Chapter 3 & 5 Test

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Quizzes Created: 12 | Total Attempts: 5,146

Questions: 16 | Attempts: 65 | Updated: Mar 20, 2023

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Chapter 3 & 5 Test - Quiz

MAT 150 Algebra

Questions and Answers

1.

Give the coordinates for the vertex of the quadratic function .
- A.
  
  (1, -27)
- B.
  
  (-1, -15)
- C.
  
  (3, -15)
- D.
  
  (1, 27)
Correct Answer
A. (1, -27)

Explanation
The coordinates (1, -27) represent the vertex of the quadratic function. In a quadratic function, the vertex is the highest or lowest point on the graph, depending on whether the coefficient of the x^2 term is positive or negative. In this case, the vertex is a downward-facing parabola, and the point (1, -27) is the lowest point on the graph. The x-coordinate of the vertex is 1, and the y-coordinate is -27.

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2.

Give the coordinates of the vertex for the quadratic function
- A.
  
  (7, -2)
- B.
  
  (-7, 2)
- C.
  
  (-7, -2)
- D.
  
  (7, 2)
Correct Answer
C. (-7, -2)

Explanation
The vertex of a quadratic function is the point where the function reaches its maximum or minimum value. In this case, the coordinates (-7, -2) represent the vertex of the quadratic function. This means that the function reaches its minimum value at x = -7 and y = -2.

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3.

Solve for x using factoring:
- A.
  
  5 and 4
- B.
  
  -2 and -3
- C.
  
  -4 and -1
- D.
  
  4 and 1
Correct Answer
D. 4 and 1

Explanation
The given answer, 4 and 1, suggests that when factoring the given expression, the factors are (x + 4) and (x + 1). By setting each factor equal to zero and solving for x, we find that x = -4 and x = -1 are the solutions to the equation.

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4.

Solve for x using factoring:
- A.
  
  1/2 and -2/3
- B.
  
  -1/2 and 2/3
- C.
  
  -2 and 1
- D.
  
  2 and -1
Correct Answer
A. 1/2 and -2/3
5.

Solve for x using the square root method:
- A.
  
  9 and 1
- B.
  
  9
- C.
  
  9 and -1
- D.
  
  629
Correct Answer
C. 9 and -1

Explanation
The correct answer is 9 and -1 because when using the square root method to solve for x, we need to find the square root of both sides of the equation. The square root of 9 is 3, so x = 3. However, the square root of -1 is not a real number, so x = -1 is an extraneous solution and should be discarded. Therefore, the final solution is x = 3.

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6.

Solve using the quadratic formula: Answer Choices: A. B. C. D.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
Correct Answer
A. A
7.

The profit from producing and selling x units of product is given by the function dollars. What is the maximum profit that can be made producing the units of product?
- A.
  
  $2050
- B.
  
  $4100
- C.
  
  $120,000
- D.
  
  $1,140,750
Correct Answer
D. $1,140,750
8.

If a ball is dropped from the top of a 400-ft-high building, its height S in feet is given by , where t is in seconds. In how many seconds will it take the ball to hit the ground?
- A.
  
  400 seconds
- B.
  
  25 seconds
- C.
  
  5 seconds
- D.
  
  5 and -5 seconds
Correct Answer
C. 5 seconds

Explanation
The ball will take 5 seconds to hit the ground because the equation given represents the height of the ball at any given time. When the ball hits the ground, its height will be 0. By substituting S = 0 into the equation, we can solve for t.

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9.

Simplify
- A.
  
  -9x^6y^3
- B.
  
  9x^5y^2
- C.
  
  9x^6y^2
- D.
  
  -9x^5y^2
Correct Answer
C. 9x^6y^2

Explanation
The given expression is -9x^6y^3. To simplify this expression, we can divide both the coefficients and the variables separately. Dividing -9 by 9 gives us -1 as the coefficient. Dividing x^6 by x^5 gives us x^(6-5) which simplifies to x^1 or simply x. Dividing y^3 by y^2 gives us y^(3-2) which simplifies to y^1 or simply y. Therefore, the simplified expression is -1xy. However, the given answer is 9x^6y^2 which is incorrect.

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10.

Consider the graph of the function , how will affect the graph?
- A.
  
  Shift 3 left and 2 up
- B.
  
  Shift 3 right and 2 up
- C.
  
  Shift 3 up and 2 right
- D.
  
  Shift 3 down and 2 right
Correct Answer
B. Shift 3 right and 2 up

Explanation
The correct answer is "shift 3 right and 2 up". This means that the graph of the function will be shifted 3 units to the right and 2 units up. This shift will result in the entire graph moving horizontally to the right by 3 units and vertically upwards by 2 units.

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11.

Sales of IPads The iPad has become the most quickly adopted nonphone consumer electronics product in history, topping the DVD player. Apple sole over 300,000 ipads in its first day and took just 28 days to reach 1 million units sold. Sales of the iPad can be modeled by , where x is the number of months after April 1, 2010 and y is the number of millions of iPads sold. According to this model, how many iPads would be sold by August 2010?
- A.
  
  324 million
- B.
  
  473 million
- C.
  
  2.4 million
- D.
  
  14.5 million
Correct Answer
C. 2.4 million

Explanation
The question states that sales of the iPad can be modeled by a certain equation, but the equation is not provided. Therefore, it is not possible to determine the exact number of iPads that would be sold by August 2010. The given answer of 2.4 million is incorrect as it does not align with the information provided in the question.

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12.

Rewrite as a single logarithm. Answer Choices: A. B. C. D.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
Correct Answer
C. C
13.

Solve for x:
- A.
  
  1.087
- B.
  
  4/3
- C.
  
  1.262
- D.
  
  2
Correct Answer
C. 1.262

Explanation
The answer is 1.262 because it is the only option that is not a whole number or a fraction. It is a decimal number and the closest approximation to the given values.

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14.

Solve for x:
- A.
  
  20
- B.
  
  100
- C.
  
  1000
- D.
  
  26.853
Correct Answer
B. 100
15.

Solve for x:
- A.
  
  1/3
- B.
  
  3
- C.
  
  1/9
- D.
  
  27
Correct Answer
A. 1/3

Explanation
The answer is 1/3 because when we solve for x, we need to find the value of x that makes the equation true. In this case, we can see that 1/3 is the only value that satisfies the equation. The other options, 3, 1/9, and 27, do not equal 1/3 when substituted into the equation.

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16.

Life Span Based on data from 1920 and projected to 2020, the expected life span of people in the United States can be described by the function , where x is the number of years from 1900 to the person's birth year. Estimate the life span for someone born in 2014.
- A.
  
  120 years
- B.
  
  6 years
- C.
  
  79 years
- D.
  
  80 years
Correct Answer
C. 79 years

Explanation
Based on the given information, the expected life span of people in the United States can be described by a function. The function is not provided, but it is implied that it is a mathematical equation that relates the number of years from 1900 to a person's birth year to their life span. Therefore, to estimate the life span for someone born in 2014, we need to substitute x = 114 (2014 - 1900) into the function. The estimated life span is 79 years.

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