Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:02 minutes

Problem 124

Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. 5𝜋 is a real number.

Verified step by step guidance

Step 1: Understand the problem statement. We need to identify the property of real numbers illustrated by the statement '5𝜋 is a real number.'

Step 2: Recall the definition of real numbers. Real numbers include all the numbers on the number line, including rational numbers (like fractions and integers) and irrational numbers (like π and √2).

Step 3: Recognize that π is an irrational number, which is a subset of real numbers.

Step 4: Note that multiplying a real number (π) by another real number (5) results in a real number.

Step 5: Identify the property. The statement '5𝜋 is a real number' illustrates the Closure Property of Multiplication, which states that the product of any two real numbers is a real number.

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Key Concepts

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

Real Numbers

Real numbers include all the numbers that can be found on the number line. This encompasses rational numbers (like integers and fractions) and irrational numbers (like π). Understanding that 5π is a real number is crucial, as it highlights the inclusion of both whole numbers and non-repeating decimals in the set of real numbers.

Properties of Real Numbers

The properties of real numbers include various rules that govern their operations, such as the commutative, associative, and distributive properties. These properties help in simplifying expressions and solving equations. Recognizing that 5π is a real number allows us to apply these properties in mathematical operations involving real numbers.

Multiplication of Real Numbers

Multiplication of real numbers is a fundamental operation that combines two numbers to produce a product. In the case of 5π, it illustrates how a real number (5) can be multiplied by an irrational number (π) to yield another real number. This concept is essential for understanding how different types of numbers interact within the real number system.