Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

0. Review of College Algebra

Solving Linear Equations

Trigonometry

0. Review of College Algebra

Solving Linear Equations

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2:31 minutes

Problem 101

Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. 5r———2p - 3r

Verified step by step guidance

Substitute the given values into the expression: \( \frac{5r}{2p - 3r} \) becomes \( \frac{5(-10)}{2(-4) - 3(-10)} \).

Calculate the numerator: \( 5(-10) = -50 \).

Calculate the first part of the denominator: \( 2(-4) = -8 \).

Calculate the second part of the denominator: \( 3(-10) = -30 \).

Combine the results in the denominator: \( -8 - (-30) = -8 + 30 \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Substitution

Substitution is the process of replacing variables in an expression with their corresponding numerical values. In this question, we substitute p, q, and r with -4, 8, and -10, respectively. This step is crucial for evaluating the expression accurately, as it transforms the algebraic expression into a numerical one that can be simplified.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), this concept is essential for evaluating expressions correctly, especially when multiple operations are involved.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form by performing operations and combining like terms. In this case, after substituting the values for p, q, and r, we will simplify the expression by carrying out the arithmetic operations in the correct order, leading to a final numerical result that answers the question.