P=2(L+W), P=48, W=L-4. Width?
- A. 10
- B. 12
- C. 20
- D. 24
Correct Answer & Rationale
Correct Answer: A
To find the width (W), start with the given perimeter formula \( P = 2(L + W) \). Substituting \( P = 48 \) gives \( 48 = 2(L + W) \), which simplifies to \( L + W = 24 \). Given \( W = L - 4 \), substitute this into the equation: \( L + (L - 4) = 24 \). This simplifies to \( 2L - 4 = 24 \), leading to \( 2L = 28 \) and \( L = 14 \). Thus, \( W = 14 - 4 = 10 \). Option B (12) does not satisfy the perimeter equation. Option C (20) and Option D (24) also do not fit the derived equations, confirming that W must be 10.
To find the width (W), start with the given perimeter formula \( P = 2(L + W) \). Substituting \( P = 48 \) gives \( 48 = 2(L + W) \), which simplifies to \( L + W = 24 \). Given \( W = L - 4 \), substitute this into the equation: \( L + (L - 4) = 24 \). This simplifies to \( 2L - 4 = 24 \), leading to \( 2L = 28 \) and \( L = 14 \). Thus, \( W = 14 - 4 = 10 \). Option B (12) does not satisfy the perimeter equation. Option C (20) and Option D (24) also do not fit the derived equations, confirming that W must be 10.
Other Related Questions
Which student wrote the estimate closest to 1,592 + 8?
- A. Isabella
- B. Jayden
- C. Michael
- D. Sarah
Correct Answer & Rationale
Correct Answer: A
Isabella's estimate of 1,592 + 8 is 1,600, which is closest to the actual sum. This estimation rounds 1,592 to 1,590 and adds 10 for simplicity, yielding 1,600. Jayden likely underestimated or rounded incorrectly, resulting in a less accurate estimate. Michael may have rounded too far or added an incorrect value, leading to a larger discrepancy. Sarah's estimate might not have accounted properly for the addition, causing it to stray further from the actual result. Thus, Isabella’s approach demonstrates the most accurate estimation strategy.
Isabella's estimate of 1,592 + 8 is 1,600, which is closest to the actual sum. This estimation rounds 1,592 to 1,590 and adds 10 for simplicity, yielding 1,600. Jayden likely underestimated or rounded incorrectly, resulting in a less accurate estimate. Michael may have rounded too far or added an incorrect value, leading to a larger discrepancy. Sarah's estimate might not have accounted properly for the addition, causing it to stray further from the actual result. Thus, Isabella’s approach demonstrates the most accurate estimation strategy.
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.
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.
15 + 3(7 + 1) - 12?
- A. 21
- B. 25
- C. 27
- D. 172
Correct Answer & Rationale
Correct Answer: C
To solve the expression 15 + 3(7 + 1) - 12, follow the order of operations (PEMDAS/BODMAS). First, calculate the expression inside the parentheses: 7 + 1 equals 8. Next, multiply by 3: 3 * 8 equals 24. Now, add 15: 15 + 24 equals 39. Finally, subtract 12: 39 - 12 equals 27. Option A (21) is incorrect as it does not account for the multiplication. Option B (25) mistakenly adds instead of correctly subtracting the final value. Option D (172) is far too high, likely due to miscalculating the operations. Thus, the final result is 27, confirming option C as the correct choice.
To solve the expression 15 + 3(7 + 1) - 12, follow the order of operations (PEMDAS/BODMAS). First, calculate the expression inside the parentheses: 7 + 1 equals 8. Next, multiply by 3: 3 * 8 equals 24. Now, add 15: 15 + 24 equals 39. Finally, subtract 12: 39 - 12 equals 27. Option A (21) is incorrect as it does not account for the multiplication. Option B (25) mistakenly adds instead of correctly subtracting the final value. Option D (172) is far too high, likely due to miscalculating the operations. Thus, the final result is 27, confirming option C as the correct choice.