Correct Answer: D

Rationale: To convert a percentage to a fraction, you write the percentage as the numerator of the fraction over 100. Therefore, 290% is equivalent to 290/100, which simplifies to 29/10. Choices A, B, and C are incorrect because they do not represent 290% as a fraction by placing the percentage value over 100.

Correct Answer: B

Rationale: The area of a circle is given by the formula A = π r², where r is the radius. Since only half of the garden needs weeding, we calculate half the area. Using the given value of π (3.14) and a radius of 11.5 feet: A = 0.5 3.14 (11.5)² A = 0.5 3.14 132.25 A = 0.5 415.27 A = 207.64 square feet. Thus, the area that needs weeding is approximately 207.64 square feet, making option B the correct answer. Choice A (207.64) is incorrect as it represents the total area of the circular garden, not just half of it. Choice C (519.08) and Choice D (726.73) are also incorrect as they do not reflect the correct calculation for finding the area of half the circular garden.

Correct Answer: A

Rationale: To simplify the expression 2x + 3x - 5, follow these steps: Identify and combine like terms. The terms 2x and 3x are both 'like terms' because they both contain the variable x. Add the coefficients of the like terms: 2x + 3x = 5x. Simplify the expression. After combining the like terms, the expression becomes 5x - 5, which includes the simplified term 5x and the constant -5. Thus, the fully simplified expression is 5x - 5, making Option A the correct answer. This method ensures all terms are correctly simplified by combining similar elements and retaining constants.

Correct Answer: D

Rationale: The formula for the area of a square is given by the square of its side length: Area = side side. For this problem, the side length of the square is 75 centimeters. To find the area, you multiply 75 by itself: 75 75 = 5,625 square centimeters. Thus, the area of the square is 5,625 cm². This shows that option D is correct. Choices A, B, and C are incorrect as they do not correspond to the correct calculation of the area of a square with a side length of 75 centimeters.

Correct Answer: A

Rationale: When solving an inequality, the direction of the inequality sign changes depending on the operation performed. In this case, if the given inequality simplifies to x > 5, it means that the unknown value x must be greater than 5 for the inequality to hold true. Therefore, x > 5 is the correct solution. Option A is correct. Choices B, C, and D are incorrect because they do not correctly represent the relationship between x and 5 based on the given inequality.