Explanation Given Information: The inequality is z 2 − 4 z ≥ 0 . Formula used: According to the zero theorem, if a and b are real numbers, with a b = 0 , then, a = 0 or b = 0 To solve a quadratic inequality, perform the following steps: Step 1: The inequality is written as an equation. Step 2: Use the solution from Step 1 and determine the intervals, and graph them on a number line. Step 3: To determine the suitable intervals that satisfy the inequality substitute a test value from each interval into the original inequality. Step 4: Separately, consider the endpoints. If the end point is included then the inequality has the symbol ≤ or ≥ . Calculation: Consider the inequality, z 2 − 4 z ≥ 0 Factor the equation z 2 − 4 z = 0 , z 2 − 4 z = 0 z ( z − 4 ) = 0 Recall that according to the zero theorem, if a and b are real numbers, with a b = 0 , then, a = 0 or b = 0 Apply it, Case I: When the term z = 0 z = 0 Case II: When the term ( z − 4 ) = 0 z − 4 = 0 z = 4 Thus, the numbers 0 and 4 divide the number line into 3 intervals, Test the three intervals, by substituting a number from each interval in the inequality

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Chapter 11.8, Problem 19E

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Chapter 11.8, Problem 18E

Chapter 11.8, Problem 20E

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Q1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.

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For the problem below, what are the possible solutions for x? Select all that apply. 2 x²+8x +11 = 0 x2+8x+16 = (x+4)² = 5 1116

Chapter 11 Solutions

Beginning and Intermediate Algebra (6th Edition)

Ch. 11.1 - Concept Check Answer each question. 1. Which of...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 6E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 8E Ch. 11.1 - Solve each equation using the zero-factor...Ch. 11.1 - Prob. 10E

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The solution set of the inequality z 2 − 4 z ≥ 0 and graph it.

Solution Summary: The author explains how to solve a quadratic inequality using the zero theorem.

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Chapter 11 Solutions