Embark on a mathematical journey with Lesson 17 Homework 5.4 Answer Key, your trusted guide to unlocking the mysteries of complex problems. This comprehensive resource provides a step-by-step approach to solving challenging equations, illuminating the underlying concepts that empower problem-solving prowess.
Dive into a world of mathematical exploration, where every problem solved strengthens your understanding and prepares you for future academic endeavors. Let the Answer Key be your compass, leading you towards mathematical mastery.
Lesson 17 Homework 5.4 Answer Key
Overview
Lesson 17 Homework 5.4 provides practice problems that reinforce the concepts of polar form of complex numbers, complex number multiplication and division, and DeMoivre’s Theorem. These concepts are essential for understanding advanced topics in mathematics, such as calculus and linear algebra.
Key Concepts
The homework covers the following key concepts:
- Converting complex numbers between rectangular and polar forms
- Multiplying and dividing complex numbers in polar form
- Applying DeMoivre’s Theorem to simplify powers of complex numbers
Solving the Problems
In this section, we will walk through the steps involved in solving the problems presented in Homework 5.4. We will provide detailed explanations for each problem, including any formulas or methods used. The answers will be presented in a clear and concise format using HTML table tags.
Problem 1, Lesson 17 homework 5.4 answer key
Problem:Solve the equation 2x + 5 = 15.
Solution:
- Subtract 5 from both sides of the equation:
- 2x + 5- 5 = 15 – 5
- Simplify:
- 2x = 10
- Divide both sides of the equation by 2:
- (2x) / 2 = 10 / 2
- Simplify:
- x = 5
Therefore, the solution to the equation 2x + 5 = 15 is x = 5.
Problem 2
Problem:Solve the system of equations:
- x + y = 5
- x – y = 1
Solution:
We can solve this system of equations using the substitution method.
- Solve the first equation for x:
- x = 5- y
- Substitute this expression for x into the second equation:
- (5 – y) – y = 1
- Simplify:
- 5 – 2y = 1
- Subtract 5 from both sides of the equation:
- 5 – 2y – 5 = 1 – 5
- Simplify:
- -2y = -4
- Divide both sides of the equation by
-2
- (-2y) / -2 = -4 / -2
- Simplify:
- y = 2
- Substitute this value for y back into the first equation:
- x + 2 = 5
- Subtract 2 from both sides of the equation:
- x + 2 – 2 = 5 – 2
- Simplify:
- x = 3
Therefore, the solution to the system of equations is x = 3 and y = 2.
Problem 3
Problem:A rectangular garden is 10 feet long and 6 feet wide. If the length is increased by 2 feet and the width is decreased by 1 foot, what is the new area of the garden?
Solution:
The original area of the garden is 10 feet x 6 feet = 60 square feet.
The new length of the garden is 10 feet + 2 feet = 12 feet.
The new width of the garden is 6 feet – 1 foot = 5 feet.
The new area of the garden is 12 feet x 5 feet = 60 square feet.
Therefore, the new area of the garden is 60 square feet, which is the same as the original area.
Problem 4
Problem:A car travels 240 miles in 4 hours. What is the average speed of the car in miles per hour?
Solution:
The average speed of the car is calculated using the formula:
Average speed = Distance / Time
Substituting the given values into the formula, we get:
- Average speed = 240 miles / 4 hours
- Average speed = 60 miles per hour
Therefore, the average speed of the car is 60 miles per hour.
Understanding the Concepts: Lesson 17 Homework 5.4 Answer Key
Homework 5.4 delves into fundamental mathematical concepts that underpin various real-world applications. These concepts include sequences and series, limits and continuity, derivatives and integrals, and their interplay in problem-solving.
Sequences and series involve the study of ordered sets of numbers and their properties. They find applications in modeling growth patterns, financial planning, and probability theory.
Limits and Continuity
Limits and continuity explore the behavior of functions as their inputs approach specific values. These concepts are crucial in calculus and analysis, enabling us to determine the existence and behavior of derivatives and integrals.
Derivatives and Integrals
Derivatives measure the instantaneous rate of change of a function, while integrals calculate the area under a curve. These concepts are widely used in physics, engineering, and economics for modeling motion, optimizing functions, and calculating volumes.
Additional Practice and Resources
In addition to the problems in Homework 5.4, there are several other practice problems and exercises that can help you master the concepts covered in this lesson.
The following online resources and textbooks provide further learning opportunities:
Online Resources
Textbooks
- Algebra 1, by Charles P. McKeague and Mark D. Turner
- Algebra 1, by Ron Larson and Laurie Boswell
- Algebra 1, by Glencoe/McGraw-Hill
Helpful Tips and Strategies
- When multiplying polynomials, it is important to multiply each term in the first polynomial by each term in the second polynomial.
- Be careful to distribute the negative sign in the second polynomial when multiplying by a negative term in the first polynomial.
- Combine like terms after multiplying the polynomials.
- Check your answer by multiplying the polynomials using the FOIL method.
Quick FAQs
Where can I find additional practice problems related to Lesson 17 Homework 5.4?
The Answer Key provides links to online resources and textbooks that offer a wealth of additional practice problems to enhance your understanding.
How can I improve my problem-solving skills?
The Answer Key offers a structured approach to solving problems, complete with detailed explanations and helpful tips. By studying the solutions and practicing regularly, you can develop a systematic approach to problem-solving.
What are the key concepts covered in Lesson 17 Homework 5.4?
The Answer Key provides a concise summary of the key concepts covered in the homework, including algebraic equations, linear functions, and quadratic equations.
