messages listlengths 2 2 | instruction_seed stringlengths 43 759 | response_seed stringlengths 43 759 | _source stringclasses 1
value | _fasttext_score float64 1 1 | reasoning stringlengths 1.41k 73.4k | deepseek_solution stringlengths 489 2.54k | __original_row_idx int64 181 31.5k | final_reasoning_trace stringlengths 2.07k 75.1k | conversations listlengths 2 2 |
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[
{
"content": "In a trapezoid, the measures of the two base angles are $60^\\circ$ and $70^\\circ$, while the measures of the other two interior angles are equal. Determine the degree measure of the largest interior angle of this trapezoid.",
"role": "user"
},
{
"content": "The interior angles of a t... | In a trapezoid, the measures of the two base angles are $60^\circ$ and $70^\circ$, while the measures of the other two interior angles are equal. Determine the degree measure of the largest interior angle of this trapezoid. | In a trapezoid, the measures of the two base angles are $60^\circ$ and $70^\circ$, while the measures of the other two interior angles are equal. Determine the degree measure of the largest interior angle of this trapezoid. | ai2-adapt-dev/openmath-2-math | 0.99811 | Okay, so I have this trapezoid problem here. Let me try to figure it out step by step. The problem says: In a trapezoid, the measures of the two base angles are 60 degrees and 70 degrees, while the measures of the other two interior angles are equal. We need to determine the degree measure of the largest interior angle... | Given a trapezoid with two base angles measuring \(60^\circ\) and \(70^\circ\), and the other two interior angles being equal, we need to determine the degree measure of the largest interior angle.
1. **Sum of Interior Angles**: The sum of the interior angles of any quadrilateral is \(360^\circ\).
2. **Given Angles**:... | 17,335 | <think>
Okay, so I have this trapezoid problem here. Let me try to figure it out step by step. The problem says: In a trapezoid, the measures of the two base angles are 60 degrees and 70 degrees, while the measures of the other two interior angles are equal. We need to determine the degree measure of the largest interi... | [
{
"from": "human",
"value": "In a trapezoid, the measures of the two base angles are $60^\\circ$ and $70^\\circ$, while the measures of the other two interior angles are equal. Determine the degree measure of the largest interior angle of this trapezoid."
},
{
"from": "gpt",
"value": "<think>\nO... |
[
{
"content": "The sum of the squares of two numbers is $13$, and the product of the two numbers is $-4$. Find the absolute value of the difference between the two numbers.",
"role": "user"
},
{
"content": "Let the two numbers be $x$ and $y$. We know:\n\n1. The sum of the squares of the two numbers i... | The sum of the squares of two numbers is $13$, and the product of the two numbers is $-4$. Find the absolute value of the difference between the two numbers. | The sum of the squares of two numbers is $13$, and the product of the two numbers is $-4$. Find the absolute value of the difference between the two numbers. | ai2-adapt-dev/openmath-2-math | 0.99854 | Okay, so I need to find the absolute value of the difference between two numbers. The problem says that the sum of their squares is 13, and their product is -4. Hmm, let me think about how to approach this.
First, let's call the two numbers x and y. Then, according to the problem:
1. \( x^2 + y^2 = 13 \)
2. \( xy = -... | Given two numbers \( x \) and \( y \) such that the sum of their squares is 13 and their product is -4, we need to find the absolute value of the difference between the two numbers.
We start with the given equations:
1. \( x^2 + y^2 = 13 \)
2. \( xy = -4 \)
We use the identity for the square of the difference of two ... | 16,145 | <think>
Okay, so I need to find the absolute value of the difference between two numbers. The problem says that the sum of their squares is 13, and their product is -4. Hmm, let me think about how to approach this.
