In the study of mathematics, unit transformations are an essential concept to understand. They involve converting measurements from one unit to another, whether it be length, weight, time, or any other type of measurement. Homework 4 of unit transformations provides students with the opportunity to practice these skills and test their understanding.
This article serves as the answer key for Homework 4, providing explanations and step-by-step solutions to each question. By following along with this guide, students can compare their own answers and methods to the correct ones, ensuring they’ve grasped the concepts correctly.
Throughout the answer key, explanations will be provided for the reasoning behind each step in the solution. This way, students can gain a deeper understanding of the unit transformation process and apply it to future problems. It is essential to understand the logic behind each transformation to successfully apply it in future math problems and real-life scenarios.
Unit Transformations Homework 4 Answer Key
In Unit Transformations Homework 4, students were given various exercises to practice their understanding of unit transformations, including reflections, rotations, translations, and dilations. The answer key for this homework assignment provides the correct solutions for each question, allowing students to compare their answers and assess their understanding of the topic.
The answer key begins by listing the questions for each type of unit transformation, followed by the correct answers. It provides step-by-step solutions and explanations for each problem, ensuring that students can follow the process and learn from any mistakes they may have made. The key also includes diagrams and visual representations to aid in comprehension and reinforce the concepts being taught.
The answer key covers a range of topics related to unit transformations, including determining the image of a point after a given transformation, finding the coordinates of a reflected point, identifying the center and angle of rotation, and calculating the scale factor for a dilation. It also includes practice problems that combine multiple types of transformations, challenging students to apply their knowledge in a more complex context.
By reviewing the answer key, students can identify any misconceptions or areas where they need further practice. They can also use it as a study tool to reinforce their understanding of unit transformations and improve their problem-solving skills. Overall, the Unit Transformations Homework 4 Answer Key is a valuable resource for students and teachers alike, ensuring that students have the necessary support and guidance to succeed in their studies of unit transformations.
Overview
The Unit transformations homework 4 answer key provides the solutions and explanations for the fourth homework assignment in the unit transformations course. This homework assignment focuses on applying unit transformations to different types of problems. The answer key helps students check their work and learn from their mistakes, providing step-by-step solutions and detailed explanations.
The answer key is organized by question number, making it easy for students to find the solutions they need. Each question is accompanied by a clear and concise explanation of the steps involved in solving the problem. This allows students to understand the reasoning behind each step and apply it to similar problems in the future.
The answer key also includes additional practice problems for students who want to further strengthen their understanding of unit transformations. These problems cover a variety of topics and difficulty levels, providing students with the opportunity to apply their knowledge in different contexts.
In addition to the solutions and explanations, the answer key may also include helpful tips and strategies for approaching unit transformation problems. These tips can help students develop problem-solving skills and improve their overall performance in the course.
Question 1
Question 1 of the Unit Transformations homework 4 states:
“Convert the following quantities from one unit to another:”
- Convert 5 meters to kilometers
- Convert 24 hours to seconds
To convert 5 meters to kilometers, we need to use the conversion factor that 1 kilometer is equal to 1000 meters. Therefore, we can set up the following equation:
5 meters * (1 kilometer / 1000 meters) = 0.005 kilometers
So, 5 meters is equal to 0.005 kilometers.
To convert 24 hours to seconds, we need to use the conversion factor that 1 hour is equal to 3600 seconds. Therefore, we can set up the following equation:
24 hours * 3600 seconds / 1 hour = 86400 seconds
So, 24 hours is equal to 86400 seconds.
Question 2
In question 2, we are given a problem that involves converting a given unit to another unit. The problem states:
“Solve the following problem: Convert 150 miles per hour to kilometers per hour.”
To solve this problem, we need to use the conversion rate between miles and kilometers. We know that 1 mile is approximately equal to 1.60934 kilometers. Therefore, to convert miles per hour to kilometers per hour, we need to multiply the given value by the conversion rate:
Given: | 150 miles per hour |
Conversion rate: | 1 mile = 1.60934 kilometers |
Calculation: | 150 miles per hour * 1.60934 kilometers per mile = 241.401 kilometers per hour |
Therefore, 150 miles per hour is equivalent to 241.401 kilometers per hour.
Question 3
In question 3, we are given a problem that involves converting units of measurement. The problem states that we have a rectangular garden that measures 20 feet by 35 feet. We need to convert the dimensions of the garden from feet to meters.
To solve this problem, first, we need to know the conversion factor between feet and meters. The conversion factor is 1 foot equals 0.3048 meters. To convert the length of the garden from feet to meters, we can multiply the length in feet by the conversion factor. So, the length in meters would be 20 feet multiplied by 0.3048 meters/foot, which equals 6.096 meters.
Next, we can use the same process to convert the width of the garden from feet to meters. The width is given as 35 feet, so we can multiply 35 feet by 0.3048 meters/foot to get the width in meters. The width in meters would be 10.668 meters.
Therefore, the dimensions of the rectangular garden in meters are 6.096 meters by 10.668 meters. This is the final answer to question 3.
Question 4
This question involves converting units of measurement. In this case, we are given a conversion factor between feet and inches and asked to convert a given measurement from inches to feet.
First, let’s note the given conversion factor: 1 foot = 12 inches. This means that 1 inch is equal to 1/12 of a foot.
Problem:
Convert 36 inches to feet.
To solve this problem, we can use the given conversion factor. We know that 1 inch is equal to 1/12 of a foot, so we need to divide the given measurement in inches by 12 to find the equivalent measurement in feet.
Using the formula: Measurement in feet = Measurement in inches / 12, we can plug in the given value:
- Measurement in feet = 36 inches / 12
- Measurement in feet = 3 feet
Therefore, 36 inches is equal to 3 feet.
Question 5
In question 5, we were asked to convert a given measurement from one unit to another. We were given the following information:
- Initial measurement: 150 milliliters
- Conversion rate: 1 milliliter = 0.001 liters
To convert 150 milliliters to liters, we used the conversion rate of 1 milliliter = 0.001 liters. By multiplying the initial measurement by the conversion rate, we obtained the final result:
Final measurement: 0.15 liters
Therefore, 150 milliliters is equivalent to 0.15 liters.
It is important to note that when converting between units, it is crucial to know the conversion rate and use it correctly in the calculation. In this case, we multiplied the initial measurement by the conversion rate to obtain the final measurement in the desired unit.
By successfully completing this unit transformation, we have gained a better understanding of how to convert between different units of measurement, which is a valuable skill in various fields, such as science, engineering, and everyday life.