Explanation Consider the polygon has 9 diagonals. Theorem: If the number of diagonals in a polygon of n sides is given by D = n ( n − 3 ) 2 Where n is number of sides of the polygon. Given that D = 9 . Substitute the value of D = 9 in the above equation to get the following, 9 = n ( n − 3 ) 2 Then multiply by 2 on both sides of the equation to get the following, 9 × 2 = n ( n − 3 ) × 2 2 18 = n ( n − 3 ) n 2 − 3 n = 18 Subtract 18 on both sides to get the following, n 2 − 3 n − 18 = 18 − 18 n 2 − 3 n − 18 = 0 The general form of the quadratic equation is given below, a x 2 + b x + c = 0 Where a is the number multiplied by x 2 , b is the number multiplied by x , and c is the constant term. Quadratic formula: The solution for a x 2 + b x + c = 0 when a ≠ 0 is given below, x = − b ± b 2 − 4 a c 2 a ... ( 1 ) Compare the given equation with general equation to get the following, a x 2 + b x + c = 0 ⇒ n 2 − 3 n − 18 = 0 Therefore, a = 1 , b = − 3 and c = − 18

Elementary Geometry for College Students

6th Edition

ISBN: 9781285195698

Author: Daniel C. Alexander, Geralyn M. Koeberlein

Publisher: Cengage Learning

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Chapter A.5, Problem 35E

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To find the number of sides in a polygon that has 9 diagonals.

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Chapter A.5, Problem 34E

Chapter A.5, Problem 36E

Chapter A Solutions

Elementary Geometry for College Students

Ch. A.1 - Name the four parts of a mathematical system....Ch. A.1 - Prob. 2E Ch. A.1 - Which axiom of equality is illustrated in each of...Ch. A.1 - Prob. 4E Ch. A.1 - Prob. 5E Ch. A.1 - Prob. 6E Ch. A.1 - Prob. 7E Ch. A.1 - Prob. 8E Ch. A.1 - Prob. 9E Ch. A.1 - Prob. 10E