First, let's call the two numbers x and y. Then, according to the problem:
1. \( x^2 + y^2 = 13 \)
2. \... | [
{
"from": "human",
"value": "The sum of the squares of two numbers is $13$, and the product of the two numbers is $-4$. Find the absolute value of the difference between the two numbers."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the absolute value of the difference between ... |
[
{
"content": "The ratio of the areas of two similar triangles is 4:9, and the length of the corresponding side of the larger triangle is 6 cm. Find the length of the corresponding side of the smaller triangle.",
"role": "user"
},
{
"content": "Since the ratio of the areas of the two similar triangle... | The ratio of the areas of two similar triangles is 4:9, and the length of the corresponding side of the larger triangle is 6 cm. Find the length of the corresponding side of the smaller triangle. | The ratio of the areas of two similar triangles is 4:9, and the length of the corresponding side of the larger triangle is 6 cm. Find the length of the corresponding side of the smaller triangle. | ai2-adapt-dev/openmath-2-math | 0.998805 | Okay, so I need to find the length of a corresponding side of the smaller triangle when the ratio of the areas is 4:9 and the larger triangle's side is 6 cm. Hmm, let me think.
First, I remember that when two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding si... | The ratio of the areas of two similar triangles is given as 4:9. Since the ratio of the areas of similar triangles is the square of the ratio of their corresponding sides, we first find the ratio of the sides by taking the square root of the area ratio:
\[
\sqrt{\frac{4}{9}} = \frac{2}{3}
\]
This means the ratio of t... | 23,002 | <think>
Okay, so I need to find the length of a corresponding side of the smaller triangle when the ratio of the areas is 4:9 and the larger triangle's side is 6 cm. Hmm, let me think.
First, I remember that when two triangles are similar, the ratio of their areas is equal to the square of the ratio of their correspo... | [
{
"from": "human",
"value": "The ratio of the areas of two similar triangles is 4:9, and the length of the corresponding side of the larger triangle is 6 cm. Find the length of the corresponding side of the smaller triangle."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the len... |
[{"content":"Given a function $f(n)$ that calculates the product of the digits of positive integer $(...TRUNCATED) | "Given a function $f(n)$ that calculates the product of the digits of positive integer $n$, determin(...TRUNCATED) | "Given a function $f(n)$ that calculates the product of the digits of positive integer $n$, determin(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | 0.998277 | "Okay, so I need to figure out which values could be the result of f(2n) given that f(n) = 24. Let m(...TRUNCATED) | "Given a function \\( f(n) \\) that calculates the product of the digits of a positive integer \\( n(...TRUNCATED) | 20,860 | "<think>\nOkay, so I need to figure out which values could be the result of f(2n) given that f(n) = (...TRUNCATED) | [{"from":"human","value":"Given a function $f(n)$ that calculates the product of the digits of posit(...TRUNCATED) |
[{"content":"Let $(b_1,b_2,b_3,\\ldots,b_{12})$ be a sequence of 12 distinct positive integers such (...TRUNCATED) | "Let $(b_1,b_2,b_3,\\ldots,b_{12})$ be a sequence of 12 distinct positive integers such that the sum(...TRUNCATED) | "Let $(b_1,b_2,b_3,\\ldots,b_{12})$ be a sequence of 12 distinct positive integers such that the sum(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | 0.998887 | "Alright, let's try to tackle this problem step by step. The problem says:\n\nWe have a sequence of (...TRUNCATED) | "Given a sequence of 12 distinct positive integers \\((b_1, b_2, b_3, \\ldots, b_{12})\\) such that (...TRUNCATED) | 477 | "<think>\nAlright, let's try to tackle this problem step by step. The problem says:\n\nWe have a seq(...TRUNCATED) | [{"from":"human","value":"Let $(b_1,b_2,b_3,\\ldots,b_{12})$ be a sequence of 12 distinct positive i(...TRUNCATED) |
