Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 10 - Radical Expressions and Equations - 10-2 Simplifying Radicals - Practice and Problem-Solving Exercises: 78

Answer

$\frac{5}{6}$

Work Step by Step

The formula for the distance between the x intercept and y intercept is $d = \sqrt ( (\frac{C}{A})^{2} + (\frac{C}{B})^{2} )$ for the equation Ax+ By = C Given the equation 4x - 3y = 2 where A=4, B=-3 and C=2 so we substitute it into the equation $d = \sqrt ( (\frac{C}{A})^{2} + (\frac{C}{B})^{2} )$ $d = \sqrt ( (\frac{2}{4})^{2} + (\frac{2}{-3})^{2} )$ We simplify the fractions by dividing the numerator by the denominator. $d = \sqrt ( (\frac{1}{2})^{2} + (\frac{2}{-3})^{2} )$ $d = \sqrt ( \frac{1}{4})+ (\frac{4}{9}) $ We add the fractions together and get $d = \sqrt ( \frac{25}{36}) $ *** Square root of 25 is 5 because 5 x 5 =25 *** Square root of 36 is 6 because 6 x 6 =36 $d = \frac{5}{6}$
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