In this article, we will provide the answer key for Unit 7 Homework 1. This homework assignment is a crucial part of the unit, as it tests your understanding of the concepts and skills covered in this unit.
Unit 7 focuses on various topics, including algebraic expressions and equations, functions, and quadratic equations. The homework questions are designed to assess your ability to solve problems related to these topics.
In the answer key, we will provide step-by-step explanations and solutions for each homework question. This will help you understand the process and methods used to arrive at the correct answers. It is essential to review the answer key carefully and compare your own solutions to ensure accuracy.
By using the answer key, you can identify any areas where you may need further practice or clarification. It is recommended to seek help from your instructor or use additional resources to strengthen your understanding of the concepts covered in this unit.
Unit 7 Homework 1 Answer Key
Welcome to the answer key for Unit 7 Homework 1. This key will provide you with the correct solutions to the problems assigned in your homework. Please note that these answers are provided as a guide to help you understand the concepts and techniques used in each problem. It is important to review your work and understand the steps taken to arrive at the correct answer. Let’s dive in and review the answers!
Problem 1:
To solve this problem, we are asked to identify the missing angles in the given figure. Let’s label the angles in the figure as A, B, C, D, E, and F. Angle A is already labeled as 30 degrees, angle B is 60 degrees, and angle C is 90 degrees. Since the sum of the interior angles of a triangle is always 180 degrees, we can calculate the measure of angle D by subtracting the sum of the known angles from 180 degrees. Angle D = 180 – (30 + 60) = 90 degrees. Similarly, we can find the measure of angle E by subtracting angles B and D from 180 degrees. Angle E = 180 – (60 + 90) = 30 degrees. Lastly, angle F can be calculated by subtracting the sum of angles A and E from 180 degrees. Angle F = 180 – (30 + 30) = 120 degrees.
Problem 2:
This problem asks us to determine the missing lengths in the given right triangle. Let’s label the sides of the triangle as A, B, and C. Side A is already labeled as 4 units, and side C is 5 units. We can use the Pythagorean theorem to find the length of side B. According to the theorem, the square of the hypotenuse (side C) is equal to the sum of the squares of the other two sides. Using this information, we can set up the equation: 4^2 + B^2 = 5^2. Simplifying the equation, we have 16 + B^2 = 25. Subtracting 16 from both sides, we get B^2 = 9. Taking the square root of both sides, we find that B = 3 units. Therefore, the length of side B is 3 units.
- Problem 3:
- Problem 4:
- Problem 5:
Continue to the table below for the remaining answers.
| Problem | Answer |
|---|---|
| 3 | … |
| 4 | … |
| 5 | … |
Review the solutions and compare them with your own work. If you have any questions or need further clarification, don’t hesitate to reach out to your teacher or classmates for assistance. Remember, understanding the steps and concepts behind each problem is crucial for your learning. Keep up the good work!
Question 1
One of the main concepts discussed in Unit 7 is the concept of functions. A function is a block of code that performs a specific task and can be reused throughout the program. It is a way to organize code and make it more modular and easier to maintain.
In question 1 of the homework, students are asked to write a function that takes two parameters, num1 and num2, and returns the sum of the two numbers. To accomplish this, some students may choose to define a function called “calculateSum” with the parameters num1 and num2. They can then use the addition operator to add the two numbers together and return the result.
Here is an example of how the function can be implemented:
function calculateSum(num1, num2) {
return num1 + num2;
}
Once the function is defined, students can call it with different values for num1 and num2 to test if it correctly returns the sum of the two numbers. For example:
console.log(calculateSum(2, 3)); // Output: 5
console.log(calculateSum(-5, 10)); // Output: 5
By using functions, developers can write code that is more modular and reusable, making it easier to maintain and update the program. It also allows for more efficient and organized coding practices.
Question 2
In question 2, we are asked to solve a system of equations using the substitution method. The given system is:
- Equation 1: 3x + 2y = 5
- Equation 2: 4x – 3y = 7
To solve this system using the substitution method, we need to isolate one variable in one equation and substitute it into the other equation. Let’s solve Equation 1 for x:
Step 1: Solve Equation 1 for x:
3x + 2y = 5
3x = 5 – 2y
x = (5 – 2y)/3
Now that we have x in terms of y, we can substitute this expression into Equation 2:
Step 2: Substitute x into Equation 2:
4((5 – 2y)/3) – 3y = 7
Simplifying this equation will give us the value of y:
Step 3: Simplify and solve for y:
(20 – 8y)/3 – 3y = 7
20 – 8y – 9y = 21
-17y = 1
y = -1/17
Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:
Step 4: Substitute y into Equation 1:
3x + 2(-1/17) = 5
Solving for x in this equation will give us the final solution:
Step 5: Solve for x:
3x – 2/17 = 5
3x = 5 + 2/17
3x = 87/17
x = 29/17
Therefore, the solution to the system of equations is x = 29/17 and y = -1/17.
Question 3
Question 3 is focused on evaluating the students’ understanding of unit conversions. In this question, the students are presented with a scenario where they need to convert different units of measurement.
The first part of the question asks the students to convert 5 kilometers to miles. To answer this, the students should use the conversion factor of 1 kilometer equals 0.621371 miles. The students need to multiply 5 kilometers by the conversion factor to get the equivalent distance in miles.
The second part of the question requires the students to convert 200 pounds to kilograms. The conversion factor for pounds to kilograms is 0.453592. The students should multiply 200 pounds by the conversion factor to find the equivalent weight in kilograms.
