messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Calculate and solve this equation. 48x^2 + 87 + 5x = 151"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 48x^2 + 87 + 5x = 151 $\n\nMove all terms to the left (standard form):\n$ 48x^2 + 5x + -64 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2300
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Compute the indefinite integral: $\\int (2x + -7)e^{6x}\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (2x + -7)e^{6x}\\,dx $\n\nUse standard antiderivatives (and integrat... | {
"type": "calculus",
"seed": 1337,
"index": 2301
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-5&-7\\\\\\1&-2\\end{pmatrix},\\quad b=\\begin{pmatrix}-52\\\\\\7\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-5&-7\\\\\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2302
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((-157 + -343/7) * 11) + 12^4 - log_3(243) + (-487 mod 3) + floor(-43/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-157 + -343/7) * 11) + 12^4 - log_3(243) + (-487 mod 3) + f... | {
"type": "arithmetic",
"seed": 1337,
"index": 2303
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. -25x + 187 - 175x^2 = -28"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -25x + 187 - 175x^2 = -28 $\n\nMove all terms to the left (standard form):\n$ -175x^2 + -25x + 215 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2304
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((-57 + 28/14) * 18) + 3^4 - log_3(243) + (-455 mod 11) + round(-67/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-57 + 28/14) * 18) + 3^4 - log_3(243) + (-455 mod 11) + round(-67/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 2305
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\... | {
"type": "optimization",
"seed": 1337,
"index": 2306
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Compute the determinant: $A=\\begin{pmatrix}2&-5\\\\-4&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}2&-5\\\\\\-4&3\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2307
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. 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 general so... | {
"type": "trigonometry",
"seed": 1337,
"index": 2308
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. 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": 2309
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Compute the indefinite integral: $\\int -3\\sin(4x) + -7\\cos(6x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -3\\sin(4x) + -7\\cos(6x)\\,dx $\n\nUse standard antiderivat... | {
"type": "calculus",
"seed": 1337,
"index": 2310
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Evaluate: ((-77 + 140/10) * 9) + 4^2 - log_5(15625) + (106 mod 2) + ceil(-197/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-77 + 140/10) * 9) + 4^2 - log_5(15625) + (106 mod 2) + ceil(-197/2) ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2311
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{... | {
"type": "optimization",
"seed": 1337,
"index": 2312
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. Compute the indefinite integral: $\\int (1x + 3)\\sin(2x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (1x + 3)\\sin(2x)\\,dx $\n\nUse standard antiderivatives (and integratio... | {
"type": "calculus",
"seed": 1337,
"index": 2313
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. 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$... | {
"type": "trigonometry",
"seed": 1337,
"index": 2314
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Compute the determinant: $A=\\begin{pmatrix}2&4\\\\-9&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}2&4\\\\\\-9&2\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2315
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. 233x - 344 = -332"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 233x - 344 = -332 $\n\nMove all terms to the left (standard form):\n$ 233x + -12 = 0 $\n\nIsolate the $x$ term:\n$ 233x = 12 $\n\nDivide both sid... | {
"type": "linear_equation",
"seed": 1337,
"index": 2316
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Solve for $x$ (in radians): cos(x) = 0."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 0 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(0) = 1.5708 $\n\nThe general so... | {
"type": "trigonometry",
"seed": 1337,
"index": 2317
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Compute the determinant: $A=\\begin{pmatrix}-8&6\\\\7&4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-8&6\\\\\\7&4\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2318
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. 42x^2 - 127 + 50x = 34"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 42x^2 - 127 + 50x = 34 $\n\nMove all terms to the left (standard form):\n$ 42x^2 + 50x + -161 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2319
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 2320
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Differentiate with respect to $x$: $f(x) = \\ln(5x + 0)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(5x + 0) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{... | {
"type": "calculus",
"seed": 1337,
"index": 2321
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. Evaluate: ((-171 + 507/13) * 4) + 5^3 - log_5(25) + (468 mod 11) + floor(73/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-171 + 507/13) * 4) + 5^3 - log_5(25) + (468 mod 11) + floor(73/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 2322
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Prove that $f(x,y)=\\frac12(1x^2+1y^2)+3x+5y+-8$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(1x^2+1y^2)+3x+5y+-8 $\n\n$ \\frac{\\partial^2 f}{\... | {
"type": "optimization",
"seed": 1337,
"index": 2323
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. 501 + 931x = 970"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 501 + 931x = 970 $\n\nMove all terms to the left (standard form):\n$ 931x + -469 = 0 $\n\nIsolate the $x$ term:\n$ 931x = 469 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 2324
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Evaluate: ((-37 + -75/5) * 17) + 3^3 - log_5(3125) + (-445 mod 28) + floor(-15/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-37 + -75/5) * 17) + 3^3 - log_5(3125) + (-445 mod 28) + flo... | {
"type": "arithmetic",
"seed": 1337,
"index": 2325
} |
[
{
"role": "user",
"content": "Solve the mathematical problem presented. Prove that $(\\mathbb{Z}_2, +)$ is a group under addition modulo 2."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_2=\\{0,1,\\dots,1\\}$ with operation $+$ modulo $2$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$,... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2326
