id
stringlengths 6
6
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stringlengths 50
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072385 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Are the areas of the shaded and un-shaded regions in the rectangle equal?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Each small rectangle within the larger rectangle ABCD is divided by a diagonal into two triangles of equal area. The diagonals ensure that the shaded and un-shaded regions in each small rectangle have equal area. Consequently, for the entire larger rectangle, the shaded and un-shaded regions have equal areas. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/072385.png | 072385 |
039928 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what type of graph is displayed?\nChoices:\nA. line graph\nB. bar graph\nC. pie chart\nD. scatter plot"
},
{
"from": "gpt",
"value": "The image shows a collection of points plotted in the coordinate plane, which defines it as a scatter plot. So the answer is D\nAnswer: D"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/039928.png | 039928 |
058819 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the vertical height of the cone, considering the measurements of radius and slant height? Ensure the accuracy to two decimal points."
},
{
"from": "gpt",
"value": "Using the dimensions of radius (9.1 cm) and slant height (13.7 cm) provided in the image, the vertical height of the cone is determined through the Pythagorean theorem. Following the formula: Height = \\sqrt{(13.7)^2 - (9.1)^2} cm. Start by squaring both the slant height and the radius, subtract the latter from the former, and extract the square root of this outcome to find the vertical height. Accurate calculation calls for rounding the result to two decimal points, therefore \\sqrt{187.69 - 82.81} cm is approximately \\sqrt{104.88} cm ≈ 10.24 cm. So the answer is 10.24 cm\nThe answer is 10.24 cm"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/058819.png | 058819 |
077545 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Were the company funds for research and development in 1973 $2 billion?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "According to the analysis, the company funds for research and development totalled $2 billion in 1973. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/077545.png | 077545 |
009809 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how many axes of symmetry can be identified for the shape?\nChoices:\nA. None\nB. One\nC. Two\nD. Multiple"
},
{
"from": "gpt",
"value": "The number of axes of symmetry can be determined based on the type of geometric shape depicted and its visible properties in the image. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/009809.png | 009809 |
065910 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, which number was spun the least number of times?"
},
{
"from": "gpt",
"value": "Compare the counts of X's in each column and find the minimum. Number 1 has the least with 1 X. So the answer is 1\nThe answer is 1"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/065910.png | 065910 |
062667 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, calculate the slope of the line provided."
},
{
"from": "gpt",
"value": "The slope formula $m = (y_2 - y_1) / (x_2 - x_1)$ requires two points on the line, which are $(0,4)$ and $(3,6)$. Calculating the difference in y-coordinates and x-coordinates, we get: $m = (6-4)/(3-0) = 2/3$. So the answer is 2/3\nThe answer is 2/3"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/062667.png | 062667 |
017615 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, does each side of the inner square equal to the length provided in the analysis?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Each side of the inner square is noted to be 14 inches, matching the provided figure. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/017615.png | 017615 |
012160 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how many axes of symmetry does the shape have?\nChoices:\nA. One\nB. Two\nC. Three\nD. Four"
},
{
"from": "gpt",
"value": "If the image depicts a common symmetric geometric figure, counting the axes through the center which divides the figure into identical halves helps ascertain the count. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/012160.png | 012160 |
071177 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Does the equation $w + 25 + 90 = 180$ hold true?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "This equation is set up according to the interior angle sum of a triangle, which states that all interior angles sum up to 180 degrees. As this is a fundamental property of triangles, the equation must hold true. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/071177.png | 071177 |
055404 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what geometric property justifies ER being parallel to BD?"
},
{
"from": "gpt",
"value": "The justification of ER being parallel to BD comes from the properties of similar triangles and corresponding angles. Setting up an equivalence of angles (EA X equals DA B and AE X equals AD B) confirms the parallel nature of these two segments through the geometric relationship between them. So the answer is Similarity and corresponding angles\nThe answer is Similarity and corresponding angles"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/055404.png | 055404 |
021417 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what geometric shapes comprise the figure whose surface area needs to be calculated?\nChoices:\nA. Two cylinders\nB. Two spheres\nC. One cylinder and one cone\nD. Two cubes"
},
{
"from": "gpt",
"value": "The figure is made up of two cylinders, one with a large radius and another with a small radius, attached at their bases. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/021417.png | 021417 |
058712 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how would you compute the curved surface area of a cylinder?"
},
{
"from": "gpt",
"value": "The formula to compute the curved surface area of a cylinder requires the radius and the height, which are both given in the image or can be measured. \nThe formula used is CSA = 2\\pi r h, where r is the radius, and h is the height. So the answer is 2\\pi r h\nThe answer is 2\\pi r h"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/058712.png | 058712 |
051675 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the measure of the angle opposite the side with length 57 units?"
