Textbook Question
Add or subtract, as indicated. See Example 6. √6 + √6
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem 89
Simplify each inequality if needed. Then determine whether the statement is true or false. 7 ≤ 7
Verified step by step guidance1
Identify the inequality given: \(7 \leq 7\).
Recall that the symbol \(\leq\) means "less than or equal to," so the statement says "7 is less than or equal to 7."
Since both sides of the inequality are equal, the "equal to" part of the inequality holds true.
Therefore, the inequality \(7 \leq 7\) is true because 7 is indeed equal to 7.
No further simplification is needed as the inequality is already in its simplest form.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Inequality Symbols and Their Meaning
Inequality symbols like ≤ (less than or equal to) compare two values to show their relative size. The symbol ≤ means the left side is either less than or exactly equal to the right side. Understanding these symbols is essential to interpret and solve inequalities correctly.
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Finding the Domain and Range of a Graph
Evaluating Inequalities
To determine if an inequality is true or false, substitute the values and check the relationship. For example, 7 ≤ 7 means 7 is less than or equal to 7, which is true because both sides are equal. This evaluation step confirms the validity of the inequality.
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7:28Evaluate Composite Functions - Values Not on Unit Circle
Simplification of Inequalities
Simplifying inequalities involves reducing expressions to their simplest form without changing their truth value. In this case, the inequality 7 ≤ 7 is already simplified, so no further steps are needed before evaluating its truthfulness.
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5:10Finding the Domain and Range of a Graph
Related Practice
Textbook Question
Factor each polynomial completely. See Example 6. 8t³ + 125
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Textbook Question
Simplify each complex fraction. See Examples 5 and 6. [(y + 3)/y − 4/(y − 1)] / [(y/y + 1/y) / (y − 1) + 1/y]
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Textbook Question
(Modeling) Distance from the Origin of the Nile River The Nile River in Africa is about 4000 mi long. The Nile begins as an outlet of Lake Victoria at an altitude of 7000 ft above sea level and empties into the Mediterranean Sea at sea level (0 ft). The distance from its origin in thousands of miles is related to its height above sea level in thousands of feet (x) by the following formula.
Distance = (7 − x) / (0.639x + 1.75)
For example, when the river is at an altitude of 600 ft, x = 0.6 (thousand), and the distance from the origin is
Distance ≈ (7 − 0.6) / (0.639 × 0.6 + 1.75) ≈ 3, which represents 3000 mi. (Data from The World Almanac and Book of Facts.) What is the distance from the origin of the Nile when the river has an altitude of 7000 ft?
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Textbook Question
Add or subtract, as indicated. See Example 6. √6 + √7
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Textbook Question
Simplify each inequality if needed. Then determine whether the statement is true or false. 0 ≤ -5
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