messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Evaluate: ((-195 + 240/15) * 9) + 4^3 - log_4(64) + (-98 mod 12) + round(41/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-195 + 240/15) * 9) + 4^3 - log_4(64) + (-98 mod 12) + round(41/2) $\n\nCompute ea... | {
"type": "arithmetic",
"seed": 1337,
"index": 4800
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Prove that $f(x,y)=\\frac12(4x^2+2y^2)+3x+-3y+7$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(4x^2+2y^2)+3x+-3y+7 $\n\n$ \\frac{\\partial^2 f}{\\parti... | {
"type": "optimization",
"seed": 1337,
"index": 4801
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. 601x + 647 = 582"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 601x + 647 = 582 $\n\nMove all terms to the left (standard form):\n$ 601x + 65 = 0 $\n\nIsolate the $x$ term:\n$ 601x = -65 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4802
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. -434 + 686 = -321x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -434 + 686 = -321x $\n\nMove all terms to the left (standard form):\n$ 321x + 252 = 0 $\n\nIsolate the $x$ term:\n$ 321x = -252 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4803
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve for $x$ (in radians): sin(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\a... | {
"type": "trigonometry",
"seed": 1337,
"index": 4804
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. -47x + 1 + 105 = -167x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47x + 1 + 105 = -167x^2 $\n\nMove all terms to the left (standard form):\n$ 167x^2 + -47x + 106 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4805
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Find $A^{-1}$ for $A=\\begin{pmatrix}5&-7\\\\-9&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 5 & -7 \\\\ -9 & 5 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4806
} |
[
{
"role": "user",
"content": "Determine the answer to the equation shown. -47x^2 + 121 - 187x = 181"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47x^2 + 121 - 187x = 181 $\n\nMove all terms to the left (standard form):\n$ -47x^2 + -187x + -60 = 0 $\n\nApply the quadratic for... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4807
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Find the modular inverse of 19 modulo 26, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $19\\cdot a^{-1} \\equiv 1 \\pmod{26}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4808
} |
[
{
"role": "user",
"content": "Solve the following math equation. Compute $(-21+129) \\bmod 15$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-21+129) \\bmod 15 $\n\nUse the rule that addition is compatible with reduction modulo $n... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4809
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? -27 - 46x + 136 = 88x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -27 - 46x + 136 = 88x^2 $\n\nMove all terms to the left (standard form):\n$ -88x^2 + -46x + 109 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4810
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Evaluate: ((-45 + -25/25) * 1) + 2^4 - log_7(2401) + (-360 mod 8) + ceil(-114/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-45 + -25/25) * 1) + 2^4 - log_7(2401) + (-360 mod 8) + ceil(-114/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4811
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Evaluate: ((137 + -468/12) * 6) + 3^5 - log_8(8) + (257 mod 17) + ceil(-82/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((137 + -468/12) * 6) + 3^5 - log_8(8) + (257 mod 17) + ceil(-82/2) $\n\nCom... | {
"type": "arithmetic",
"seed": 1337,
"index": 4812
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -47 - 109x - 62x^2 = -18"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47 - 109x - 62x^2 = -18 $\n\nMove all terms to the left (standard form):\n$ -62x^2 + -109x + -29 = 0 $\n\nApply the quadratic f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4813
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Find the modular inverse of 4 modulo 39, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $4\\cdot a^{-1} \\equiv 1 \\pmod{39}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees intege... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4814
} |
[
{
"role": "user",
"content": "Solve the equation and return the answer. -444x + 879 = 968"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -444x + 879 = 968 $\n\nMove all terms to the left (standard form):\n$ -444x + -89 = 0 $\n\nIsolate the $x$ term:\n$ -444x = 89 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4815
} |
[
{
"role": "user",
"content": "Solve this equation step by step. Differentiate with respect to $x$: $f(x) = (2x + 9)\\sin(3x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (2x + 9)\\sin(3x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{2\\sin(3... | {
"type": "calculus",
"seed": 1337,
"index": 4816
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Evaluate: ((163 + -286/22) * 16) + 12^3 - log_5(5) + (-13 mod 17) + round(-168/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((163 + -286/22) * 16) + 12^3 - log_5(5) + (-13 mod 17) + round(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 4817
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Compute the indefinite integral: $\\int \\ln(1x + 9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + 9)\\,dx $\n\nUse standard antiderivatives (and integration by parts if n... | {
"type": "calculus",
"seed": 1337,
"index": 4818