},
{
"from": "gpt",
"value": "Using the tangent trigonometric function helps in calculating angle measures with opposite and adjacent sides known. Here, the angle opposite the side with length 57 units can be calculated as follows:\n\n\\(\\tan b = \\frac{\\text{opposite}}{\\text{adjacent}}\\) corresponds to \\(\\tan b = \\frac{57}{42}\\). Solving for b yields:\n\\(b = \\tan^{-1}\\left(\\frac{57}{42}\\right)\\).\n\nCalculate using a calculator to get b to one decimal place. So the answer is 53.6 degrees\nThe answer is 53.6 degrees"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/051675.png | 051675 |
046837 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which mathematical constant is necessary to calculate the circumference of the Ferris wheel?\nChoices:\nA. $e$\nB. $\\pi$\nC. $\\phi$\nD. $\\sqrt{2}$\nE. None of these"
},
{
"from": "gpt",
"value": "The mathematical constant $\\pi$ is necessary to calculate the circumference of the Ferris wheel as the formula used is $C = \\pi D$. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/046837.png | 046837 |
022707 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the gradient of the incline of the line?\nChoices:\nA. -2\nB. 2\nC. -1/2\nD. 1/2"
},
{
"from": "gpt",
"value": "The gradient or slope of a line on a graph determines its steepness relative to the x-axis. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/022707.png | 022707 |
042756 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the increase in investment value per year?\nChoices:\nA. $100\nB. $200\nC. $300\nD. $400"
},
{
"from": "gpt",
"value": "The formula V_n = 1000 + 200n suggests that the investment increases by $200 each year. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/042756.png | 042756 |
053637 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how long is the side of the triangle opposite the 69-degree angle considering the triangle is right-angled?"
},
{
"from": "gpt",
"value": "From the right triangle in the image, with a known hypotenuse of 23.4, calculate the opposite side using the sine of the given angle which is 69 degrees: \\sin 69^\\circ = \\frac{x}{23.4}. To find x, rearrange and calculate x = 23.4 \\times \\sin 69^\\circ. So the answer is 21.85\nThe answer is 21.85"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/053637.png | 053637 |
053352 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, explain the steps to find the precise perimeter if partial lengths are given and others are calculated."
},
{
"from": "gpt",
"value": "Compile all given side lengths from the image along with any side lengths computed such as through using parts (a) and (b). Once all lengths are known, add them together to find the perimeter, ensuring to follow any specific order or operation instructions given in the image. So the answer is Add together both given and calculated side lengths\nThe answer is Add together both given and calculated side lengths"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/053352.png | 053352 |
078846 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: If the least division on a scale is 5 kg, does this make the absolute error 2.5 kg?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Based on the guideline that the absolute error is half of the least division, a division of 5 kg will naturally result in an absolute error of 2.5 kg. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/078846.png | 078846 |
077537 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: In 1987, was the percentage of company funds from the total research and development budget more than 45%?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "With $8 billion of company funds and total funds of $16 billion, the contribution was 50%, which is greater than 45%. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/077537.png | 077537 |
007853 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the radius of the circle from which the sector is derived?\nChoices:\nA. 5.68 mm\nB. 11.35 mm\nC. 22.7 mm\nD. 45.4 mm"
},
{
"from": "gpt",
"value": "The sector is depicted with a radius that is half of 22.7 mm, making the radius 11.35 mm. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/007853.png | 007853 |
083164 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Form an expression for the average increase in the number of spectators in the stadium per minute in the first x minutes."
},
{
"from": "gpt",
"value": "How many people will have entered the stadium after x minutes? We need to consider the number that entered through the north entrance plus the number that entered through the south entrance.\n\nHow can we use this total amount to find the average rate that people enter the stadium?\n\nAfter x minutes, there will be 5x^2+9x^2 spectators in the stadium.\n\nTo find the average audience increase, we can imagine that all the 5x^2+9x^2 spectators arrive in a steady stream of people. The rate that these people will be flowing into the stadium will then be given by the fraction \\frac{\\text{total number of people }}{\\text{total time taken }}.\n\nAverage = \\frac{5x^2+9x^2}{x}spectators per minute\n\nEvaluate the addition in the numerator.\n\nAverage = \\frac{14x^2}{x} spectators per minute\n\nSimplify the fraction by dividing the numerator and the denominator by x. \\n 14x So the answer is 14x\nThe answer is 14x"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/083164.png | 083164 |
048636 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how many hundreds are there?\nChoices:\nA. 1\nB. 3\nC. 5\nD. 7"
},
{
"from": "gpt",
"value": "By observing the hundreds column formed by small cubes, there are 5 hundreds clearly displayed. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/048636.png | 048636 |
046671 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which principle can be used to find the circumference of the object?\nChoices:\nA. Pythagorean theorem\nB. Quadratic formula\nC. Circumference formula\nD. Area formula"
},
{
"from": "gpt",
"value": "As the object is circular, the circumference formula (2πr) should be used. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/046671.png | 046671 |
069804 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Is y=36 when x=1, using the expression y=45-9x?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Substituting x = 1 in the expression y=45-9x results in y = 45 - 9, which simplifies to y = 36. Hence, the answer is yes. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/069804.png | 069804 |
027393 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which point lies on the x-axis?\nChoices:\nA. Point Q\nB. Point V\nC. Both points\nD. Neither point"
},
{
"from": "gpt",
"value": "Point V is given as $V(1.2,0)$ which is on the x-axis, while point Q $(0.6,0.2)$ does not lie on the x-axis. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/027393.png | 027393 |
057257 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, calculate the combined perimeter of rectangles A and B."
},
{
"from": "gpt",
"value": "Rectangle A has dimensions 3 feet by 9 feet and rectangle B has dimensions 7 feet by 2 feet. Calculating their perimeters individually we get:\n$$P_A = 2(3 + 9) = 2 \\times 12 = 24 \\text{ feet}$$\n$$P_B = 2(7 + 2) = 2 \\times 9 = 18 \\text{ feet}$$\nAdding these perimeters provides the total perimeter of the two rectangles:\n$$24 + 18 = 42 \\text{ feet}$$ So the answer is 42 feet\nThe answer is 42 feet"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/057257.png | 057257 |
077986 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Considering a mathematics major student, is it correct to conclude that their favourite high school subject was probably not mathematics?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Yes, considering only the maths majors, a significant number, 43, indicated a preference for science rather than mathematics, demonstrating that favourite high school subjects can differ from their university major. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/077986.png | 077986 |
023332 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the maximum error possible in measuring the width of the box?\nChoices:\nA. 0 mm\nB. 0.5 mm\nC. 1 mm\nD. 2 mm"
},
{
"from": "gpt",
"value": "Given the measurements are made to the nearest millimeter, the maximum possible measurement error is 0.5 mm, which represents the half of the smallest measurement unit. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/023332.png | 023332 |
073976 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Is the formula for the area of a square equal to twice the product of the base and height?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "In fact, the formula of the area of a square is the square of its side length, not twice the product of the base and height. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/073976.png | 073976 |
065826 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how many cities are represented by the bar corresponding to 10-14 billboards on the graph?"
