Which graph shows a line described by 4x - 3y = 12?
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A.
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B.
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C.
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D.
Correct Answer & Rationale
Correct Answer: D
To determine which graph represents the line described by the equation 4x - 3y = 12, we can rearrange it into slope-intercept form (y = mx + b). This yields y = (4/3)x - 4. The slope (m) is 4/3, indicating the line rises 4 units for every 3 units it runs to the right, and the y-intercept (b) is -4, meaning the line crosses the y-axis at (0, -4). Option D correctly displays a line with a positive slope and a y-intercept at -4. Options A, B, and C either have the wrong slope or intercept, indicating they do not accurately represent the given equation.
To determine which graph represents the line described by the equation 4x - 3y = 12, we can rearrange it into slope-intercept form (y = mx + b). This yields y = (4/3)x - 4. The slope (m) is 4/3, indicating the line rises 4 units for every 3 units it runs to the right, and the y-intercept (b) is -4, meaning the line crosses the y-axis at (0, -4). Option D correctly displays a line with a positive slope and a y-intercept at -4. Options A, B, and C either have the wrong slope or intercept, indicating they do not accurately represent the given equation.
Other Related Questions
Type your answer in the box. You may use numbers, a decimal point (.), and/or a negative sign (-) in your answer.
A company received a shipment of 8 boxes of metal brackets.
• There are 20 metal brackets in each box.
• The total weight of the shipment is 48 pounds.
What is the weight, in pounds, of each metal bracket?
Correct Answer & Rationale
Correct Answer: 0.3
To find the weight of each metal bracket, first calculate the total number of brackets by multiplying the number of boxes (8) by the number of brackets per box (20), resulting in 160 brackets. Next, divide the total weight of the shipment (48 pounds) by the total number of brackets (160). This calculation yields a weight of 0.3 pounds per bracket. Other options may include numbers that misrepresent the division or assume incorrect values for the total brackets or shipment weight. For example, using a weight of 1 pound per bracket would imply only 48 brackets, which contradicts the initial information provided.
To find the weight of each metal bracket, first calculate the total number of brackets by multiplying the number of boxes (8) by the number of brackets per box (20), resulting in 160 brackets. Next, divide the total weight of the shipment (48 pounds) by the total number of brackets (160). This calculation yields a weight of 0.3 pounds per bracket. Other options may include numbers that misrepresent the division or assume incorrect values for the total brackets or shipment weight. For example, using a weight of 1 pound per bracket would imply only 48 brackets, which contradicts the initial information provided.
A shipping box for a refrigerator is shaped like a rectangular prism. The box has a depth of 34.25 inches (in.), a height of 69.37 in., and a width of 32.62 in. To the nearest hundredth cubic inch, what is the volume of the shipping bax?
- A. 2,262.85
- B. 77,502.59
- C. 136.24
- D. 25,834.20
Correct Answer & Rationale
Correct Answer: B
To determine the volume of a rectangular prism, the formula \( V = \text{length} \times \text{width} \times \text{height} \) is applied. Given the dimensions—depth (length) of 34.25 in., width of 32.62 in., and height of 69.37 in.—the calculation yields a volume of approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, indicating a miscalculation. Option C (136.24) is implausibly low, likely resulting from using incorrect units or dimensions. Option D (25,834.20) is also incorrect, as it does not reflect the correct multiplication of the given dimensions. Thus, only option B accurately represents the calculated volume.
To determine the volume of a rectangular prism, the formula \( V = \text{length} \times \text{width} \times \text{height} \) is applied. Given the dimensions—depth (length) of 34.25 in., width of 32.62 in., and height of 69.37 in.—the calculation yields a volume of approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, indicating a miscalculation. Option C (136.24) is implausibly low, likely resulting from using incorrect units or dimensions. Option D (25,834.20) is also incorrect, as it does not reflect the correct multiplication of the given dimensions. Thus, only option B accurately represents the calculated volume.
The mass of an amoeba is approximately 4.0 × 10^(-6) grams. Approximately how many amoebas are present in a sample that weighs 1 gram?
- A. 2.5 × 10^5
- B. 4.0 × 10^7
- C. 4.0 × 10^5
- D. 2.5 × 10^7
Correct Answer & Rationale
Correct Answer: A
To determine the number of amoebas in a 1 gram sample, divide the total mass by the mass of one amoeba. The mass of an amoeba is 4.0 × 10^(-6) grams. Thus, the calculation is: 1 gram / (4.0 × 10^(-6) grams/amoeba) = 2.5 × 10^5 amoebas. Option B (4.0 × 10^7) is incorrect as it suggests a significantly larger quantity, likely resulting from a miscalculation. Option C (4.0 × 10^5) overestimates the number of amoebas by a factor of 2, while option D (2.5 × 10^7) also miscalculates, indicating confusion in the division process.
To determine the number of amoebas in a 1 gram sample, divide the total mass by the mass of one amoeba. The mass of an amoeba is 4.0 × 10^(-6) grams. Thus, the calculation is: 1 gram / (4.0 × 10^(-6) grams/amoeba) = 2.5 × 10^5 amoebas. Option B (4.0 × 10^7) is incorrect as it suggests a significantly larger quantity, likely resulting from a miscalculation. Option C (4.0 × 10^5) overestimates the number of amoebas by a factor of 2, while option D (2.5 × 10^7) also miscalculates, indicating confusion in the division process.
What is the slope of a line perpendicular to the line given by the equation 5x - 2y = -10?
- A. -0.4
- B. 2\5
- C. 5\2
- D. -2.5
Correct Answer & Rationale
Correct Answer: B
To find the slope of a line perpendicular to the given equation \(5x - 2y = -10\), we first convert it to slope-intercept form (y = mx + b). Rearranging gives \(y = \frac{5}{2}x + 5\), revealing a slope (m) of \(\frac{5}{2}\). The slope of a line perpendicular to another is the negative reciprocal, which is \(-\frac{2}{5}\). Option A (-0.4) is equivalent to \(-\frac{2}{5}\), which is incorrect as it represents a decimal form. Option C (\(\frac{5}{2}\)) is the slope of the original line, not its perpendicular. Option D (-2.5) does not represent the correct negative reciprocal either.
To find the slope of a line perpendicular to the given equation \(5x - 2y = -10\), we first convert it to slope-intercept form (y = mx + b). Rearranging gives \(y = \frac{5}{2}x + 5\), revealing a slope (m) of \(\frac{5}{2}\). The slope of a line perpendicular to another is the negative reciprocal, which is \(-\frac{2}{5}\). Option A (-0.4) is equivalent to \(-\frac{2}{5}\), which is incorrect as it represents a decimal form. Option C (\(\frac{5}{2}\)) is the slope of the original line, not its perpendicular. Option D (-2.5) does not represent the correct negative reciprocal either.