Textbook Question
Add or subtract, as indicated. See Example 6. 5√3 + √12
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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 93
Simplify each inequality if needed. Then determine whether the statement is true or false. -6 < 7 + 3
Verified step by step guidance1
First, write down the inequality clearly: \(-6 < 7 + 3\).
Simplify the right-hand side by adding the numbers: \(7 + 3 = 10\), so the inequality becomes \(-6 < 10\).
Interpret the inequality: check if \(-6\) is less than \(10\) on the number line.
Since \(-6\) is indeed less than \(10\), the inequality holds true.
Therefore, the statement \(-6 < 7 + 3\) is true.
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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 <, >, ≤, and ≥ compare two values to show their relative size. The symbol '<' means 'less than,' indicating the value on the left is smaller than the value on the right. Understanding these symbols is essential to interpret and solve inequalities correctly.
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Finding the Domain and Range of a Graph
Simplifying Inequalities
Simplifying inequalities involves performing algebraic operations such as addition, subtraction, multiplication, or division on both sides to isolate variables or constants. This process helps clarify the inequality and makes it easier to determine its truth value.
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6:36Simplifying Trig Expressions
Evaluating the Truth of an Inequality
To determine if an inequality is true or false, substitute or simplify both sides and compare their values. If the relationship holds as stated, the inequality is true; otherwise, it is false. This step is crucial for verifying solutions or statements involving inequalities.
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7:28Evaluate Composite Functions - Values Not on Unit Circle
Related Practice
Textbook Question
Factor each polynomial completely. See Example 6. t⁴ - 1
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. 2 • 5 ≥ 4 + 6
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