},
{
"from": "gpt",
"value": "Look at the bar graph and identify the bar that correlates to the 10-14 billboards range. Check the vertical axis for the value that corresponds to the height of this bar. So the answer is 1 city\nThe answer is 1 city"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/065826.png | 065826 |
084609 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Which line segment is a diameter?\nChoices:\nA. $A B$\nB. $A C$\nC. $B D$\nD. $O E$\nE. $A E$"
},
{
"from": "gpt",
"value": "$A C$ is a diameter because its endpoints are on the circle, and it passes through the center of the circle.$A C$ So the answer is B\nAnswer: $A C$"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/084609.png | 084609 |
015963 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, does any side of triangle XYZ measure exactly 30 km?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Compare each side length to 30 km. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/015963.png | 015963 |
081665 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Which of the following is most likely to be its slope?\nChoices:\nA. 0.33\nB. 0.03\nC. 3\nD. 0.3"
},
{
"from": "gpt",
"value": "The line is very nearly horizontal and so its slope will be very close to that of a horizontal line.\n\nWhat is the slope of a horizontal line? Which of these options is closest to that value?\n\n0.03 So the answer is B\nAnswer: 0.03"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/081665.png | 081665 |
084018 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: How much larger is the perimeter of the large rectangle than the perimeter of the small rectangle?\n\nForm an algebraic expression in factorised form."
},
{
"from": "gpt",
"value": "To find the difference, we need to find the perimeter of the larger rectangle and subtract from it the perimeter of the smaller rectangle.\n\nThe perimeter of a rectangle is equal to twice the sum of its length and width.\n\nThe larger rectangle has a length and width of 8 and 5.\n\nThe smaller rectangle has a length and width of x and x+3\n\n= 2\\left(8+5\\right)-2\\left(x+x+3\\right)\n\nCombine like terms within the brackets.\n\n= 2\\times 13-2\\left(2x+3\\right)\n\nEvaluate the product.\n\n= 26-2\\left(2x+3\\right)\n\nApply the Distributive Property A\\left(B+C\\right)=AB+AC.\n\n= 26-4x-6\n\nCombine the constant terms.\n\n= 20-4x\n\nFactor out the common factor.\n\n20 and 4 have a highest common factor of 4.\n\nTherefore, we can factor out 4. \\n 4\\left(5-x\\right) So the answer is 4\\left(5-x\\right)\nThe answer is 4\\left(5-x\\right)"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/084018.png | 084018 |
028765 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the value of y-coordinate of the first maximum point of the graph $y=5\\sin x+1$ for $x \\ge 0$?\nChoices:\nA. 1\nB. 5\nC. 6\nD. 0\nE. -1"
},
{
"from": "gpt",
"value": "The graph of $y=5 \\sin x+1$ is the graph of $y=\\sin x$ stretched vertically by a factor of 5 and translated 1 unit upwards. Hence, the first maximum occurs at $(x, y)=(90^\\circ, 6)$ So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/028765.png | 028765 |
027035 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what could be said about the zeroes of g in relation to f?\nChoices:\nA. Same zeroes as f\nB. Different zeroes from f\nC. g has more zeroes\nD. g has fewer zeroes"
},
{
"from": "gpt",
"value": "The vertical scaling does not affect the x-positions at which the graph intersects the x-axis. Therefore, the zeroes of g remain consistent with those of f. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/027035.png | 027035 |
058730 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the maximum possible volume that can be calculated from the given dimensions, assuming all measurements have been rounded down to the nearest whole number?"
},
{
"from": "gpt",
"value": "Given the rounding downwards rule, we add 0.5 cm to each length to find the maximum possible values before they were rounded. If the dimensions are width, length, and height, the max volume is calculated by multiplying these adjusted lengths. For instance, if the rounded dimensions observed are 13 cm, 13 cm, and 10 cm, then the adjusted dimensions would be 13.5 cm, 13.5 cm, and 10.5 cm. The maximum possible volume then is the product of these dimensions. So the answer is maximum volume = (13.5 cm x 13.5 cm x 10.5 cm) = 1913.625 cubic cm\nThe answer is maximum volume = (13.5 cm x 13.5 cm x 10.5 cm) = 1913.625 cubic cm"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/058730.png | 058730 |
076573 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Is the function equation y=2*sin(x)+3 displayed with a vertical shift of 3 units upwards?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Given that the function equation derived is y=2*sin(x)+3, it incorporates a vertical shift of 3 units upwards. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/076573.png | 076573 |
058019 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the radius of the cylindrical top piece?"
