Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-2 Multiplying and Factoring - Practice and Problem-Solving Exercises - Page 496: 42


$a.\quad 3$ $b.\quad n-3$ $c.\displaystyle \quad \frac{1}{2}n^{2}-\frac{3}{2}n$ $d.\quad 20$

Work Step by Step

a. The polygon has six sides. From one vertex: three diagonals. b. It will have $n-3 $ diagonals, \\ as we can not join the vertex with itself and its two neighboring vertices to form a diagonal. c. $\displaystyle \frac{n}{2}(n-3)\qquad...$apply the Distributive Property. $=\displaystyle \frac{n^{2}}{2}-\frac{3n}{2}$ $=\displaystyle \frac{1}{2}n^{2}-\frac{3}{2}n$ d. Substitute $n=8$ into the diagonal formula $D=\displaystyle \frac{8}{2}(8-3)\qquad...$apply the Distributive Property. $D=4\cdot 5$ $D=20$. The polygon has 20 diagonals
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.