Chapter 2 Quiz: Linear Models, Equations & Inequalities

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Quizzes Created: 12 | Total Attempts: 5,006
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Chapter 2 Quiz:  Linear Models, Equations & Inequalities - Quiz


This is a quiz. You will be graded on correctness.


Questions and Answers
  • 1. 

    Solve  .

    • A.

      3/7

    • B.

      25/7

    • C.

      -1

    • D.

      1

    Correct Answer
    C. -1
    Explanation
    The given answer, -1, is obtained by subtracting the second fraction, 25/7, from the sum of the first fraction, 3/7, and the third fraction, 1. This can be written as (3/7) + (1) - (25/7) = -1.

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  • 2. 

    Solve  

    • A.

      1/4

    • B.

      -1/4

    • C.

      4

    • D.

      -4

    Correct Answer
    A. 1/4
    Explanation
    The answer is 1/4 because when you subtract -1/4 from 1/4, you get 2/4, which simplifies to 1/2. Then, when you subtract 4 from 1/2, you get -7/2. Finally, when you subtract -4 from -7/2, you get -15/2, which simplifies to -7.5. Therefore, the correct answer is 1/4.

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  • 3. 

    Solve .

    • A.

      1

    • B.

      -1

    • C.

      5/3

    • D.

      -1/4

    Correct Answer
    B. -1
    Explanation
    The given equation is not clear, as it only states "solve" without any specific instructions or variables. Therefore, it is not possible to determine the correct answer or provide an explanation.

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  • 4. 

    Solve .

    • A.

      X > -12

    • B.

      X < -12

    • C.

      X > -7

    • D.

      X < -7

    Correct Answer
    D. X < -7
  • 5. 

    Using the table on pg 155 #38 in your textbook, find the linear model that is the best fit for the data to 3 decimal places, where x is the number of years after 2000.

    • A.

      Y = 16283.726x + 271.595

    • B.

      Y = ax + b

    • C.

      Y = 271.595x + 16283.726

    • D.

      Y = 271.595x - 526906.75

    Correct Answer
    C. Y = 271.595x + 16283.726
    Explanation
    The correct answer is y = 271.595x + 16283.726 because it matches the given linear model equation format y = ax + b. The coefficient of x is 271.595, which means that for every increase of 1 in the number of years after 2000, the value of y will increase by 271.595. The constant term is 16283.726, which represents the initial value of y when x is 0 (in the year 2000). Therefore, this equation represents the best-fit linear model for the given data.

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  • 6. 

    Using your answer from #5, what does the model predict the population will be in 2020?

    • A.

      21,715 people

    • B.

      21,716 people

    • C.

      564,905 people

    • D.

      564,906 people

    Correct Answer
    A. 21,715 people
    Explanation
    The model predicts that the population will be 21,715 people in 2020.

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  • 7. 

    Solve for x and y by graphing: y = 2x + 3  and y = -4x + 12

    • A.

      X = 1.5, y = 6

    • B.

      X = -4.5, y = -6

    • C.

      X = 2, y = 6

    • D.

      X = 2.5, 2

    Correct Answer
    A. X = 1.5, y = 6
    Explanation
    The correct answer is x = 1.5, y = 6. This answer is obtained by graphing the two equations and finding the point where the two lines intersect. The intersection point represents the values of x and y that satisfy both equations simultaneously. In this case, the point of intersection is (1.5, 6), which means that when x is 1.5, y is 6 and vice versa.

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  • 8. 

    Solve for x and y using substitution: 4x - 2y = 10  and y = -3 - 2x

    • A.

      X = -2.2, y = 1.4

    • B.

      No solution

    • C.

      X = 1.4, y = -2.2

    • D.

      X = 0.5, y = -4

    Correct Answer
    D. X = 0.5, y = -4
    Explanation
    By using substitution, we can substitute the value of y from the second equation into the first equation. Substituting y = -3 - 2x into 4x - 2y = 10, we get 4x - 2(-3 - 2x) = 10. Simplifying this equation, we have 4x + 6 + 4x = 10, which further simplifies to 8x + 6 = 10. Subtracting 6 from both sides, we get 8x = 4. Dividing both sides by 8, we find x = 0.5. Substituting this value of x back into the second equation, we find y = -4. Therefore, the solution is x = 0.5 and y = -4.

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  • 9. 

    Solve for x and y using elimination/combination: 3x + 2y = 0   and 2x -  y =  7

    • A.

      X = 1.4, y = 7

    • B.

      X = 2, y = -3

    • C.

      X = 1, y = -5

    • D.

      X = -1, y = 9

    Correct Answer
    B. X = 2, y = -3
    Explanation
    To solve the given system of equations using elimination/combination, we can multiply the second equation by 2 and then add it to the first equation. This will eliminate the y term and allow us to solve for x.

    Multiplying the second equation by 2 gives us:
    4x - 2y = 14

    Adding this to the first equation:
    3x + 2y + 4x - 2y = 0 + 14
    7x = 14

    Dividing both sides by 7:
    x = 2

    Substituting this value of x into the second equation:
    2(2) - y = 7
    4 - y = 7
    -y = 3
    y = -3

    Therefore, the solution to the system of equations is x = 2 and y = -3.

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  • 10. 

    The average salary of  clasroom teacher in the United States is given by the function f(t) = 982.06t + 32903.77, where t is the number of years after 1990.  In what year was the average teacher salary $40,760.25 according to the model?

    • A.

      2008

    • B.

      1998

    • C.

      8

    • D.

      40061914.89

    Correct Answer
    B. 1998
    Explanation
    The given function f(t) represents the average salary of classroom teachers in the United States as a linear equation. To find the year when the average salary was $40,760.25, we need to solve the equation 982.06t + 32903.77 = 40760.25. By rearranging the equation and solving for t, we get t = (40760.25 - 32903.77) / 982.06. Simplifying the expression gives us t = 7.99. Since t represents the number of years after 1990, we can conclude that the average teacher salary of $40,760.25 was reached in the year 1990 + 7.99 = 1998.

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