},
{
"from": "gpt",
"value": "From the calculation, it is necessary to know the radius for surface area computation, given as 5 mm in the problem analysis. So the answer is 5 mm\nThe answer is 5 mm"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/058019.png | 058019 |
031539 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, if the line is extended, which y-coordinate will correspond to an x-coordinate of -5?\nChoices:\nA. -11\nB. 5\nC. -5\nD. 0"
},
{
"from": "gpt",
"value": "Using the given line equation $y=\\frac{6}{5}x-5$, substituting x = -5: $y = \\frac{6}{5}(-5) - 5 = -6 - 5 = -11$. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/031539.png | 031539 |
022680 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the ratio of the radii of Cylinder I to Cylinder II?\nChoices:\nA. 25:18\nB. 18:25\nC. 36:50\nD. 50:36"
},
{
"from": "gpt",
"value": "Use the circumferences given for both cylinders to find each radius using $r = \\frac{C}{2\\pi}$. Then, form the ratio of the radii of Cylinder I to Cylinder II. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/022680.png | 022680 |
086426 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: The scatter plot above shows the perimeters and areas of 10 rectangles. What is the perimeter, in centimeters, of the rectangle represented by the data point that is farthest from the line of best fit (not shown)?\nChoices:\nA. 12\nB. 17\nC. 20\nD. 23"
},
{
"from": "gpt",
"value": "In the scatter plot, the first coordinate represents the perimeter of the rectangle and the second coordinate represents the area of the rectangle. Since the data point that is farthest from the line of best fit is located at $(20,12)$, the perimeter of the rectangle is 20 . So the answer is C\nAnswer: 20"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/086426.png | 086426 |
032328 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, identify the function that seems to have the steepest ascent?\nChoices:\nA. f\nB. g\nC. h"
},
{
"from": "gpt",
"value": "The graph of function g in the image shows a sharp rise, indicating it has the steepest slope. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/032328.png | 032328 |
085603 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: A polynomial p is graphed.\nWhat could be the equation of p?\nChoose 1 answer:\nChoices:\nA. p(x)=(2 x-1)^2(x-2)^3\nB. p(x)=(2 x-1)^3(x-2)^3\nC. p(x)=(2 x-1)^2(x-2)^2\nD. p(x)=(2 x-1)^3(x-2)^2"
},
{
"from": "gpt",
"value": "All the options have the same linear factors: $(2 x-1)$ and $(x-2)$. This makes sense, as the graph has zeros at $x=\\frac{1}{2}$ and $x=2$.\n\nThe difference between the options is in the multiplicity of the zeros. To determine which option is correct, we need to think about multiplicity:\n- If the multiplicity of a zero is an odd number, the graph will cross the $\\boldsymbol{x}$-axis at that zero.\n- If the multiplicity of a zero is an even number, the graph will only touch the $x$-axis at that zero.\n\nWe see that the graph crosses the $x$-axis at $x=\\frac{1}{2}$. So its multiplicity must be an odd number.\n\nWe see that the graph touches the $x$-axis at $x=2$. So its multiplicity must be an even number.\n\nIn conclusion, this is the correct answer:\n$$\np(x)=(2 x-1)^3(x-2)^2\n$$ \\n p(x)=(2 x-1)^3(x-2)^2 So the answer is D\nAnswer: p(x)=(2 x-1)^3(x-2)^2"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/085603.png | 085603 |
076569 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Is the formula of the function y = sin(x) only?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "The formula is defined in the analysis as y = sin(x) + 5, implying that y = sin(x) only is incorrect. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/076569.png | 076569 |
009695 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, determine the radius of the circle.\nChoices:\nA. equal to diameter\nB. half of the diameter\nC. twice the diameter\nD. unrelated"
},
{
"from": "gpt",
"value": "The radius is always half the measure of the diameter in every circle. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/009695.png | 009695 |
027094 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how does the graph of $g(x)$ differ from $f(x)$ in terms of vertical shift?\nChoices:\nA. Shifted up\nB. Shifted down\nC. No vertical shift\nD. Shifted both up and down"
},
{
"from": "gpt",
"value": "The dotted red line, representing $g(x)$, runs parallel to $f(x)$ without any apparent upward or downward shift, indicating no vertical translation. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/027094.png | 027094 |
050433 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, identify the type of triangle shown."
},
{
"from": "gpt",
"value": "Using the sides and angles given or visually depicted in the image, classify the triangle as isosceles, equilateral, or scalene. So the answer is scalene\nThe answer is scalene"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/050433.png | 050433 |
073343 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: With side length ratios given as 42:18 for two pentagons, is the perimeter ratio also 7:3?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "42:18 simplifies to 7:3. Hence, the perimeter ratio remains consistent with the side ratio. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/073343.png | 073343 |
065345 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how does the Difficulty Factor change over the years and what impact does it have on the cut off marks?"
},
{
"from": "gpt",
"value": "The Difficulty Factor increases from CET 1991 to CET 1990, but the cut off marks don't consistently increase; they mostly decrease, indicating that increased difficulty does not lead to higher cut off marks. So the answer is The Difficulty Factor increases over the years but inversely impacts the cut off marks by mostly leading to a decrease.\nThe answer is The Difficulty Factor increases over the years but inversely impacts the cut off marks by mostly leading to a decrease."
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/065345.png | 065345 |
060555 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the graph, what is the equation of the horizontal asymptote for the coffee's temperature as time passes?"
},
{
"from": "gpt",
"value": "To determine the equation of the horizontal asymptote, we observe the temperature graph as time approaches infinity. A horizontal asymptote indicates the value that the function approaches but does not necessarily reach. In this scenario, as time increases, the coffee's temperature graph levels out, and we mark a horizontal line at this level. So the answer is $C=20^{\\circ} \\mathrm{C}$\nThe answer is $C=20^{\\circ} \\mathrm{C}$"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/060555.png | 060555 |
063881 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what algebraic condition defines the domain of the logarithmic function?"