[{"content":"If $(x+2)(x-3)=14$, find the sum of the possible values of $x$.","role":"user"},{"conte(...TRUNCATED) | If $(x+2)(x-3)=14$, find the sum of the possible values of $x$. | If $(x+2)(x-3)=14$, find the sum of the possible values of $x$. | ai2-adapt-dev/openmath-2-math | 0.998318 | "Okay, so I need to solve the equation (x + 2)(x - 3) = 14 and find the sum of the possible values o(...TRUNCATED) | "To solve the equation \\((x + 2)(x - 3) = 14\\) and find the sum of the possible values of \\(x\\),(...TRUNCATED) | 29,550 | "<think>\nOkay, so I need to solve the equation (x + 2)(x - 3) = 14 and find the sum of the possible(...TRUNCATED) | [{"from":"human","value":"If $(x+2)(x-3)=14$, find the sum of the possible values of $x$."},{"from":(...TRUNCATED) |
[{"content":"The graph of the equation \\[\\sqrt{x^2+y^2} + |y+2| = 5\\]consists of portions of two (...TRUNCATED) | "The graph of the equation \\[\\sqrt{x^2+y^2} + |y+2| = 5\\]consists of portions of two different pa(...TRUNCATED) | "The graph of the equation \\[\\sqrt{x^2+y^2} + |y+2| = 5\\]consists of portions of two different pa(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | 0.997659 | "Okay, let's try to tackle this problem. The equation given is √(x² + y²) + |y + 2| = 5. Hmm, I (...TRUNCATED) | "The given equation is \\(\\sqrt{x^2 + y^2} + |y + 2| = 5\\). We need to analyze this equation by co(...TRUNCATED) | 6,715 | "<think>\nOkay, let's try to tackle this problem. The equation given is √(x² + y²) + |y + 2| = 5(...TRUNCATED) | [{"from":"human","value":"The graph of the equation \\[\\sqrt{x^2+y^2} + |y+2| = 5\\]consists of por(...TRUNCATED) |
[{"content":"In the expansion of $(x+y+z)^6$, determine the coefficient of the $x^2y^2z^2$ term.","r(...TRUNCATED) | In the expansion of $(x+y+z)^6$, determine the coefficient of the $x^2y^2z^2$ term. | In the expansion of $(x+y+z)^6$, determine the coefficient of the $x^2y^2z^2$ term. | ai2-adapt-dev/openmath-2-math | 0.999228 | "Okay, so I need to find the coefficient of the term \\(x^2y^2z^2\\) in the expansion of \\((x + y +(...TRUNCATED) | "To determine the coefficient of the \\(x^2y^2z^2\\) term in the expansion of \\((x + y + z)^6\\), w(...TRUNCATED) | 20,165 | "<think>\nOkay, so I need to find the coefficient of the term \\(x^2y^2z^2\\) in the expansion of \\(...TRUNCATED) | [{"from":"human","value":"In the expansion of $(x+y+z)^6$, determine the coefficient of the $x^2y^2z(...TRUNCATED) |
[{"content":"The product $P$ of three positive integers is $7$ times the square of the largest numbe(...TRUNCATED) | "The product $P$ of three positive integers is $7$ times the square of the largest number, and two o(...TRUNCATED) | "The product $P$ of three positive integers is $7$ times the square of the largest number, and two o(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | 0.998939 | "Okay, let's try to tackle this problem. So, we have three positive integers, let's call them a, b, (...TRUNCATED) | "Given three positive integers \\(a\\), \\(b\\), and \\(c\\) such that their product \\(P\\) is 7 ti(...TRUNCATED) | 4,211 | "<think>\nOkay, let's try to tackle this problem. So, we have three positive integers, let's call th(...TRUNCATED) | [{"from":"human","value":"The product $P$ of three positive integers is $7$ times the square of the (...TRUNCATED) |
[{"content":"The measures of the angles of a triangle are in the ratio 5:6:7. What is the number of (...TRUNCATED) | "The measures of the angles of a triangle are in the ratio 5:6:7. What is the number of degrees in t(...TRUNCATED) | "The measures of the angles of a triangle are in the ratio 5:6:7. What is the number of degrees in t(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | 0.997509 | "Okay, so the problem is about a triangle where the measures of the angles are in the ratio 5:6:7. I(...TRUNCATED) | "The measures of the angles of a triangle are in the ratio 5:6:7. To find the number of degrees in t(...TRUNCATED) | 22,398 | "<think>\nOkay, so the problem is about a triangle where the measures of the angles are in the ratio(...TRUNCATED) | [{"from":"human","value":"The measures of the angles of a triangle are in the ratio 5:6:7. What is t(...TRUNCATED) |
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