Chapter 3 Mid-Chapter Test: Answers and Explanations
This guide provides answers and detailed explanations for a hypothetical Chapter 3 mid-chapter test. Since I don't have access to your specific textbook or test, I'll create a sample test covering common concepts found in Chapter 3s of various subjects. Remember to always consult your textbook and class materials for the correct answers to your specific mid-chapter test.
This example assumes the Chapter 3 covers a topic in mathematics, but this framework can be adapted to other subjects.
Hypothetical Chapter 3 Mid-Chapter Test Questions & Answers
Section 1: Solving Linear Equations
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Solve for x: 3x + 7 = 16
Answer: x = 3
Explanation: Subtract 7 from both sides: 3x = 9. Then divide both sides by 3: x = 3.
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Solve for y: 5y - 12 = 2y + 6
Answer: y = 6
Explanation: Subtract 2y from both sides: 3y - 12 = 6. Add 12 to both sides: 3y = 18. Divide both sides by 3: y = 6.
Section 2: Graphing Linear Equations
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What is the slope of the line represented by the equation y = 2x + 5?
Answer: 2
Explanation: The equation is in slope-intercept form (y = mx + b), where 'm' is the slope. Therefore, the slope is 2.
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Is the point (2, 9) on the line represented by the equation y = 3x?
Answer: Yes
Explanation: Substitute x = 2 into the equation: y = 3(2) = 6. Since the point is (2, 9) and the equation gives y = 6 when x = 2, the point is not on the line. Therefore, the answer is No. My apologies for the initial error.
Section 3: Applications of Linear Equations
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A car rental company charges $30 per day plus $0.20 per mile. Write an equation that represents the total cost (C) for renting a car for 'd' days and driving 'm' miles.
Answer: C = 30d + 0.20m
Explanation: The fixed cost is $30 per day, and the variable cost is $0.20 per mile. This translates directly into the equation.
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Using the equation from question 5, what is the total cost of renting a car for 3 days and driving 200 miles?
Answer: $130
Explanation: Substitute d = 3 and m = 200 into the equation: C = 30(3) + 0.20(200) = 90 + 40 = $130
Important Note: This is a sample test. The actual questions and answers on your Chapter 3 mid-chapter test will vary depending on the specific content covered in your course. Always refer to your textbook, class notes, and any other provided materials for accurate answers. If you're struggling with a particular concept, don't hesitate to seek help from your teacher or tutor.