},
{
"from": "gpt",
"value": "The algebraic condition defining the domain of the logarithmic function in the image is derived from the requirement to prevent the argument of the logarithm from reaching non-positive values. The algebraic inequality $$2x - 3y + 1 > 0$$ precisely captures this requirement, and manipulating it provides the specific condition for permissible $(x, y)$ pairs. So the answer is The condition is $y < \\frac{2}{3}x + \\frac{1}{3}$, defining where the function is real and defined.\nThe answer is The condition is $y < \\frac{2}{3}x + \\frac{1}{3}$, defining where the function is real and defined."
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/063881.png | 063881 |
055142 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the $x$-coordinate common to points $B$ and $C$?"
},
{
"from": "gpt",
"value": "The image provides that points $B$ and $C$ share the same $x$-coordinate labeled as $a$. Therefore, the common $x$-coordinate for both points is $a$. So the answer is a\nThe answer is a"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/055142.png | 055142 |
073013 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Is the degree measure of arc ADC equivalent to that of two right angles?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "Since each right angle is 90 degrees and two would make 180 degrees, which is the measure of a semicircle like arc ADC. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/073013.png | 073013 |
069352 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the exact length of the hypotenuse in the triangle?"
},
{
"from": "gpt",
"value": "Using the values of $a = 8\\sqrt{2}$ and $b = 4$ in a right triangle, applying the Pythagorean theorem to find the hypotenuse $c$:\n$$\nc^2 = a^2 + b^2 \\\\\nc^2 = (8\\sqrt{2})^2 + (4)^2 \\\\\nc^2 = 128 + 16 \\\\\nc^2 = 144 \\\\\nc = 12 \n$$ So the answer is 12\nThe answer is 12"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/069352.png | 069352 |
056212 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the measure of the minor arc UV?"
},
{
"from": "gpt",
"value": "The measure of the minor arc UV can be determined by analyzing the total degrees in a circle minus the degrees of the major arc, which contains UV. Since the circle totals 360 degrees and the major arc is given as 198 degrees, the minor arc UV equals 360 degrees minus 198 degrees. So the answer is 162 degrees\nThe answer is 162 degrees"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/056212.png | 056212 |
022274 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, to what extent must the height of the pyramid be rounded off?\nChoices:\nA. To one decimal\nB. To two decimals\nC. To three decimals\nD. Exact figure"
},
{
"from": "gpt",
"value": "Reviewing the requirements for rounding off the computed height of the pyramid, a specific rounding precision is suggested in the process. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/022274.png | 022274 |
022541 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, is the aluminum block standalone or attached to another object?\nChoices:\nA. Standalone\nB. Attached"
},
{
"from": "gpt",
"value": "The image exhibits the aluminum block as a standalone object without any apparent attachments. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/022541.png | 022541 |
050617 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, find the final value for side $a$ after performing the calculation."
},
{
"from": "gpt",
"value": "After calculating $a^2 = 128$, the next step is taking the square root to find the value of $a$, which involves arithmetic operation visible in the image. So the answer is $8 \\sqrt{2}$\nThe answer is $8 \\sqrt{2}$"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/050617.png | 050617 |
022728 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the surface area formula of the conical part of the grain silo?\nChoices:\nA. pi r (r + sqrt(h^2 + r^2))\nB. 2 pi r h\nC. pi r (h + r)\nD. pi r^2 h"
},
{
"from": "gpt",
"value": "The surface area of a cone is calculated using the formula πr(r + sqrt(h^2 + r^2)), where r is the radius and h is the height. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/022728.png | 022728 |
028669 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, identify the midline of the function y=2-5\\cos x.\nChoices:\nA. y = 0\nB. y = 2\nC. y = -5\nD. y = 5"
},
{
"from": "gpt",
"value": "The midline of the function y=2-5\\cos x can be found by taking the average of the maximum and minimum values. Since the graph is centered around y = 2, that is the midline. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/028669.png | 028669 |
045678 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how many $\frac{3}{8}$ size pieces can you make from 1 whole?\nChoices:\nA. 2\nB. 3\nC. 4\nD. 6"
},
{
"from": "gpt",
"value": "Each $\frac{3}{8}$ size piece is made up of three $\frac{1}{8}$ size pieces. Count how many $\frac{3}{8}$ pieces you can make from 1 whole. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/045678.png | 045678 |
034731 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, find the area of the region by calculating the final integral $\\int_{-\\sqrt{2}}^{\\sqrt{2}} (4-2x^2) dx$.\nChoices:\nA. $\\frac{4 \\sqrt{2}}{3}$\nB. $\\frac{8 \\sqrt{2}}{3}$\nC. $\\frac{12 \\sqrt{2}}{3}$\nD. $\\frac{16 \\sqrt{2}}{3}$"
},
{
"from": "gpt",
"value": "To complete the area calculation of the region $D$, integrate the expression $(4-2x^2)$ from $x=-\\sqrt{2}$ to $x=\\sqrt{2}$. This evaluates to $\\frac{16 \\sqrt{2}}{3}$. So the answer is D\nAnswer: D"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/034731.png | 034731 |
044792 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which observation is correct regarding the students' interaction with the app's functionalities?\nChoices:\nA. Utilize login feature more\nB. Utilize posting feature more\nC. Utilize both features equally\nD. No specific utilization pattern observed"
},
{
"from": "gpt",
"value": "Observing that most of the plotted points have higher x values than y values indicates that students utilize the login feature of the app more than the posting feature. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/044792.png | 044792 |
