012 2 / 31 Class P: Problems that are solvable by polynomial-time algorithms (O(nk ) where n is the size of the input to the problem and k is some constant) Examples: Sorting Shortest path problems Minimum Spanning Tree problems Maximum Flow problems ... Pham Quang Dung () Algorithm Analysis and Design
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Invertible matrix 1 Invertible matrix In linear algebra an n-by-n (square) matrix A is called invertible or nonsingular or nondegenerate‚ if there exists an n-by-n matrix B such that where I n denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case‚ then the matrix B is uniquely determined by A and is called the inverse of A‚ denoted by A −1 . It follows from the theory of matrices that if for finite square matrices A and B
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NUMBER SYSTEM Definition It defines how a number can be represented using distinct symbols. A number can be represented differently in different systems‚ for instance the two number systems (2A) base 16 and (52) base 8 both refer to the same quantity though the representations are different. When we type some letters or words‚ the computer translates them in numbers as computers can understand only numbers. A computer can understand positional number system where there are only a few symbols
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Mangaldan National High School Lesson Exemplar in Intermediate Algebra General Statement Quarter 3 Radical Expressions and Equations Topic Addition and Subtraction of Radical Expressions Time Frame 1 day Stage 1: Results/Outcomes Content Standard: The learner demonstrates understanding of the concepts of addition and subtraction of radical expressions. Performance Standard: The learner can add and subtract radicals. Essential Understanding: Understanding addition and subtraction of radicals
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A NEW APPROACH TO PORTFOLIO MATRIX ANALYSIS FOR STRATEGIC MARKETING PLANNING 1 2 Vladimir Dobrić ‚ Boris Delibašić Faculty of organizational science‚ vdobric@fon.rs 2 Faculty of organizational science‚ delibasic.boris@fon.rs 1 Abstract: Portfolio matrix is probably the most important tool for strategic marketing planning‚ especially in the strategy selection stage. Position of the organization in the portfolio matrix and it’s corresponding marketing strategy depends on the aggregation
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determine whether x-1 is a factor of 2√2 x3 + 5√2x2+7√2 Q 2 Find the value of a‚ if x+a‚is a factor of the polynomials: a) x3+ax2-2x+a+4 b) x4—a2x2+3x-6a Q 3 Factorise a) p2+q2+9r2+2pq+6qr+6pr b) 4a2+b2+4ab+8a+4b+4 Q 4 Find 553+(-25)3+(-30)3 Q 5 Factorise 2y3 – y2 – 13y -6 Q 6 If 3x+y+z = 0 show that 27x3+y3+z3=9xyz Q 7 Simplify (a+b+c)2+(a-b+c)2+(a+b-c)2 Q 8 The polynomial p(x) = 3x2-5x+k and q(x)=2x3-6x2+5k-3 ‚when divided by (x+2) leave remainder r1 and r2 respectively. Find the
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