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Tussy and Gustafson - Elem & Intermediate Alg 5/e (Homework)

James Finch

Math - High School, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 7 / 30

Due : Monday, January 28, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9 10
1/1 0/2 2/2 –/1 3/3 –/7 –/3 –/3 –/7 1/1
Total
7/30 (23.3%)

  • Instructions

    WebAssign provides a wide range of exercises that enable you to:
    • Let students self-remediate with question-level help (#1–4: Learn Its, Read It, Watch It)
    • Support the learning process outside the classroom (#5–6: Concept Check, Example Problem)
    • Reduce math anxiety and reveal content relevance (#7–10: Math Mindset, College Success, Responsive Question, and Are You Ready)
    Please read the information in the box at the top of each exercise to learn more about the features, content, and/or grading. We encourage you to try correct and incorrect answers in any answer blanks.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 1/1 points  |  Previous Answers TGEIAlg5 6.7.032. My Notes
Question Part
Points
Submissions Used
1
1/1
2/100
Total
1/1
 
  • This exercise lets students self-remediate with question-level help.
  • Learn It modules address your students' knowledge gaps with just-in-time instruction. Application Learn Its provide targeted instruction and practice on that application topic using narrative, videos, and tutorials that utilize Polya's problem solving process. If the topic is still too challenging, students can choose to continue learning through associated prerequisite Learn Its.

Solve the equation. (Enter your answers as a comma-separated list.)
x2 − 13x + 36 = 0
x =
4,9
Correct: Your answer is correct. webMathematica generated answer key
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2. 0/2 points  |  Previous Answers TGEIAlg5 2.6.041. My Notes
Question Part
Points
Submissions Used
1 2
0/1 0/1
1/100 1/100
Total
0/2
 
  • This exercise lets students self-remediate with question-level help.
  • Learn It modules address your students' knowledge gaps with just-in-time instruction. Application Learn Its provide targeted instruction and practice on that application topic using narrative, videos, and tutorials that utilize Polya's problem solving process. If the topic is still too challenging, students can choose to continue learning through associated prerequisite Learn Its.

To make low-fat cottage cheese, milk containing 4% butterfat is mixed with milk containing 1% butterfat to obtain 24 gallons of a mixture containing 2% butterfat. How many gallons of each milk must be used?
1% milk Incorrect: Your answer is incorrect. seenKey

16

 gal 4% milk Incorrect: Your answer is incorrect. seenKey

8

 gal
Suggested tutorial: Learn It: Solve a percent mixture application using a linear equation in one variable.
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3. 2/2 points  |  Previous Answers TGEIAlg5 5.4.051. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/100 1/100
Total
2/2
 
  • This exercise will let students self-remediate with question-level help.
  • Read It links are available as a learning tool under each question so students can quickly jump to the corresponding section of the eTextbook.

Evaluate the expression.
6t2 + 2t − 8 for
(a)
t = −1
Correct: Your answer is correct. seenKey

-4
(b)
t = 0
Correct: Your answer is correct. seenKey

-8
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4. –/1 points TGEIAlg5 4.3.104. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
  • This exercise will let students self-remediate with question-level help.
  • Students get just-in-time learning support with Watch It videos that contain narrated and closed-captioned videos walking students through the proper steps to solve a similar problem.

Use the elimination method to solve the system.
4(x + 1)
34
 = 
15
17
 − 
3(y − 1)
34
 
0.2(x + 0.2) + 0.3(y − 0.3) = 2.45
(x, y) = 

Need Help? Watch It

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5. 3/3 points  |  Previous Answers TGEIAlg5 4.5.CC.001. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
1/100 1/100 1/100
Total
3/3
 
  • This exercise will support the learning process outside the classroom.
  • Concept Check questions provide students with short, multi-step videos reviewing math concepts. The student is required to answer a question after each video to help confirm understanding of each concept.