019235 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how is the volume of the internal cylinder in the pipe determined?\nChoices:\nA. Using diameter\nB. Using radius\nC. Using circumference\nD. Using area"
},
{
"from": "gpt",
"value": "The volume of the internal cylinder is determined using its radius. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/019235.png | 019235 |
030344 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how does the steepness of the graph of y=4^x change as x increases?\nChoices:\nA. Increases\nB. Decreases\nC. Remains constant"
},
{
"from": "gpt",
"value": "The graph of y=4^x exhibits increasing steepness as x increases due to the exponential growth nature of the function, making the curve become steeper as x increases. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/030344.png | 030344 |
001697 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, calculate side $y$ where the hypotenuse is clearly marked as 10 units.\nChoices:\nA. 8 units\nB. 8.66 units\nC. 9 units\nD. 9.5 units"
},
{
"from": "gpt",
"value": "Implementing the Pythagorean theorem with defined triangle sides:\n$$y^2 + 5^2 = 10^2$$\n$$y^2 = 100 - 25$$\n$$y^2 = 75$$\n$$y = \\sqrt{75}$$\n$$y = 8.66$$ So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/001697.png | 001697 |
045736 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, are all the squares in the diagram of equal sizes?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "From the visual observation on the image, all the squares appear to be of equal size. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/045736.png | 045736 |
034732 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, at what points do the curves $y=1-x^2$ and $y=x^2-3$ intersect?\nChoices:\nA. $x = -1, x = 1$\nB. $x = 0, x = 3$\nC. $x = -\\sqrt{2}, x = \\sqrt{2}$\nD. $x = -2, x = 2$"
},
{
"from": "gpt",
"value": "Observing the image which includes the curves $y=1-x^2$ and $y=x^2-3$, they intersect where both equations yield the same $y$ value for the same $x$. Solving $1-x^2 = x^2-3$ gives the points of intersection as $x = -\\sqrt{2}, x = \\sqrt{2}$. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/034732.png | 034732 |
078889 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Is the fraction of the shaded area exactly 1 81/100?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "The analysis calculates the fraction of the shaded total as 1 81/100, where the first grid is completely shaded and the second grid has 81 of its 100 blocks shaded. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/078889.png | 078889 |
074793 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Is it possible to determine from the given information if the slowest speed was between 12 pm and 1 pm?\nChoices:\nA. Yes\nB. No"
},
{
"from": "gpt",
"value": "The provided information specifically discusses the fastest segment between 9 am and 10 am but does not provide comparative details about the slowest speed or time segment. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/074793.png | 074793 |
001487 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how is the straight line OP defined by the positions of O, B, and P?\nChoices:\nA. It is undefined\nB. It is defined as a segment\nC. It is defined by the collinearity of points O, B, and P\nD. It is defined as a bisector"
},
{
"from": "gpt",
"value": "Given the clear explanation that angle OBP equals 180 degrees, it signifies that points O, B, and P must lie in a straight alignment on line OP, highlighting their collinearity.\n\nThis relationship distinctly determines line OP's nature as defined by the collinear arrangement of these points. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/001487.png | 001487 |
021706 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, determine the base area of the cuboid.\nChoices:\nA. 130 cm^2\nB. 150 cm^2\nC. 169 cm^2\nD. 260 cm^2"
},
{
"from": "gpt",
"value": "The base area of a cuboid is calculated by multiplying its length and width. From the cuboid, we have length = 13 cm and width = 13 cm. Thus, Base Area = 13 x 13 = 169 cm^2. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/021706.png | 021706 |
083669 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: The given circle has centre at O, with AC=BC.Hence calculate \\angle ACO."
},
{
"from": "gpt",
"value": "Notice that \\angle ACO and \\angle BCO are supplementary angles.We can form an equation by stating that the sum of the two angles is 180^\\circ .State your reason:\\angle ACO+\\angle BCO=180(Angles forming a straight line are supplementary (sum to 180°)).Since \\angle ACO=\\angle BCO, we can rewrite \\angle ACO+\\angle BCO=180 in terms of \\angle ACO only.2\\angle ACO=180.\\n \\angle ACO=90 So the answer is \\angle ACO=90\nThe answer is \\angle ACO=90"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/083669.png | 083669 |
087295 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: This model shows $3 \\times 0.11$.\n\nMultiply. You can use the model to help.\n$$\n3 \\times 0.11=\n$$"
},
{
"from": "gpt",
"value": "This model shows $3 \\times 0.11$. There are 3 groups of blocks. Each group has 1 tenth and 1 hundredth, which is the same as 0.11 .\n\nTo find $3 \\times 0.11$, first find the total number of hundredths. Each of the 3 groups of blocks has 1 hundredth.\n$$\n3 \\times 1 \\text { hundredth }=3 \\text { hundredths }\n$$\n\nNow, find the total number of tenths. Each of the 3 groups of blocks has 1 tenth.\n$$\n3 \\times 1 \\text { tenth }=3 \\text { tenths }\n$$\n\nThere are $\\mathbf{3}$ tenths and $\\mathbf{3}$ hundredths in all. This is the same as 0.33 .\n$$\n3 \\times 0.11=0.33\n$$ So the answer is 0.33\nThe answer is 0.33"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/087295.png | 087295 |
000742 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the relationship between sides $a$, $b$, and $c$ in a right triangle?\nChoices:\nA. a^2 + b^2 = c^2\nB. a + b = c\nC. a^2 + c^2 = b^2\nD. a + c = b"
},
{
"from": "gpt",
"value": "In a right triangle, the relationship between the lengths of the sides is given by the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/000742.png | 000742 |
056359 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the total length of the straight segments of the quarter circle?"
