Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 6 - Section 6.1 - The Greatest Common Factor - Exercise Set: 100

Answer

(a) $450,000$ (b) $480,000$ (c) $30(-x^2+6x+7)$

Work Step by Step

$-30x^2+180x+210$ $x$ represents the years since 2003 (a) Let $x=2$ because 2005 is 2 years since 2003 and evaluate: $-30x^2+180x+210$ $-30(2)^2+180(2)+210$ $=-30(4)+360+210$ $=-120+570$ $=450$ This answer is in thousands of visitors so the approximate number of visitors to the White House in 2005 is $450,000$. (b) To find the approximate number of visitors to the White House in 2006, set $x=3$ because 2006 is 3 years since 2003 and evaluate $-30x^2+180x+210$ $-30(3)^2+180(3)+210$ $=-30(9)+540+210$ $=-270+750$ $=480$ Once again, the answer above is in thousands of visitors so the correct answer is $480,000$ visitors to the White House in 2006. (c) The greatest common factor, or GCF, in $-30x^2+180x+210$ is $30$: $30\bullet-x^2+30\bullet6x+30\bullet7$ $=30(-x^2+6x+7)$
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