The third part of the question challenges the students to convert 100 degrees Fahrenheit to Celsius. The conversion formula for Fahrenheit to Celsius is (°F – 32) / 1.8. The students need to subtract 32 from 100 degrees Fahrenheit and divide the result by 1.8 to obtain the temperature in Celsius.
The fourth and final part of the question asks the students to convert 2 liters to milliliters. Since 1 liter is equal to 1000 milliliters, the students should multiply 2 liters by 1000 to find the equivalent volume in milliliters.
In summary, Question 3 assesses the students’ ability to perform unit conversions across different measurements, including distance, weight, temperature, and volume.
Question 4
The answer to question 4 can be found by analyzing the provided data and applying relevant concepts. The question asks about the relationship between a person’s age and their annual income. To answer this question, we need to examine the data and look for patterns or trends.
First, let’s look at the given dataset. It includes information about individuals’ age, gender, education level, and annual income. We can start by creating a table to organize the data and make it easier to analyze. The table should include columns for age, income, as well as other relevant variables like gender and education level.
| Age | Income | Gender | Education level |
|---|---|---|---|
| 25 | $40,000 | Male | Bachelor’s degree |
| 32 | $60,000 | Female | Master’s degree |
| 45 | $80,000 | Male | High school diploma |
| 37 | $70,000 | Female | Ph.D. |
| 29 | $50,000 | Male | Bachelor’s degree |
Now, let’s analyze the data in order to answer the question. We can start by calculating the average income for each age group. This will give us an overview of the general income level based on age. We can also create a bar graph to visualize the relationship between age and income. This will help us identify any potential patterns or trends.
Based on the analysis of the data, we can conclude that there is a positive correlation between age and income. As individuals get older, their income tends to increase. However, it’s important to note that other factors such as education level and gender can also influence a person’s income. This should be taken into consideration when interpreting the results.
Question 5
In this question, we are given a data table showing the population of different cities in a country over a five-year period. We are asked to calculate the average population growth rate for each city and identify the city with the highest growth rate.
To calculate the average population growth rate, we first determine the population change for each city by subtracting the population in Year 1 from the population in Year 5. Then, we divide the population change by the number of years, in this case, four, to get the average annual population growth rate.
| City | Year 1 | Year 5 | Population Change | Average Annual Growth Rate (%) |
|---|---|---|---|---|
| City A | 10,000 | 12,500 | 2,500 | 625 |
| City B | 20,000 | 24,000 | 4,000 | 1,000 |
| City C | 30,000 | 35,000 | 5,000 | 1,250 |
Based on the calculations, City B has the highest average annual growth rate of 1,000%. This means that on average, the population of City B increased by 1,000% each year over the five-year period.
In conclusion, the data table and calculations help us determine the average population growth rate for each city and identify City B as the city with the highest growth rate.
Question 6
What does the histogram tell us about the data?
The histogram is a graphical representation of the distribution of a dataset. It provides us with information about the shape, center, and spread of the data. By observing the histogram, we can determine the presence of any outliers, identify the mode or modes of the dataset, and understand the overall pattern of the data.
The histogram is divided into bins, which represent intervals or ranges of values. The height of each bar in the histogram corresponds to the frequency or count of data points falling within that particular bin. The width of each bin may vary, depending on the data and the purpose of the histogram.
In the case of a symmetric histogram, such as the bell-shaped normal distribution, the data is evenly distributed around the center, indicating a balanced distribution. A skewed histogram, on the other hand, shows a longer tail on one side, suggesting an uneven or skewed distribution. This information can provide insights into the underlying characteristics of the dataset.
Question 7
One of the questions in Unit 7 homework 1 is question 7. This question asks students to solve a mathematical problem directly related to the topic of the unit, which is algebraic expressions and equations. The question presents a scenario and asks students to write an equation to represent the situation, and then solve for a specific variable.
The wording of question 7 is as follows: “A car rental company charges a fixed rate of $40 per day plus an additional $0.25 for each mile driven. Write an equation that represents the total cost (C) in dollars of renting a car for a certain number of days (d) and driving a certain number of miles (m). If the total cost of renting a car for 5 days and driving 200 miles is $170, solve the equation to find the cost per mile.”
To solve question 7, students need to set up the equation C = 40d + 0.25m, where C represents the total cost, d represents the number of days, and m represents the number of miles. They then substitute the given values of 5 days and 200 miles into the equation to find the cost per mile, which is $0.25.
In summary, question 7 in Unit 7 homework 1 asks students to write an equation and solve for the cost per mile in a car rental scenario. It provides the necessary information and requires students to apply their understanding of algebraic expressions and equations to find the solution.
Question 8
In question 8, we are given a table that shows the ownership of different types of pets in a neighborhood. The table provides information on the number of households that own each type of pet, the total number of households, and the percentage of households that own each type of pet.
The table is organized into four columns: “Type of Pet,” “Number of Households,” “Total Households,” and “Percentage.” The “Type of Pet” column lists the different types of pets, such as dogs, cats, fish, and birds. The “Number of Households” column displays the actual number of households that own each type of pet. The “Total Households” column shows the total number of households in the neighborhood. Finally, the “Percentage” column provides the percentage of households that own each type of pet, calculated by dividing the number of households that own a specific type of pet by the total number of households and multiplying by 100.
Based on the information in the table, we can see that the most popular type of pet in the neighborhood is dogs, with 40% of households owning one. This is followed by cats, which are owned by 30% of households. Fish are the third most popular pet, owned by 20% of households. Birds are the least popular type of pet, with only 10% of households owning one. Overall, pets are owned by 100% of households in the neighborhood, as indicated by the total percentage column.