This comprehensive answer key provides detailed solutions for Weekly Math Review Q1 7. We'll cover each problem step-by-step, ensuring you understand the underlying concepts and can confidently tackle similar problems in the future. Remember, understanding the how is just as important as knowing the what.
Disclaimer: This answer key is intended to be used as a learning tool. Please refer to your original problem set for the exact wording and any specific instructions provided by your instructor. Slight variations in problem phrasing may exist.
Section 1: Algebra
Problem 1: Solving for x
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Problem: 3x + 7 = 16
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Solution:
- Subtract 7 from both sides: 3x = 9
- Divide both sides by 3: x = 3
- Answer: x = 3
Problem 2: Simplifying Expressions
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Problem: 2(4x - 5) + 6x
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Solution:
- Distribute the 2: 8x - 10 + 6x
- Combine like terms: 14x - 10
- Answer: 14x - 10
Problem 3: Solving a System of Equations
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Problem: y = 2x + 1 and y = x - 3
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Solution: Since both equations are solved for y, we can set them equal to each other:
2x + 1 = x - 3
- Subtract x from both sides: x + 1 = -3
- Subtract 1 from both sides: x = -4
- Substitute x = -4 into either original equation to solve for y. Using y = 2x + 1: y = 2(-4) + 1 = -7
- Answer: x = -4, y = -7
Section 2: Geometry
Problem 4: Area of a Triangle
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Problem: Find the area of a triangle with a base of 10 cm and a height of 6 cm.
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Solution: The formula for the area of a triangle is (1/2) * base * height.
Area = (1/2) * 10 cm * 6 cm = 30 cm²
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Answer: 30 cm²
Problem 5: Circumference of a Circle
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Problem: Find the circumference of a circle with a radius of 5 inches. Use π ≈ 3.14
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Solution: The formula for the circumference of a circle is 2πr, where r is the radius.
Circumference = 2 * 3.14 * 5 inches = 31.4 inches
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Answer: 31.4 inches
Section 3: Word Problems
Problem 6: Rate Problem
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Problem: A car travels at 60 miles per hour. How far will it travel in 2.5 hours?
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Solution: Distance = Speed x Time
Distance = 60 mph * 2.5 hours = 150 miles
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Answer: 150 miles
Problem 7: Percentage Problem
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Problem: What is 20% of 80?
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Solution: To find 20% of 80, multiply 80 by 0.20 (which is the decimal equivalent of 20%).
20% of 80 = 0.20 * 80 = 16
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Answer: 16
This detailed answer key provides a thorough explanation for each problem in Weekly Math Review Q1 7. Remember to review your notes and seek help from your teacher or tutor if you have any further questions. Consistent practice is key to mastering these mathematical concepts.