Concept Check
Solving Systems of Linear Inequalities
Graph the solution set of a system of linear inequalities.
Watch the following videos and then answer the questions.
Concept Check 1

Click here for transcript.
The solution set of a system of linear inequalities is the intersection Correct: Your answer is correct. seenKey

intersection

 of the solution sets of the individual inequalities.
Concept Check 2

Click here for transcript.
To graph the solution set of
y ≥ 2x + 1,
 shade in above Correct: Your answer is correct. seenKey

above

 the boundary line
y = 2x + 1.
Concept Check 3

Click here for transcript.
If the inequality contains the symbol < or >, then the boundary line is drawn as a dashed Correct: Your answer is correct. seenKey

dashed

 line.
You have now completed the Concept Check.
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6. –/7 points TGEIAlg5 4.2.E05. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
–/1 –/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/7
 
  • This exercise will support the learning process outside the classroom.
  • Example Problems are created from your textbook questions ensure your students understand the section topics before moving on.

EXAMPLE 5
Solve the system: 
 
y
4
 = − 
x
2
 − 
3
4
 
2x − y = −1 + y − x
.
Strategy
We will use properties of equality to write each equation of the system in simpler, equivalent form. Then we will use the substitution method to solve the resulting system.
Why
The first equation will be easier to work with if we clear it of fractions. The second equation will be easier to work with if we eliminate the variable terms on the right side.
Solution












 We can clear the first equation of fractions by multiplying both sides by the LCD.
(1)      
y
4
 		 = 
− 
x
2
 − 
3
4
 		This is the first equation of the system.
4
y
4
 		 = 
4
− 
x
2
 − 
3
4
 		Multiply both sides by the LCD, 4. Don't forget the parentheses.
4
y
4
 		 = 
4
− 
x
2
 − 4
3
4
 		Distribute the multiplication by 4.
y
 		 = 
−2x − 3
 		Simplify. Call this result equation 1.
We can write the second equation of the system in standard Ax + By = C form by adding x and subtracting y from both sides.
(2)       2x − y  =  −1 + y − x This is the second equation of the system
2x − y + x − y  =  −1 + y − x + x − y
3x − 2y  =  −1 Combine like terms. Call this equation 2.
Step 1:    Equations 1 and 2 form an equivalent system, which has the same solution as the original one. To find x, we proceed as follows.
(1)
y = −2x − 3 This is the substitution equation.
(2) 3x − 2y = −1
Step 2:     To find x, substitute −2x − 3 for y in equation 2 and proceed as follows.
3x − 2y  =  −1 This is equation 2. It has two variables.
3x − 2(−2x − 3)  =  −1 Substitute −2x − 3 for y. Don't forget the parentheses.
3x + x + 6  =  −1 Distribute the multiplication by −2.
x + 6  =  −1 Combine like terms: 3x + 4x = 7x.
x  =  −7 To isolate the variable term, 7x, subtract 6 from both sides.
x  =  Divide both sides by 7. This is the x-value of the solution.
Step 3:     To find y, we substitute −1 for x in equation 1.
y  =  −2x − 3 This is equation 1.
y  =  −2(−1) − 3 Substitute −1 for x.
y  =  − 3 Do the multiplication.
y  =  Subtract. This is the y-value of the solution.
Step 4:    The solution is (−1, −1). Check it in the original system.
Self Check 5 Solve the system:
 
y
12
 = 
x
4
 + 
1
3
 
4x − y = −5 + y − x
.

(x, y) = 
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7. –/3 points mathsuccess1 1.1.001.defective My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/100 0/100 0/100
Total
–/3
 
  • This exercise will reduce math anxiety and reveal content relevance.
  • Math Mindset Modules prepare students for challenging math topics with interactive and reflective exercises on relevant topics.

What Is Growth Mindset?

