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OpenStax - Elementary Algebra 2/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 7 / 22

Due : Sunday, January 27, 2030 23:59 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8
1/1 4/4 2/2 0/1 –/1 –/1 –/6 –/6
Total
7/22 (31.8%)

  • Instructions

    Elementary Algebra, 2nd edition, written by Lynn Marecek and MaryAnne Anthony-Smith and published by OpenStax is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

    This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

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 OSElemAlg2 3.4.250. My Notes
Question Part
Points
Submissions Used
1
1/1
2/100
Total
1/1
 
  • This question allows the student an opportunity to use mathematics in a real-world application using the Pythagorean Theorem.

Brian borrowed a 21–foot extension ladder to use when he paints his house. If he sets the base of the ladder six feet from the house, how many feet up the side of the house will the top of the ladder reach? (Round your answer to one decimal place.)
21'
6'
Correct: Your answer is correct. seenKey

20.1

 ft


†

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2. 4/4 points  |  Previous Answers OSElemAlg2 5.6.319. My Notes
Question Part
Points
Submissions Used
1 2 3 4
1/1 1/1 1/1 1/1
2/100 1/100 2/100 2/100
Total
4/4
 
  • This question demonstrates how images can be randomized in addition to the standard practice of randomized numbers for problem solving.

Translate to a system of inequalities and solve.
Jocelyn is pregnant and needs to eat at least 400 more calories a day than usual. When buying groceries one day with a budget of $15 for the extra food, she buys bananas that have 90 calories each and chocolate granola bars that have 150 calories each. The bananas cost $0.40 each and the granola bars cost $2.50 each.
(a)
Write a system of inequalities to model this situation. (Let b represent the bananas bought and let g represent the number of granola bars bought. Enter your answers as a comma-separated list of inequalities.)
90b+150g≥400 , 0.4b+2.5g≤15
Correct: Your answer is correct. webMathematica generated answer key
(b)
Graph the system.

Correct: Your answer is correct.
(c)
Could she buy 7 bananas and 6 granola bars?
     Correct: Your answer is correct.
(d)
Could she buy 6 bananas and 4 granola bars?
     Correct: Your answer is correct.


†

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3. 2/2 points  |  Previous Answers OSElemAlg2 6.5.937.Tut. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
2/100 2/100
Total
2/2
 
  • This question enforces the answer in simplified form including prompts for specific form using only positive or negative exponents for rational expressions.

Consider the following expression.
m5n2p5
m4n6
(a) Simplify the expression. (Give your answer using only positive exponents.)
mp5n4​
Correct: Your answer is correct. webMathematica generated answer key

(b) Rewrite the simplified expression using only negative exponents.
n−4m−1p−5​
Correct: Your answer is correct. webMathematica generated answer key


Solution or Explanation

  • Part 1 of 3

    (a) Simplify the expression.

    The numerator and the denominator of the given quotient contain exponential expressions that share a common base. Simplify by applying the quotient rule to those exponential expressions.

    Notice that the exponential expressions in the numerator and denominator have like bases m and n. Divide them by keeping the bases the same and subtracting their exponents.
    m5n2p5
    m4n6
    		 = m(5 − 4)n
    2 − 6
    p5
     = mn-4p5

  • Part 2 of 3

    Simplify by changing the negative exponent to a positive exponent. Remember that for any nonzero real number x and integer n,
    xn = 
    1
    x−n
    .


    Write
    n−4
     using a positive exponent. Think of
    mn−4p5
     as the following.
    mn−4p5
    1
    Change the sign of the exponent on
    n−4,
     and then move the expression to the denominator.
    mn−4p5
    1
     = 
    mp5
    \[{\color{red}n^4}\]
    Thus, the simplification process results in the following expression.
    \[\frac{mp^{{\color{red}5}}}{n^{{\color{red}4}}}\]

  • Part 3 of 3

    (b) Rewrite the simplified expression using only negative exponents.

    Change the positive exponents to negative exponents. Remember that for any nonzero real number x and integer n,
    xn = 
    1
    x−n
    .


    Write
    n4,
     m, and
    p5
     using negative exponents. Remember that the exponent 1 is understood on m. Change the signs of the exponents on m and
    p5,
     and then move the expressions to the denominator. Change the sign of the exponent on
    n4
     and move the expression to the numerator.
    mp5
    n4
     = 
    n−4
    \[m^{-1}p^{-{\color{red}5}}\]
    Thus, rewriting the simplified expression using only negative exponents gives the following result.
    \[\frac{n^{-{\color{red}4}}}{m^{-1}p^{-{\color{red}5}}}\]

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4. 0/1 points  |  Previous Answers OSElemAlg2 7.6.318. My Notes
Question Part
Points
Submissions Used
1
0/1
1/100
Total
0/1
 
  • This question includes prompts to direct the student to enter either a comma-separated list of values or enter NO SOLUTION.

Solve. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
(3b + 1)(6b + 1) = 0
b =
no solution
Incorrect: Your answer is incorrect. webMathematica generated answer key


†

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5. –/1 points OSElemAlg2 8.6.351. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
  • This question features grading for exact answers for solving rational equations.

Solve.
1
p
 + 
6
q
 = 4
 for p
p =


†

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6. –/1 points OSElemAlg2 9.5.360. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
  • This question shows simplifying and rationalizing grading for square roots.

Simplify and rationalize the denominator.
8
45


†

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7. –/6 points OSElemAlg2 10.5.920.Tut. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100
Total
–/6
 
  • This question includes a step-by-step tutorial that walks students through on how to find the axis of symmetry, the vertex, x- and y-intercepts, and graph a quadratic equation.

For the quadratic equation, state the axis of symmetry, vertex, and any intercepts.
y = x2 − 4x − 5
axis of symmetry    
vertex    
(x, y) = 
y-intercept    
(x, y) = 
x-intercept    
(x, y) = 
 (smaller x-value)
x-intercept
(x, y) = 
 (larger x-value)

Graph the quadratic equation.

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8. –/6 points OSElemAlg2 3.5.RQ.001. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100
Total
–/6
 
  • 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

    How can I predict how long it will take me to travel a nature trail?
    Use some information about a path or trail that you have previously traveled to predict your rate of travel. Recall that distance traveled is equal to the product of the rate of travel and the time:
    d = rt.
    The values you enter in this part will be used to make later calculations.
    Consider a path or trail that you have traveled before.
    How long is this path in miles?
    mi
    How long, in hours, does it take you to travel this path from beginning to end?
    hr

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