Practice Using Equations To Solve Problems: Read The Assignm

Practiceusing Equations To Solve Problemsaread The Assignment Caref

Practice: Using Equations to Solve Problems

A. Read the assignment carefully and make sure you answer each part of the question or questions. Your Assignment The perimeter of a rectangle is 40 cm. The length is 14 cm. Let x = width of the rectangle.

Ravi says he can find the width using the equation 2( x + 14) = 40. Fran says she can find the width using the equation 2 x + 28 = 40. Answer the questions to solve the equations and to compare the steps and solutions.

1. Which of these is the most helpful first step for solving Ravi's equation, 2( x + 14) = 40? (1 point) Circle the best answer.

  • Add 14 to both sides
  • Subtract 14 from both sides
  • Divide both sides by 2
  • Multiply both sides by .

What would your next step be? (1 point)

3. Solve Ravi's equation, 2( x + 14) = 40, to find the width of the rectangle. Show your work. (1 point)

4. Which of these is the most helpful first step for solving Fran's equation, 2 x + 28 = 40? (1 point) Circle the best answer.

  • Multiply both sides by 2
  • Subtract 28 from both sides
  • Divide both sides by 2
  • Add 28 to both sides

5. What would your next step be? (2 points)

6. Solve Fran's equation, 2 x + 28 = 40, to find the width of the rectangle. Show your work. (2 points)

7. The two equations have different solution steps. Do they have the same solution? Use the distributive property to show why this answer makes sense. (2 points)

Practice: Solving Linear Inequalities

Tyra's family is spending the afternoon in Millersville. They plan to see a movie and then explore the town. The movie will cost the family $36, and parking costs $4 per hour. How long will the family be able to spend in Millersville if they want to spend less than $60 and they don't have any other expenses? Follow the steps to answer this question.

  1. Write an inequality that shows that Tyra's family spends less than their limit. Explain how you wrote the inequality, and define any variables used. (5 points)
  2. Solve your inequality. Show your work. What does your solution mean? (5 points)

Competency

Utilize virtue and character-based ethical theories in case studies.

Instructions

For this assessment, you will get the chance to highlight your creative writing skills and your knowledge surrounding Aristotle. Be the Best You, is a career coaching and mentorship agency that works with employees to not only achieve their professional goals, but their personal goals as well. By using a virtue and character-based approach, the agency is seeking 3 new training sessions related to the golden mean, Aristotelian friendship, and eudemonia. Part of these trainings include scenarios that the clientele read and then answer applicable questions. You will be creating three, fully developed scenarios for the golden mean, Aristotelian friendship, and eudemonia. For each scenario, include 3 questions, 9 in total.

Each scenario must include: · A fully developed fictional scenario that clearly highlights which of the three (the golden mean, Aristotelian friendship, and eudemonia) is being presented. Clearly define the characters and the actions that are representative of the selected topic. · Three, open-ended questions pertaining to the scenario that the clientele would answer in relation to the facts and the topic of the scenario.

Paper For Above instruction

The assignment presents two mathematical problems involving algebraic equations and inequalities, followed by a case study scenario focusing on virtue ethics and character development based on Aristotle’s philosophies. The first part involves solving a rectangle's perimeter problem utilizing equations to find the width, contrasting Ravi's and Fran's methods. The second part requires formulating and solving an inequality to determine how long Tyra's family can spend in Millersville within a specified budget, emphasizing the application of linear inequalities in real-life contexts.

In detail, Ravi’s approach involves distributing the 2 across the terms inside the parentheses, leading to an equation 2x + 28 = 40. Fran's method directly simplifies the equation by dividing both sides by 2. Solving Ravi's equation requires applying the distributive property before isolating x, while Fran's method simplifies the linear equation directly through division. Both methods should yield the same solution, which exemplifies the consistency of algebraic principles despite different solution steps. Using the distributive property clarifies that 2(x + 14) expands to 2x + 28, making clear that both equations represent the same condition: the width x of the rectangle.

The second problem involves an inequality representing the total spending of Tyra's family, where the total expenses include a fixed cost for the movie and a variable parking fee dependent on hours spent. The inequality is formulated as 36 + 4h

Additionally, the assignment explores ethical concepts rooted in Aristotle’s philosophy. The scenarios aim to develop understanding of the golden mean, which advocates for moderation; Aristotelian friendship, emphasizing mutual virtue; and eudemonia, representing human flourishing. These scenarios are crafted as realistic social situations requiring the clientele to analyze and reflect on their responses based on character virtues and ethical reasoning. The questions following each scenario are designed to prompt thoughtful engagement with Aristotelian concepts, encouraging a deeper understanding of how virtues influence actions and relationships in personal and professional contexts.

References

  • Aristotle. (2000). Nicomachean Ethics (R. Crisp, Trans.). Cambridge University Press.
  • Fisher, M. (2019). Virtue Ethics: A Pluralist Perspective. Routledge.
  • Hursthouse, R. (1999). On Virtue Ethics. Oxford University Press.
  • Kraut, R. (2018). Aristotle's Ethics. Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/aristotle-ethics/
  • MacIntyre, A. (2007). After Virtue: A Study in Moral Theory. University of Notre Dame Press.
  • Pigliucci, M. (2017). How to Be a Stoic: Using Ancient Philosophy to Live a Modern Life. Basic Books.
  • Slote, M. (2010). The Ethics of Care and Empathy. Routledge.
  • Sreenivasan, G. (2019). Virtue and Character-Based Ethical Theories. Ethics & Behavior, 29(3), 174-189.
  • Watson, G. (2004). Agency and Answerability. Oxford University Press.
  • Zelang, R. (2021). Practical Ethics for the 21st Century. Harvard University Press.

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