(2x+3y-7)-(2x-3y-8)?
- A. 1
- B. -15
- C. 6y+1
- D. 6y-15
Correct Answer & Rationale
Correct Answer: C
To simplify the expression \((2x + 3y - 7) - (2x - 3y - 8)\), start by distributing the negative sign across the second set of parentheses. This results in \(2x + 3y - 7 - 2x + 3y + 8\). The \(2x\) terms cancel each other out, leaving \(3y + 3y - 7 + 8\), which simplifies to \(6y + 1\). Option A (1) is incorrect as it ignores the \(6y\) term. Option B (-15) miscalculates the constants, failing to account for the combined \(+1\). Option D (6y - 15) incorrectly subtracts instead of adding the constants. Thus, the simplification leads to \(6y + 1\), confirming option C.
To simplify the expression \((2x + 3y - 7) - (2x - 3y - 8)\), start by distributing the negative sign across the second set of parentheses. This results in \(2x + 3y - 7 - 2x + 3y + 8\). The \(2x\) terms cancel each other out, leaving \(3y + 3y - 7 + 8\), which simplifies to \(6y + 1\). Option A (1) is incorrect as it ignores the \(6y\) term. Option B (-15) miscalculates the constants, failing to account for the combined \(+1\). Option D (6y - 15) incorrectly subtracts instead of adding the constants. Thus, the simplification leads to \(6y + 1\), confirming option C.
Other Related Questions
Greatest?
- A. 245 thousandths
- B. 24 hundredths
- C. 3 tenths
- D. 2 fifths
Correct Answer & Rationale
Correct Answer: D
To determine the greatest value among the options, it’s essential to convert each to a common decimal format. A: 245 thousandths equals 0.245. B: 24 hundredths equals 0.24. C: 3 tenths equals 0.3. D: 2 fifths equals 0.4 (since 2 divided by 5 is 0.4). Comparing these values, 0.4 (D) is greater than 0.3 (C), 0.24 (B), and 0.245 (A). Thus, option D represents the largest value. Options A, B, and C are all less than D, making them incorrect choices.
To determine the greatest value among the options, it’s essential to convert each to a common decimal format. A: 245 thousandths equals 0.245. B: 24 hundredths equals 0.24. C: 3 tenths equals 0.3. D: 2 fifths equals 0.4 (since 2 divided by 5 is 0.4). Comparing these values, 0.4 (D) is greater than 0.3 (C), 0.24 (B), and 0.245 (A). Thus, option D represents the largest value. Options A, B, and C are all less than D, making them incorrect choices.
Caterpillar 1 ft in 7.5 min. 18 min?
- A. 2.4
- B. 8
- C. 11.5
- D. 25.5
Correct Answer & Rationale
Correct Answer: A
To determine how far the caterpillar travels in 18 minutes, first calculate its speed. It moves 1 foot in 7.5 minutes, which equates to \( \frac{1 \text{ ft}}{7.5 \text{ min}} \). In 18 minutes, the distance covered can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Converting 18 minutes into feet: \[ \text{Distance} = \left(\frac{1 \text{ ft}}{7.5 \text{ min}}\right) \times 18 \text{ min} = 2.4 \text{ ft} \] Option B (8) overestimates the distance, while C (11.5) and D (25.5) significantly exceed the calculated distance, demonstrating a misunderstanding of the speed-time relationship.
To determine how far the caterpillar travels in 18 minutes, first calculate its speed. It moves 1 foot in 7.5 minutes, which equates to \( \frac{1 \text{ ft}}{7.5 \text{ min}} \). In 18 minutes, the distance covered can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Converting 18 minutes into feet: \[ \text{Distance} = \left(\frac{1 \text{ ft}}{7.5 \text{ min}}\right) \times 18 \text{ min} = 2.4 \text{ ft} \] Option B (8) overestimates the distance, while C (11.5) and D (25.5) significantly exceed the calculated distance, demonstrating a misunderstanding of the speed-time relationship.
50 acres, 23 apple. Percent left?
- A. 27%
- B. 46%
- C. 54%
- D. 77%
Correct Answer & Rationale
Correct Answer: C
To determine the percentage of land left after allocating 23 acres for apple trees from a total of 50 acres, first calculate the remaining land: 50 - 23 = 27 acres. Then, to find the percentage of land left, divide the remaining acres by the total acres and multiply by 100: (27/50) * 100 = 54%. Option A (27%) miscalculates the percentage of land used instead of what remains. Option B (46%) incorrectly assumes a different allocation of land. Option D (77%) mistakenly represents a higher percentage than what is left. Thus, option C accurately reflects the remaining percentage of land.
To determine the percentage of land left after allocating 23 acres for apple trees from a total of 50 acres, first calculate the remaining land: 50 - 23 = 27 acres. Then, to find the percentage of land left, divide the remaining acres by the total acres and multiply by 100: (27/50) * 100 = 54%. Option A (27%) miscalculates the percentage of land used instead of what remains. Option B (46%) incorrectly assumes a different allocation of land. Option D (77%) mistakenly represents a higher percentage than what is left. Thus, option C accurately reflects the remaining percentage of land.
Cover floor? Select ALL.
- A. 15s4r
- B. 8s10r
- C. 5s12r
Correct Answer & Rationale
Correct Answer: A,C
To determine which options cover the floor effectively, we analyze the dimensions given. Option A (15s4r) indicates a larger area, suggesting it can cover more floor space due to its higher values. This makes it suitable for extensive coverage. Option B (8s10r) has moderate dimensions but does not provide sufficient area to cover larger floors, making it less effective compared to A and C. Option C (5s12r) also presents a viable coverage area, complementing A's larger dimensions. Thus, A and C collectively ensure adequate floor coverage, while B falls short.
To determine which options cover the floor effectively, we analyze the dimensions given. Option A (15s4r) indicates a larger area, suggesting it can cover more floor space due to its higher values. This makes it suitable for extensive coverage. Option B (8s10r) has moderate dimensions but does not provide sufficient area to cover larger floors, making it less effective compared to A and C. Option C (5s12r) also presents a viable coverage area, complementing A's larger dimensions. Thus, A and C collectively ensure adequate floor coverage, while B falls short.