},
{
"from": "gpt",
"value": "The quarter circle includes two straight segments, each equal to the radius, which is 1 foot, thus totaling 2 feet. So the answer is 2 feet\nThe answer is 2 feet"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/056359.png | 056359 |
062059 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the area of the triangle formed by the points (0,0), (-4,0), and (-4,-6)?"
},
{
"from": "gpt",
"value": "The area of a right triangle is given by 0.5 multiplied by the product of the lengths of its legs. The lengths of the legs are 4 units and 6 units respectively. So the answer is 0.5 * 4 units * 6 units\nThe answer is 0.5 * 4 units * 6 units"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/062059.png | 062059 |
051166 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, calculate the new area of the rectangle if both dimensions were increased by the rounding error:"
},
{
"from": "gpt",
"value": "With each dimension (length and width) increased by \\(0.05\\) meters due to rounding errors, the revised dimensions are calculated as \\(15.3 + 0.05\\) for length and \\(6.1 + 0.05\\) for width. Multiplying these adjusted dimensions gives the area: \\((15.35) \\times (6.15) = 94.4025\\) square meters. So the answer is 94.4025 square meters\nThe answer is 94.4025 square meters"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/051166.png | 051166 |
021822 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the total surface area of the two identical side walls?\nChoices:\nA. 30 m^2\nB. 60 m^2\nC. 120 m^2\nD. 240 m^2"
},
{
"from": "gpt",
"value": "Given the dimensions of the rectangle for each side wall are 10 m and 6 m:\n\nSurface area of one side wall = 10 m * 6 m = 60 m^2.\n\nTo find the total surface area for both side walls, multiply the area of one side wall by 2: \n\n60 m^2 * 2 = 120 m^2. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/021822.png | 021822 |
038039 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which industry has the smallest number of employees per establishment?\nChoices:\nA. Construction\nB. Wholesale Trade\nC. Retail Trade\nD. Manufacturing\nE. Transportation and Warehousing"
},
{
"from": "gpt",
"value": "Calculate the number of employees per establishment by dividing total employees by total establishments for each industry and identify the one with the smallest ratio. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/038039.png | 038039 |
085815 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Consider the graph of the equation $y=4^{x}$.\n\nWhat do we call the horizontal line $y=0$, which $y=4^{x}$ gets closer and closer to but never intersects?\nChoices:\nA. A horizontal asymptote of the curve.\nB. An $x$-intercept of the curve.\nC. A $y$-intercept of the curve."
},
{
"from": "gpt",
"value": "Notice that the graph approaches $y=0$ for very large negative values of $x$. Which options can we exclude?\n\nA $y$-intercept is a point where the graph crosses the $y$-axis.\n\nAn $x$-intercept is a point where the graph crosses the $x$-axis.\n\nA horizontal asymptote of the curve. So the answer is A\nAnswer: A horizontal asymptote of the curve."
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/085815.png | 085815 |
012889 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what fraction of the total area is not shaded?\nChoices:\nA. $1 / 2$\nB. $1 / 4$\nC. 3/4\nD. 1"
},
{
"from": "gpt",
"value": "Considering the total area of the square is 1, and the shaded area is about half of it, the unshaded area would account for the other half. Thus, the fraction of the area that is unshaded is also $1 / 2$. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/012889.png | 012889 |
056622 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what fraction represents the perimeter of the larger pentagon as compared to the smaller pentagon?"
},
{
"from": "gpt",
"value": "The image provides dimensions that can be used to derive the ratio of the side lengths of two pentagons, recorded as 7 and 3. Since the perimeter of a pentagon is the sum of its side lengths, the total perimeter of each pentagon is directly proportional to the lengths of its sides. With side length proportions given, the ratio of perimeters is calculated by setting up a ratio $$\\frac{7}{3} = \\frac{P_1}{P_2}$$, thus expressing $$P_1:P_2$$ in fractional form as $$\\frac{7}{3}$$. So the answer is 7/3\nThe answer is 7/3"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/056622.png | 056622 |
043922 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, which decade had a reduction in fossil fuel consumption?\nChoices:\nA. 1960-1970\nB. 1970-1980\nC. 1980-1990\nD. None"
},
{
"from": "gpt",
"value": "If any portion of the graph shows a downward trend over a decade, that decade experienced a reduction in consumption. So the answer is D\nAnswer: D"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/043922.png | 043922 |
079868 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Find the area of the rectangle shown."
},
{
"from": "gpt",
"value": "Area Of Rectangle $=$ Length $\\times$ Width\n\nMultiply the length by the width to find the area.\n\nArea $=7 \\times 4 \\mathrm{~cm}^{2}$\n\nEvaluate the expression.\n\nArea $=28 \\mathrm{~cm}^{2}$ So the answer is Area $=28 \\mathrm{~cm}^{2}$\nThe answer is Area $=28 \\mathrm{~cm}^{2}$"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/079868.png | 079868 |
053465 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the angle adjacent to theta?"