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. 722 + 431x = -97"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 722 + 431x = -97 $\n\nMove all terms to the left (standard form):\n$ 431x + 819 = 0 $\n\nIsolate the $x$ term:\n$ 431x = -819 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 4819
} |
[
{
"role": "user",
"content": "Calculate the solution to this math equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 4820
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. -790 + 627x = -212"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -790 + 627x = -212 $\n\nMove all terms to the left (standard form):\n$ 627x + -578 = 0 $\n\nIsolate the $x$ term:\n$ 627x = 578 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 4821
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Compute the determinant: $A=\\begin{pmatrix}-6&-6\\\\-4&-1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-6&-6\\\\\\-4&-1\\end{pmatrix} ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4822
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((137 + -792/18) * 6) + 12^4 - log_7(16807) + (-437 mod 9) + ceil(46/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((137 + -792/18) * 6) + 12^4 - log_7(16807) + (-437 mod 9) + ceil(46/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4823
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 4824
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Evaluate: ((-81 + -50/5) * 16) + 6^5 - log_3(81) + (-435 mod 7) + ceil(-127/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-81 + -50/5) * 16) + 6^5 - log_3(81) + (-435 mod 7) + ceil(-127/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4825
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$... | {
"type": "trigonometry",
"seed": 1337,
"index": 4826
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. -655x - 49 = 99"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -655x - 49 = 99 $\n\nMove all terms to the left (standard form):\n$ -655x + -148 = 0 $\n\nIsolate the $x$ term:\n$ -655x = 148 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4827
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Evaluate: ((119 + 374/22) * 20) + 11^3 - log_5(25) + (494 mod 6) + ceil(95/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((119 + 374/22) * 20) + 11^3 - log_5(25) + (494 mod 6) + ceil(95/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4828
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Compute the indefinite integral: $\\int (-3x + 0)\\sin(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-3x + 0)\\sin(6x)\\,dx $\n\nUse standard antiderivatives (and i... | {
"type": "calculus",
"seed": 1337,
"index": 4829
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. -49x + 19x^2 + 175 = -15"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -49x + 19x^2 + 175 = -15 $\n\nMove all terms to the left (standard form):\n$ 19x^2 + -49x + 190 = 0 $\n\nApply the quadratic formula:\n$ x = ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4830
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. -675 + 41x = 452"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -675 + 41x = 452 $\n\nMove all terms to the left (standard form):\n$ 41x + -1127 = 0 $\n\nIsolate the $x$ term:\n$ 41x = 1127 $\n\nDi... | {
"type": "linear_equation",
"seed": 1337,
"index": 4831
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-7&7\\\\1&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -7 & 7 \\\\ 1 & 8 \\end{pmatrix} $\n\nCompu... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4832
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Find the modular inverse of 9 modulo 22, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $9\\cdot a^{-1} \\equiv 1 \\pmod{22}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guara... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4833
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. 127 + 737x = 261"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 127 + 737x = 261 $\n\nMove all terms to the left (standard form):\n$ 737x + -134 = 0 $\n\nIsolate the $x$ term:\n$ 737x = 134 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 4834
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Solve for $x$ (in radians): tan(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 0 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(0) = 0 $\n\nThe genera... | {
"type": "trigonometry",
"seed": 1337,
"index": 4835
} |
[
{
"role": "user",
"content": "Can you solve the equation below? + 45x^2 + 10 = 193x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ + 45x^2 + 10 = 193x $\n\nMove all terms to the left (standard form):\n$ 45x^2 + -193x + 10 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4836
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Compute $(129+-176) \\bmod 7$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (129+-176) \\bmod 7 $\n\nUse the rule that addition is compatible with r... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4837
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Differentiate with respect to $x$: $f(x) = 7\\sin(2x) + 9\\cos(4x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7\\sin(2x) + 9\\cos(4x) $\n\nApply the standard differentiation rules:\n... | {
"type": "calculus",
"seed": 1337,
"index": 4838
} |
[
{
"role": "user",
"content": "Resolve the equation provided. -9x - 199 + 79x^2 = 47"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -9x - 199 + 79x^2 = 47 $\n\nMove all terms to the left (standard form):\n$ 79x^2 + -9x + -246 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4839