Watch the following video about Growth Mindset vs. Fixed Mindset.
Passion Over Approval
One of the key differences between the two mindsets is the idea of seeking approval. Those with a fixed mindset compare themselves against others when it comes to their ability and intelligence. They put high value on their grades because, to them, grades prove their intelligence. Being at the top of the class makes them feel smart, and they see good grades as a result of their natural intelligence. On the other hand, having others perform better than them causes them to feel inferior. In addition, if they try their hardest and still do not perform as well as others, they are more likely to give up.
If someone with a growth mindset is outperformed by their peers, they understand that it was likely because they need to put more work into their studies. They ask themselves how they can do better next time. There is nothing hard work cannot fix when it comes to their ability and knowledge. If they perform well, they know it reflects their effort, not their intelligence.
Comparing Growth and Fixed Mindsets in Math and Stats Class
The following accordion sections describe how you can approach challenges in your math and stats classes with a fixed mindset and growth mindset.
  • Scenario: You are working through an exam prep test and you encounter a word problem. You attempt the problem and it takes you a good chunk of time. You check an answer key and discover you got it wrong.
    Fixed Mindset: You give up on the problem or ask a classmate for their solution to see how they got their answer. You also put the question in a search engine and find the full solution online.
    Growth Mindset: You review your work and compare your steps with similar problems from class. You move on to other questions and return to the word problem later. You cover up your previous attempt and try again. If you are still stuck, you consult a classmate on a step, but not the entire process.
  • Scenario: Your instructor is presenting a concept, and halfway through the lecture, you find that you are completely lost.
    Fixed Mindset: You shut down and give up on the lecture. Your immediate thought is that the instructor is not explaining it well, but you do not ask questions. You may ask a classmate for their notes after class, but for the rest of your lecture, you sit there and let your attention drift.
    Growth Mindset: You immediately ask your instructor questions about what confused you. You keep working through the lecture in hopes that something is explained in a different way later on. If you end up being lost at the end of the lecture, you make an appointment to go to your instructor's office hours.
  • Scenario: You get your exam back and you see that you got a 60%. You thought you knew—really, really knew—the material going into it. Many questions have red Xs, and there are comments written next to the incorrect questions.
    Fixed Mindset: You figure you thought you knew it and it is clear you were not smart enough. You put the test in your desk drawer and never speak of it again.
    Growth Mindset: You bring your exam home and rework the questions you got incorrect. For questions you are stumped on, you make an appointment with your instructor during their office hours and ask clarifying questions about where you went wrong.
If you are worried that you have a fixed mindset, remember that the most important lesson is that mindsets can change. Approaching challenges and criticism from a different angle can help you learn from mistakes and reach higher levels of success.
📖 Journal Questions
Answer the following questions honestly to get yourself thinking about your own mindsets.
How would you describe your mindset about math? Is it a growth mindset or a fixed mindset? Do you have different mindsets for different types of math?

This answer has not been graded yet.

Describe a time when you put in effort to learn something difficult.

This answer has not been graded yet.

Identify at least one aspect of a growth mindset (i.e., approaching challenges, taking criticism, etc.) that you are going to focus on this semester.

This answer has not been graded yet.

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8. –/3 points mathsuccess1 3.9.003.defective My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/100 0/100 0/100
Total
–/3
 
  • This exercise will reduce math anxiety and reveal content relevance.
  • College Success Modules help students practice key foundational skills for effective learning by introducing a topic followed by a set of reflective questions to help students understand the concept and how it applies to their education.