Ch. A.1 - Prob. 11E Ch. A.1 - Prob. 12E Ch. A.1 - Prob. 13E Ch. A.1 - Nine pegs are evenly spaced on a board so that the...Ch. A.1 - The four owners of a shop realize a loss of 240 in...Ch. A.1 - Bill works at a weekend convention by selling...Ch. A.1 - Use the Distributive Axiom to simplify each...Ch. A.1 - Use the Distributive Axiom to simplify each...Ch. A.1 - Simplify each expression: a 6+4 c 16x2y9x2y b...Ch. A.1 - Prob. 20E Ch. A.1 - Prob. 21E Ch. A.1 - Prob. 22E Ch. A.1 - Prob. 23E Ch. A.1 - Prob. 24E Ch. A.1 - Prob. 25E Ch. A.1 - Prob. 26E Ch. A.1 - Prob. 27E Ch. A.1 - Prob. 28E Ch. A.1 - Prob. 29E Ch. A.1 - Prob. 30E Ch. A.1 - Prob. 31E Ch. A.1 - Prob. 32E Ch. A.2 - In Exercises 1 to 6, simplify by combining similar...Ch. A.2 - Prob. 2E Ch. A.2 - Prob. 3E Ch. A.2 - Prob. 4E Ch. A.2 - Prob. 5E Ch. A.2 - Prob. 6E Ch. A.2 - Prob. 7E Ch. A.2 - Prob. 8E Ch. A.2 - Prob. 9E Ch. A.2 - Prob. 10E Ch. A.2 - Prob. 11E Ch. A.2 - Prob. 12E Ch. A.2 - Prob. 13E Ch. A.2 - Prob. 14E Ch. A.2 - Prob. 15E Ch. A.2 - Prob. 16E Ch. A.2 - Prob. 17E Ch. A.2 - Prob. 18E Ch. A.2 - Prob. 19E Ch. A.2 - Prob. 20E Ch. A.2 - Prob. 21E Ch. A.2 - Prob. 22E Ch. A.2 - Prob. 23E Ch. A.2 - Prob. 24E Ch. A.2 - Prob. 25E Ch. A.2 - Prob. 26E Ch. A.2 - Prob. 27E Ch. A.2 - Prob. 28E Ch. A.2 - Prob. 29E Ch. A.2 - Prob. 30E Ch. A.2 - Prob. 31E Ch. A.2 - Prob. 32E Ch. A.2 - Prob. 33E Ch. A.2 - Prob. 34E Ch. A.2 - Prob. 35E Ch. A.2 - Prob. 36E Ch. A.3 - If line segment AB and line segment CD in the...Ch. A.3 - Prob. 2E Ch. A.3 - Prob. 3E Ch. A.3 - Prob. 4E Ch. A.3 - Prob. 5E Ch. A.3 - Prob. 6E Ch. A.3 - Prob. 7E Ch. A.3 - Prob. 8E Ch. A.3 - Prob. 9E Ch. A.3 - Of several angles, the degree measures are related...Ch. A.3 - Prob. 11E Ch. A.3 - Prob. 12E Ch. A.3 - Prob. 13E Ch. A.3 - Prob. 14E Ch. A.3 - Prob. 15E Ch. A.3 - Prob. 16E Ch. A.3 - Prob. 17E Ch. A.3 - Prob. 18E Ch. A.3 - Prob. 19E Ch. A.3 - Prob. 20E Ch. A.3 - Prob. 21E Ch. A.3 - Prob. 22E Ch. A.3 - Prob. 23E Ch. A.3 - Prob. 24E Ch. A.3 - Prob. 25E Ch. A.3 - Prob. 26E Ch. A.3 - Prob. 27E Ch. A.3 - Prob. 28E Ch. A.3 - Prob. 29E Ch. A.3 - Prob. 30E Ch. A.3 - Prob. 31E Ch. A.3 - Prob. 32E Ch. A.4 - Prob. 1E Ch. A.4 - Note: Exercises preceded by an asterisk are of a...Ch. A.4 - Prob. 3E Ch. A.4 - Prob. 4E Ch. A.4 - Prob. 5E Ch. A.4 - Prob. 6E Ch. A.4 - In Exercises 5 to 8, factor each difference of two...Ch. A.4 - In Exercises 5 to 8, factor each difference of two...Ch. A.4 - Prob. 9E Ch. A.4 - Prob. 10E Ch. A.4 - In Exercises 9 to 16, factor each trinomial...Ch. A.4 - Prob. 12E Ch. A.4 - Prob. 13E Ch. A.4 - Prob. 14E Ch. A.4 - Prob. 15E Ch. A.4 - Prob. 16E Ch. A.4 - Prob. 17E Ch. A.4 - Prob. 18E Ch. A.4 - Prob. 19E Ch. A.4 - Prob. 20E Ch. A.4 - Prob. 21E Ch. A.4 - Prob. 22E Ch. A.4 - Prob. 23E Ch. A.4 - Prob. 24E Ch. A.4 - Prob. 25E Ch. A.4 - Prob. 26E Ch. A.4 - Prob. 27E Ch. A.4 - Prob. 28E Ch. A.4 - In Exercises 25 to 32, solve each quadratic...Ch. A.4 - In Exercises 25 to 32, solve each quadratic...Ch. A.4 - Prob. 31E Ch. A.4 - Prob. 32E Ch. A.4 - Prob. 33E Ch. A.4 - Prob. 34E Ch. A.4 - Prob. 35E Ch. A.4 - Prob. 36E Ch. A.4 - Given that the area of the rectangle shown is 66,...Ch. A.4 - Determine the length x by solving either the...Ch. A.4 - Find the length a by solving the equation...Ch. A.4 - Prob. 40E Ch. A.4 - Prob. 41E Ch. A.5 - Use your calculator to find the approximate value...Ch. A.5 - Prob. 2E Ch. A.5 - Prob. 3E Ch. A.5 - Prob. 4E Ch. A.5 - Prob. 5E Ch. A.5 - Prob. 6E Ch. A.5 - Prob. 7E Ch. A.5 - Prob. 8E Ch. A.5 - Use your calculator to verify that the following...Ch. A.5 - Prob. 10E Ch. A.5 - Prob. 11E Ch. A.5 - Prob. 12E Ch. A.5 - Prob. 13E Ch. A.5 - Prob. 14E Ch. A.5 - Prob. 15E Ch. A.5 - Prob. 16E Ch. A.5 - Prob. 17E Ch. A.5 - Prob. 18E Ch. A.5 - Prob. 19E Ch. A.5 - Prob. 20E Ch. A.5 - Prob. 21E Ch. A.5 - Prob. 22E Ch. A.5 - Prob. 23E Ch. A.5 - Prob. 24E Ch. A.5 - Prob. 25E Ch. A.5 - Prob. 26E Ch. A.5 - Prob. 27E Ch. A.5 - Prob. 28E Ch. A.5 - Prob. 29E Ch. A.5 - Prob. 30E Ch. A.5 - Prob. 31E Ch. A.5 - Prob. 32E Ch. A.5 - Prob. 33E Ch. A.5 - Prob. 34E Ch. A.5 - Prob. 35E Ch. A.5 - Prob. 36E Ch. A.5 - Prob. 37E Ch. A.5 - Prob. 38E Ch. A.5 - Prob. 39E

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