Nokea
Which proportion yields a different number for the unknown compared to the others?
- A. 2/3 = x/6
- B. 4/5 = x/10
- C. 3/4 = x/8
- D. 5/6 = x/12
Correct Answer: D
Rationale: To find the value of x in each proportion, cross multiply. For proportion A, x = 4; for B, x = 8; for C, x = 6; and for D, x = 10. Hence, proportion D yields a different value for x compared to the others. Choices A, B, and C all result in unique values for x, but these values are distinct from the value obtained in proportion D.
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Solve the equation for the unknown. 3x + 2 = 20
- A. x = 2
- B. x = 4
- C. x = 6
- D. x = 8
Correct Answer: C
Rationale: Simplify the equation step by step:
Subtract 2 from both sides:
3x + 2 - 2 = 20 - 2
3x = 18
Divide both sides by 3:
x = 18 · 3
x = 6
Therefore, the correct answer is C (x = 6).
Half of a circular garden with a radius of 11.5 feet needs weeding. Find the area in square feet that needs weeding. Round to the nearest hundredth. Use 3.14 for π.
- A. 207.64
- B. 415.27
- C. 519.08
- D. 726.73
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.
Simplify the expression: 2x + 3x - 5.
- A. 5x - 5
- B. 5x
- C. x - 5
- D. 2x - 5
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.
Solve |x| = 10.
- A. -10, 10
- B. -11, 11
- C. -12, 12
- D. -13, 13
Correct Answer: A
Rationale: The absolute value of x is equal to 10 when x is either -10 or 10. Therefore, the correct answer is A. Choices B, C, and D are incorrect because they do not satisfy the equation |x| = 10. For choice B, -11 and 11 do not satisfy the condition. Choices C and D also do not provide solutions that meet the equation's requirement.
Simplify the expression 3x - 5x + 2.
- A. -2x + 2
- B. -8x
- C. 2x + 2
- D. -2x
Correct Answer: D
Rationale: When simplifying the expression 3x - 5x + 2, start by combining like terms. -5x is subtracted from 3x to give -2x. Adding 2 at the end gives the simplified expression -2x. Therefore, the correct answer is -2x. Choice A, -2x + 2, incorrectly adds 2 at the end. Choice B, -8x, incorrectly combines the coefficients of x without considering the constant term. Choice C, 2x + 2, incorrectly adds the coefficients of x without simplifying.