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Which of the following is equivalent to 3.28?
- A. (328/100)
- B. (41/5)
- C. (3/28)
- D. (7/25)
Correct Answer: D
Rationale: To convert a decimal to a fraction, we can treat it as a fraction over 1 and then simplify. For 3.28, it can be written as 3.28/1. To convert this to a fraction, we multiply by 100 to get (328/100). Then, to simplify, we divide both the numerator and denominator by 4 to get (82/25). This simplifies further to (7/25). Therefore, (7/25) is equivalent to 3.28. Choices A, B, and C are incorrect as they do not represent the decimal 3.28.
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Simplify the expression. Which of the following is the value of x? (5(4x - 5) = (3/2)(2x - 6))
- A. −(2/7)
- B. −(4/17)
- C. (16/17)
- D. (8/7)
Correct Answer: C
Rationale: To solve the given proportion 5(4x - 5) = (3/2)(2x - 6), first distribute to get 20x - 25 = 3x - 9. Then, simplify the linear equation by isolating x: 20x - 3x = 25 - 9, which leads to 17x = 16. Finally, solving for x gives x = 16/17. Choice A is incorrect as it does not match the calculated value of x. Choice B is incorrect as it does not correspond to the correct solution for x. Choice D is incorrect as it does not align with the accurate value of x obtained from solving the equation.
Which of the following lists is in order from least to greatest? (1/7), 0.125, (6/9), 0.60
- A. (1/7), 0.125, (6/9), 0.60
- B. (1/7), 0.125, 0.60, (6/9)
- C. 0.125, (1/7), 0.60, 6/9
- D. 0.125, (1/7), (6/9), 0.60
Correct Answer: C
Rationale: To determine the order from least to greatest, convert all fractions to decimals and compare them. Converting the fractions: (1/7) ≈ 0.14, (6/9) ≈ 0.67. The decimals in order from least to greatest are: 0.125 < 0.14 < 0.60 < 0.67. Therefore, the correct order is 0.125, (1/7), 0.60, 6/9, making choice C the correct answer. Choice A is incorrect as it lists (1/7) before 0.125. Choice B is incorrect as it places 0.60 before (6/9). Choice D is incorrect as it lists (6/9) before 0.60.
What is the area of a triangle with a base of 10 cm and a height of 7 cm?
- A. 70 cm²
- B. 35 cm²
- C. 140 cm²
- D. 100 cm²
Correct Answer: B
Rationale: To find the area of a triangle, you use the formula A = 1/2 base height. Substituting the given values: A = 1/2 10 cm 7 cm = 35 cm². Therefore, the correct answer is B. Choice A (70 cm²) is incorrect as it seems to be the product of the base and height rather than the area formula. Choice C (140 cm²) is incorrect as it appears to be twice the correct answer, possibly a result of a miscalculation. Choice D (100 cm²) is incorrect as it does not reflect the correct calculation based on the given base and height values.
x · 7 = x − 36. Solve the equation. Which of the following is correct?
- A. x = 6
- B. x = 42
- C. x = 4
- D. x = 252
Correct Answer: B
Rationale: To solve the equation x · 7 = x − 36, start by multiplying both sides by 7 to get 7(x · 7) = 7(x − 36), which simplifies to x = 7x − 252. Next, subtract 7x from both sides to get -6x = -252. Finally, divide both sides by -6 to solve for x, which results in x = 42. Therefore, the correct answer is x = 42. Choice A (x = 6), Choice C (x = 4), and Choice D (x = 252) are incorrect as they do not align with the correct solution derived from the equation.
Simplify the expression. What is the value of x? (5/4)x = 20
- A. 8
- B. 16
- C. 24
- D. 32
Correct Answer: D
Rationale: To solve for x, multiply both sides by the reciprocal of 5/4 to isolate x. (4/5)(5/4)x = (4/5)20; x = 16. Therefore, the correct answer is 32. Choice A (8), Choice B (16), and Choice C (24) are incorrect as they do not represent the correct value of x obtained after correctly simplifying the expression.