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Differentiate with respect to $x$: $f(x) = \\ln(6x + 2)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(6x + 2) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac... | {
"type": "calculus",
"seed": 1337,
"index": 4840
} |
[
{
"role": "user",
"content": "solve: \n\n Compute the determinant: $A=\\begin{pmatrix}-4&-9\\\\0&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&-9\\\\\\0&-4\\end{pmatrix} $\n\nUse $\\det(A)=ad-bc$: \n$ \\det(A... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4841
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Prove that $(\\mathbb{Z}_10, +)$ is a group under addition modulo 10."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_10=\\{0,1,\\dots,9\\}$ with operation $+$ modulo $10$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4842
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Evaluate: ((164 + 840/21) * 16) + 4^2 - log_3(81) + (-394 mod 3) + floor(-9/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((164 + 840/21) * 16) + 4^2 - log_3(81) + (-394 mod 3) + floor(-9/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 4843
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 29 - 62x^2 + 77 = 4x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 29 - 62x^2 + 77 = 4x $\n\nMove all terms to the left (standard form):\n$ -62x^2 + -4x + 106 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4844
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Differentiate with respect to $x$: $f(x) = 7e^{1x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 7e^{1x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{7e^{1x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 4845
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((100 + -198/9) * 3) + 3^5 - log_2(2) + (-390 mod 10) + ceil(152/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((100 + -198/9) * 3) + 3^5 - log_2(2) + (-390 mod 10) + ceil(152/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 4846
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Prove that $f(x,y)=\\frac12(10x^2+1y^2)+-2x+6y+-5$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(10x^2+1y^2)+-2x+6y+-5 $\n\n$ \\frac{\\partial^2 f}{\\partia... | {
"type": "optimization",
"seed": 1337,
"index": 4847
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. -623x - 536 = -484"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -623x - 536 = -484 $\n\nMove all terms to the left (standard form):\n$ -623x + -52 = 0 $\n\nIsolate the $x$ term:\n$ -623x = 52 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 4848
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: -66x + 929 = -326"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -66x + 929 = -326 $\n\nMove all terms to the left (standard form):\n$ -66x + 1255 = 0 $\n\nIsolate the $x$ term:\n$ -66x = -1255 $\n\nDivide both sides by the coefficient... | {
"type": "linear_equation",
"seed": 1337,
"index": 4849
} |
[
{
"role": "user",
"content": "Please work out this equation. Evaluate: ((-164 + -720/24) * 8) + 11^4 - log_2(32) + (436 mod 22) + ceil(-124/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-164 + -720/24) * 8) + 11^4 - log_2(32) + (436 mod 22) + ceil(-124/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 4850
} |
[
{
"role": "user",
"content": "Solve this equation step by step. 60 - 19 = 32x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 60 - 19 = 32x $\n\nMove all terms to the left (standard form):\n$ -32x + 41 = 0 $\n\nIsolate the $x$ term:\n$ -32x = -41 $\n\nDivide both sides by the coeff... | {
"type": "linear_equation",
"seed": 1337,
"index": 4851
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Compute $(-88+92) \\bmod 14$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-88+92) \\bmod 14 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4852
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-5&0&-1\\\\\\4&4&2\\\\\\-5&-3&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-15\\\\\\-4\\\\\\-3\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4853
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. -8 + 125 - 150x^2 = -124x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -8 + 125 - 150x^2 = -124x $\n\nMove all terms to the left (standard form):\n$ -150x^2 + 124x + 117 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4854
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}4&-5\\\\-6&7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 4 & -5 \\\\ -6 & 7 \\end{pmatrix} $\n\nCompute th... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4855
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Prove that $(\\mathbb{Z}_30, +)$ is a group under addition modulo 30."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_30=\\{0,1,\\dots,29\\}$ with operation $+$ modulo $30$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4856
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}1&5&5\\\\\\4&0&-3\\\\\\0&0&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-13\\\\\\-3\\\\\\6\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4857
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Compute $(-81+-196) \\bmod 22$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-81+-196) \\bmod 22 $\n\nUse the rule that addition is compatible with reduction m... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4858
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Prove that $(\\mathbb{Z}_15, +)$ is a group under addition modulo 15."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_15=\\{0,1,\\dots,14\\}$ with operation $+$ modulo $15$.\n\n**Closure:** If $a,b\\in\\mat... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4859
