### Understanding Polygon DiagonalsA polygon with \( n \) sides has \( D \) diagonals, where \( D \) is given by the function:\[D(n) = \frac{n(n-3)}{2}\]#### ProblemFind the number of sides \( n \) if \( 135 \leq D \leq 860 \).### Solution Approach1. **Identify the Equation**: Start with the formula for diagonals: \[ D = \frac{n(n-3)}{2} \]2. **Set Up the Inequality**: Plug in the values for \( D \): \[ 135 \leq \frac{n(n-3)}{2} \leq 860 \]3. **Solve for \( n \)**: Multiply through by 2 to eliminate the fraction: \[ 270 \leq n(n-3) \leq 1720 \]4. **Determine the Range**: Solve the quadratic inequalities to find the range of possible \( n \).#### ResultThe number of sides is \( n \) within the interval:\[\{ n \mid [ \, \leq n \leq \, ] \}\]Replace the square brackets with the calculated values of \( n \).### SummaryThis example explores how to apply inequality and quadratic solving techniques to determine the potential number of sides of a polygon when a range of diagonal counts is provided.

Given D = n(n-3)2where D = diagonals n = sides 135 ≤ D ≤ 860

Answered: n(n-3) A polygon with n sides has D…

n(n-3) A polygon with n sides has D diagonals, where D is given by the function D(n) = 2 The number of sides is {n |≤ns} Find the number of sides n if 135 ≤ D≤ 860

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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