The Process of Decision Making
Imagine that you are choosing your college major. It is unlikely that you would make such a big decision by randomly choosing the first subject that you come across. Rather, you would probably determine your interests and life goals, take a diverse set of classes, and meet with a college guidance counselor to weigh your options before arriving at a decision. Effective critical thinkers identify problems and make decisions by following a series of steps. These steps guide you through the decision-making process and enable you to see all sides of an issue before you arrive at a final decision.
The following table outlines the five steps that critical thinkers follow when identifying a problem and making a decision. It also presents scenarios about Maria, a nursing student who is considering buying a car. As you go through the steps and scenarios, notice how Maria uses critical thinking skills to identify the problem and arrive at a decision that solves the problem.
  • What is the problem that needs to be solved? Consider the issue in the following scenario.
    Maria is a nursing student. She does not own a car and relies on public transportation to get to and from campus. However, the bus does not always arrive on time, which makes her late for class. Sometimes she misses class entirely.
    What is the problem? Maria's mode of transportation is unreliable.
  • Ask yourself questions to gather the information necessary to make an informed decision. Consider the questions that Maria came up with.
    • What alternatives are there to public transportation?
    • Can I borrow my parents' car?
    • Can I invest in my own car?
    • Can I bike or walk to campus?
    • Can I ask a classmate for a ride?
  • Determine the options that are available to you. Take a look at the options that Maria came up with.
    • Option 1: Borrow my parents' car. They are willing to lend me the car two days a week. But I will still have to find alternative transportation for the other three days of class.
    • Option 2: Invest in my own car. I can use my savings as a down payment. But I will have to determine whether I can afford monthly payments.
    • Option 3: Get a ride from my classmate three days a week. But I will still have to find alternative transportation for the other two days of class.
  • When you take action, you make your choice. Review your options, and make a decision based on the information you have gathered from the previous steps in the decision-making process. Take a look at the decision Maria made.
    I can combine Options 1 and 3. I will borrow my parents' car two days a week and ride with a classmate for the other three.
  • Finally, review your decision and examine the consequences. Did you make the right decision? Or do you need to begin the process all over again? Let's look at Maria's review of her decision.
    I feel like I made the right decision. I am able to get to campus much more quickly. As a result, I am no longer late to class. I have not missed any classes, either.
Read about Felix, and help him in identifying the problem, gathering information by asking questions, identifying his options, and choosing the best option to address his problem
Halfway through the semester, Felix's car broke down. This made it much harder for him to commute to an off-campus work location and back to school.
In addition, Felix's roommate has been a major distraction. When Felix asks his roommate to try to be more quiet, the request is met with anger, and the two argue, sometimes late into the night. Normally he could handle the distractions, but this semester he is struggling in a calculus course, and there's a major midterm approaching that promises to be the most difficult exam he has ever taken. Furthermore, Felix must keep up his grades, or he risks losing his scholarship, and Felix's parents cannot afford to help him out financially.
What is the problem that needs to be solved?
    
Which of the following questions would best help Felix gather information related to his problem? Select all that apply.

Once Felix has defined the problem and gathered information, it is time to generate possible options for solving the problem. Consider the three lists of options, and pick the best list.
List 1 List 2 List 3
  1. Call the towing company, and get the car fixed.
  2. Find public transportation to and from work.
  3. Make a schedule that accounts for extra time on public transit.
  4. Visit calculus instructor during office hours with questions about the midterm.
  5. Make a study schedule to prepare for the midterm.
  6. Try once more to reason with roommate; if discussion does not go well, research options for finding a new place to live, considering dorm policy and moving costs.
  1. Sell the car for extra cash.
  2. Get a friend to drive you around.
  3. Do calculus homework while at off-campus job
  4. Tell your boss you might be late a few times because of the car.
  5. Tell the roommate to shape up or move out.
  1. Try to fix the car yourself.
  2. Find public transportation to and from work.
  3. Make a schedule that accounts for extra time on public transit.
  4. Visit calculus instructor during office hours to explain why you're not doing well.
  5. Study calculus at work.
  6. Leave notes for roommate so you don't have to talk.
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9. –/7 points TGEIAlg5 4.4.RQ.001. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
–/1 –/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/7
 
  • This exercise will reduce math anxiety and reveal content relevance.
  • Responsive Questions personalize the learning experience by asking students to use their own real data, which provides the variables needed to answer each question part.

  • Part 1

    The values you enter in this part will be used to make later calculations.
    Suppose you and your friend are on vacation and have decided to paddle a canoe to the other side of the lake. You keep track of the time it takes you to travel across the lake and then back home. The wind is blowing across the lake, and so the current of the water helps you to travel faster across the lake than on the way back.
    The distance across the lake is miles.
    The trip across the lake takes hours.
    The trip back home takes hours.
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10. 1/1 points  |  Previous Answers TGEIAlg5 4.5.AYR.002. My Notes
Question Part
Points
Submissions Used
1
1/1
2/100
Total
1/1
 
  • This exercise will reduce math anxiety and reveal content relevance.
  • Are You Ready problems prepare students for success in the section by reviewing crucial prerequisite skills.

Graph.
3x − 4y = −12
No Solution
Help
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Clear Graph
Delete Layer
Fill
Show Key

Graph LayersToggle Open/Closed

Submission Data

Correct: Your answer is correct.
seenKey

line: y=(3/4)*x+3
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