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. Prove that $f(x)=2x^2+-3x+-7$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=2x^2+-3x+-7$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ ... | {
"type": "optimization",
"seed": 1337,
"index": 4860
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Evaluate: ((84 + -156/6) * 17) + 11^2 - log_3(729) + (-71 mod 27) + round(-143/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((84 + -156/6) * 17) + 11^2 - log_3(729) + (-71 mod 27) + round(-143/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4861
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 4862
} |
[
{
"role": "user",
"content": "Calculate the result of the given equation. Find the modular inverse of 3 modulo 32, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $3\\cdot a^{-1} \\equiv 1 \\pmod{32}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarante... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4863
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Evaluate: ((51 + 312/24) * 17) + 3^2 - log_10(10) + (487 mod 29) + ceil(100/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((51 + 312/24) * 17) + 3^2 - log_10(10) + (487 mod 29) + ceil(100/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 4864
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Compute the determinant: $A=\\begin{pmatrix}5&1\\\\-1&5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}5&1\\\\\\-1&5\\end{pmatrix} $\n\nUse $\\d... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4865
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Differentiate with respect to $x$: $f(x) = -6x^3 + 9x^2 + 12x + -9$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -6x^3 + 9x^2 + 12x + -9 $\n\nApply the standard differentiation rul... | {
"type": "calculus",
"seed": 1337,
"index": 4866
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((35 + 323/17) * 13) + 11^5 - log_5(3125) + (-11 mod 22) + ceil(-9/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((35 + 323/17) * 13) + 11^5 - log_5(3125) + (-11 mod 22) + ceil(-9/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 4867
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. 48 - 101x - 50x^2 = -96"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 48 - 101x - 50x^2 = -96 $\n\nMove all terms to the left (standard form):\n$ -50x^2 + -101x + 144 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4868
} |
[
{
"role": "user",
"content": "Please determine the outcome of this equation. Solve for $x$ (in radians): sin(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 0 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(0) = 0 $\n\nThe ge... | {
"type": "trigonometry",
"seed": 1337,
"index": 4869
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Evaluate: ((162 + -437/19) * 20) + 9^2 - log_10(10) + (-146 mod 19) + round(184/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((162 + -437/19) * 20) + 9^2 - log_10(10) + (-146 mod 19) + round(184... | {
"type": "arithmetic",
"seed": 1337,
"index": 4870
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. -38x + 82x^2 + 46 = 197"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -38x + 82x^2 + 46 = 197 $\n\nMove all terms to the left (standard form):\n$ 82x^2 + -38x + -151 = 0 $\n\nApply the quadratic formula... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4871
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. Compute $(-19+71) \\bmod 24$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-19+71) \\bmod 24 $\n\nUse the rule that addition is compatible with reduction modu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4872
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}6&1\\\\\\-9&-7\\end{pmatrix},\\quad b=\\begin{pmatrix}-47\\\\\\98\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}6&1\\\\\\-9&-7\\end{pmat... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4873
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Evaluate: ((-194 + -180/6) * 2) + 2^5 - log_3(243) + (-487 mod 15) + ceil(-101/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-194 + -180/6) * 2) + 2^5 - log_3(243) + (-487 mod 15) + ceil(-101/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 4874
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. Solve for $x$ (in radians): tan(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(\\fr... | {
"type": "trigonometry",
"seed": 1337,
"index": 4875
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Evaluate: ((91 + -931/19) * 7) + 3^4 - log_10(100) + (459 mod 26) + ceil(159/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((91 + -931/19) * 7) + 3^4 - log_10(100) + (459 mod 26) + ceil(159/2) $\n\nCompute each... | {
"type": "arithmetic",
"seed": 1337,
"index": 4876
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((105 + -323/17) * 1) + 4^2 - log_3(27) + (-312 mod 30) + round(-100/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((105 + -323/17) * 1) + 4^2 - log_3(27) + (-312 mod 30) + round(-100/2) $\n\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 4877
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((33 + 875/25) * 3) + 11^5 - log_2(4) + (124 mod 10) + floor(-174/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((33 + 875/25) * 3) + 11^5 - log_2(4) + (124 mod 10) + floor(-174/2) $\n\nCompute each component:\n$ 875... | {
"type": "arithmetic",
"seed": 1337,
"index": 4878
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^2-1... | {
"type": "optimization",
"seed": 1337,
"index": 4879
} |
[
{
"role": "user",