},
{
"from": "gpt",
"value": "Examine the placement of angle theta within the triangle shown in the image. The adjacent angle to angle theta is the angle that shares a common side with angle theta and is not the right angle. So the answer is Angle at point C\nThe answer is Angle at point C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/053465.png | 053465 |
019274 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how does the relationship between 'R' and 'r' affect the torus shape?\nChoices:\nA. Varying 'R' and 'r' changes the thickness and the central hole size\nB. 'R' and 'r' must be equal for it to be a torus\nC. Decreasing 'r' has no effect\nD. Increasing 'R' decreases the overall size"
},
{
"from": "gpt",
"value": "The relative sizes of 'R' and 'r' are pivotal as they determine the thickness of the tube (via 'r') and size of the central void (via 'R'). Their proportions influence both the aesthetic and structural aspects of the torus. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/019274.png | 019274 |
021692 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what aspect of geometry does the number 33.1 correspond to regarding the cylinder?\nChoices:\nA. Is used as a multiplier\nB. Acts as a radian measure\nC. Is the height\nD. Is the radius"
},
{
"from": "gpt",
"value": "The number 33.1 pertains to the height aspect of the cylinder, essential for calculating the curved surface area using the formula 2πrh. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/021692.png | 021692 |
033072 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what does the constant 'h' specifically affect in $g(x) = f(x-h) - k$?\nChoices:\nA. Translation left/right\nB. Translation up/down\nC. Stretching\nD. Shrinking"
},
{
"from": "gpt",
"value": "The constant $h$ results in the horizontal movement, indicating a left/right translation. So the answer is A\nAnswer: A"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/033072.png | 033072 |
058001 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is the measure of the largest possible single face area from one of the boxes?"
},
{
"from": "gpt",
"value": "Among the face dimensions provided, the biggest is 25x33 units. Calculating this area requires simple multiplication of these dimensions, which would give the largest single face area. So the answer is 825 square units\nThe answer is 825 square units"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/058001.png | 058001 |
059099 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, estimate the expenditure for the marquee's material, using the per square meter price provided."
},
{
"from": "gpt",
"value": "Compute the total cost by multiplying the surface area displayed in the image by the material cost per square meter. So the answer is Total cost = Total area in m^2 × Material cost per m^2\nThe answer is Total cost = Total area in m^2 × Material cost per m^2"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/059099.png | 059099 |
052060 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, how does the total length of the shorter sides compare to one longer side of the kite?"
},
{
"from": "gpt",
"value": "The total length of the shorter sides is $6 cm + 6 cm = 12 cm$. Each longer side is 16 cm. Therefore, the total of the shorter sides is less than the length of one longer side. So the answer is The total length of two shorter sides is less than the length of one longer side.\nThe answer is The total length of two shorter sides is less than the length of one longer side."
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/052060.png | 052060 |
018053 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the coefficient of x in the area formula of the parallelogram?\nChoices:\nA. 2\nB. 6\nC. 3\nD. 1"
},
{
"from": "gpt",
"value": "Checking the simplified form of the area formula, 2x^2 + 6x, reveals that the coefficient of x is 6. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/018053.png | 018053 |
053396 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: Based on the image, what is x if you subtract the total of two 2 mm sides from a 13 mm side?"
},
{
"from": "gpt",
"value": "From the diagram, x can be determined by summing the lengths of the two shorter sides (each 2 mm) and then subtracting this total from the longest side's length (13 mm). So the answer is 9 mm\nThe answer is 9 mm"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/053396.png | 053396 |
023219 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, how many edges does the shape encompass?\nChoices:\nA. 6\nB. 8\nC. 12\nD. 14"
},
{
"from": "gpt",
"value": "The rectangular prism in the image is defined by 12 edges creating its structure. So the answer is C\nAnswer: C"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/023219.png | 023219 |
034850 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first perform reasoning, then finally select the right answer from the choices, e.g., Answer: xxx.\nQuestion: Based on the image, what is the expression for u when y=2?\nChoices:\nA. u=3\nB. u=1\nC. u=2\nD. u=4"
},
{
"from": "gpt",
"value": "In the transformed each of the boundary curves, the expression for u when y=2 has been found to be u=1. So the answer is B\nAnswer: B"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/034850.png | 034850 |
083368 | [
{
"from": "human",
"value": "<image>\nAccording to the question shown in the image, please first conduct reasoning, and then answer the question and provide the final value, e.g., The answer is xxx\nQuestion: We want to prove that the area of a quadrilateral is half the product of the diagonals times the sine of the angle between the diagonals.\n\nHence, prove the above result for the area of the quadrilateral $A C B D$."
},
{
"from": "gpt",
"value": "What is the relationship between the area of the quadrilateral and the areas of the triangles we found above?\n\nThe area of the quadrilateral is the sum of the areas of the four triangles.\n\nArea $=R+S+Q+T$\n\nUse the answers from to parts (b) to (e) to write the area of quadrilateral $A B C D$ as the sum of the areas of four triangles.\n\nArea $=\\frac{1}{2} a c \\sin \\theta+\\frac{1}{2} a d \\sin \\theta+\\frac{1}{2} b c \\sin \\theta+\\frac{1}{2} b d \\sin \\theta$\n\nTake out the common factor from each term.\n\nArea $=\\frac{1}{2} \\sin \\theta(a c+a d+b c+b d)$\n\nFactorise terms inside the brackets.\n\nArea $=\\frac{1}{2} \\sin \\theta(a(c+d)+b(c+d))$\n\nFactorise terms inside the brackets again to get an equation like the one you wrote down in part (a).\n\nArea $=\\frac{1}{2}(a+b)(c+d) \\sin \\theta$ So the answer is Area $=\\frac{1}{2}(a+b)(c+d) \\sin \\theta$\nThe answer is Area $=\\frac{1}{2}(a+b)(c+d) \\sin \\theta$"
}
]
| mavis_math_metagen_processed_new.json | LLaVA-OneVision-Data/mavis_math_metagen/083368.png | 083368 |
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