"content": "solve -673x - 861 = 88"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -673x - 861 = 88 $\n\nMove all terms to the left (standard form):\n$ -673x + -949 = 0 $\n\nIsolate the $x$ term:\n$ -673x = 949 $\n\nDivide both sides by the coefficient of $x$:\n$... | {
"type": "linear_equation",
"seed": 1337,
"index": 4880
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Solve for $x$ (in radians): tan(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 0 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(0) = 0 $\n\nTh... | {
"type": "trigonometry",
"seed": 1337,
"index": 4881
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. Prove that $(\\mathbb{Z}_11, +)$ is a group under addition modulo 11."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_11=\\{0,1,\\dots,10\\}$ with operation $+$ modulo $11$.\n\n**Closure:** If $a,b\\in\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4882
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Compute the indefinite integral: $\\int -5e^{-2x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -5e^{-2x}\\,dx $\n\nUse standard antiderivatives (and integration by parts if ne... | {
"type": "calculus",
"seed": 1337,
"index": 4883
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Prove that $f(x,y)=\\frac12(8x^2+5y^2)+-6x+-5y+-3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(8x^2+5y^2)+-6x+-5y+-3 $\n\n$ \\frac{\\partial^2 f}... | {
"type": "optimization",
"seed": 1337,
"index": 4884
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Prove that $f(x)=4x^2+9x+10$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=4x^2+9x+10$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x... | {
"type": "optimization",
"seed": 1337,
"index": 4885
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((13 + 369/9) * 20) + 7^5 - log_4(1024) + (-373 mod 29) + floor(74/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((13 + 369/9) * 20) + 7^5 - log_4(1024) + (-373 mod 29) + floor(74/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 4886
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. 11 + 957 = -510x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 11 + 957 = -510x $\n\nMove all terms to the left (standard form):\n$ 510x + 968 = 0 $\n\nIsolate the $x$ term:\n$ 510x = -968 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 4887
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}3&-9\\\\-3&1\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 3 & -9 \\\\ -3 & 1 \\end{pmatrix} $\n\nCompute t... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4888
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Prove that $f(x)=1x^2+-10x+5$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+-10x+5$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) ... | {
"type": "optimization",
"seed": 1337,
"index": 4889
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -266 + 652x = 697"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -266 + 652x = 697 $\n\nMove all terms to the left (standard form):\n$ 652x + -963 = 0 $\n\nIsolate the $x$ term:\n$ 652x = 963 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 4890
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. -12x^2 + 37 - 167 = 91x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -12x^2 + 37 - 167 = 91x $\n\nMove all terms to the left (standard form):\n$ -12x^2 + -91x + -130 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4891
} |
[
{
"role": "user",
"content": "Please calculate this equation. -47x^2 - 94 - 110 = 65x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -47x^2 - 94 - 110 = 65x $\n\nMove all terms to the left (standard form):\n$ -47x^2 + -65x + -204 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 4892
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Prove that $f(x)=5x^2+-6x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+-6x+0$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) ... | {
"type": "optimization",
"seed": 1337,
"index": 4893
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. 142 - 271x = -644"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 142 - 271x = -644 $\n\nMove all terms to the left (standard form):\n$ -271x + 786 = 0 $\n\nIsolate the $x$ term:\n$ -271x = -786 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 4894
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Compute $(146+49) \\bmod 13$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (146+49) \\bmod 13 $\n\nUse the rule that addition is compatible with reduction modulo... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4895
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Find $A^{-1}$ for $A=\\begin{pmatrix}-1&8\\\\5&-8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -1 & 8 \\\\ 5 & -8 \\end{pmatrix} $\n\nCompute th... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4896
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? -987x + 125 = -595"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -987x + 125 = -595 $\n\nMove all terms to the left (standard form):\n$ -987x + 720 = 0 $\n\nIsolate the $x$ term:\n$ -987x = -720 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 4897
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Find the modular inverse of 7 modulo 8, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $7\\cdot a^{-1} \\equiv 1 \\pmod{8}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 4898
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&-3&1\\\\\\1&-3&4\\\\\\-3&4&3\\end{pmatrix},\\quad b=\\begin{pmatrix}7\\\\\\27\\\\\\-6\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 4899
} |
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