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. -12 + 31x + 197 = 140x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -12 + 31x + 197 = 140x^2 $\n\nMove all terms to the left (standard form):\n$ -140x^2 + 31x + 185 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2327
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-8&1\\\\6&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -8 & 1 \\\\ 6 & -4 \\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2328
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Compute the indefinite integral: $\\int (3x + 1)\\sin(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (3x + 1)\\sin(1x)\\,dx $\n\nUse standard antiderivatives (and integration by parts if n... | {
"type": "calculus",
"seed": 1337,
"index": 2329
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. -955 - 735 = 710x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -955 - 735 = 710x $\n\nMove all terms to the left (standard form):\n$ -710x + -1690 = 0 $\n\nIsolate the $x$ term:\n$ -710x = 1690 $\n\nDivide bot... | {
"type": "linear_equation",
"seed": 1337,
"index": 2330
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Compute $(5+46) \\bmod 9$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (5+46) \\bmod 9 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2331
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Evaluate: ((23 + 220/20) * 4) + 2^2 - log_9(59049) + (129 mod 29) + round(93/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((23 + 220/20) * 4) + 2^2 - log_9(59049) + (129 mod 29) + round(93/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 2332
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. 35 - 72 - 115x^2 = -74x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 35 - 72 - 115x^2 = -74x $\n\nMove all terms to the left (standard form):\n$ -115x^2 + 74x + -37 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2333
} |
[
{
"role": "user",
"content": "solve: 644 + 520 = -474x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 644 + 520 = -474x $\n\nMove all terms to the left (standard form):\n$ 474x + 1164 = 0 $\n\nIsolate the $x$ term:\n$ 474x = -1164 $\n\nDivide both sides by the coefficient of $x$:... | {
"type": "linear_equation",
"seed": 1337,
"index": 2334
} |
[
{
"role": "user",
"content": "Compute the solution to this equation. -23x + 99 + 58 = -11x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23x + 99 + 58 = -11x^2 $\n\nMove all terms to the left (standard form):\n$ 11x^2 + -23x + 157 = 0 $\n\nApply the quadratic formula:\n$ x ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2335
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Prove that $f(x)=1x^2+8x+5$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=1x^2+8x+5$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 2x +... | {
"type": "optimization",
"seed": 1337,
"index": 2336
} |
[
{
"role": "user",
"content": "Please work out this equation. 87x + 817 = 535"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 87x + 817 = 535 $\n\nMove all terms to the left (standard form):\n$ 87x + 282 = 0 $\n\nIsolate the $x$ term:\n$ 87x = -282 $\n\nDivide both sides by the coef... | {
"type": "linear_equation",
"seed": 1337,
"index": 2337
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. -19x - 49x^2 + 53 = 124"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -19x - 49x^2 + 53 = 124 $\n\nMove all terms to the left (standard form):\n$ -49x^2 + -19x + -71 = 0 $\n\nApply the quadratic form... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2338
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Compute $(173+61) \\bmod 2$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (173+61) \\bmod 2 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2339
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Differentiate with respect to $x$: $f(x) = 8\\sin(6x) + 5\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 8\\sin(6x) + 5\\cos(1x) $\n\nApply the standard differentiation rul... | {
"type": "calculus",
"seed": 1337,
"index": 2340
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. Compute $(-134+-100) \\bmod 17$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-134+-100) \\bmod 17 $\n\nUse the rule that addition is compatible with reducti... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2341
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}4&-4&-1\\\\\\0&-2&-1\\\\\\-2&-5&-4\\end{pmatrix},\\quad b=\\begin{pmatrix}7\\\\\\11\\\\\\38\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g., b... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2342
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. -58 + 737x = 215"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -58 + 737x = 215 $\n\nMove all terms to the left (standard form):\n$ 737x + -273 = 0 $\n\nIsolate the $x$ term:\n$ 737x = 273 $\n\nDivide both s... | {
"type": "linear_equation",
"seed": 1337,
"index": 2343
} |
[
{
"role": "user",
"content": "Solve the equation below and give the answer. Differentiate with respect to $x$: $f(x) = 5x^3 + -8x^2 + 11x + 19$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 5x^3 + -8x^2 + 11x + 19 $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 2344
} |
[
{
"role": "user",
"content": "Solve the given mathematical expression. Compute the indefinite integral: $\\int -4\\sin(8x) + 9\\cos(8x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4\\sin(8x) + 9\\cos(8x)\\,dx $\n\nUse standard antiderivatives (and int... | {
"type": "calculus",
"seed": 1337,
"index": 2345
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Find the modular inverse of 17 modulo 30, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $17\\cdot a^{-1} \\equiv 1 \\pmod{30}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gua... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2346
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Evaluate: ((172 + -352/11) * 6) + 7^5 - log_5(125) + (-110 mod 25) + ceil(181/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((172 + -352/11) * 6) + 7^5 - log_5(125) + (-110 mod 25) + ceil(181/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2347
} |
[
{
"role": "user",
"content": "Determine the solution to the math equation provided. Evaluate: ((59 + -407/11) * 8) + 10^2 - log_5(125) + (-1 mod 17) + round(-173/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((59 + -407/11) * 8) + 10^2 - log_5(125) + (-1 mod 17) + round(-... | {
"type": "arithmetic",
"seed": 1337,
"index": 2348
} |
[
{
"role": "user",
"content": "solve Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\partial^2 f}{\\partial x\\partial y} \... | {
"type": "optimization",
"seed": 1337,
"index": 2349
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Compute $(-39+21) \\bmod 25$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-39+21) \\bmod 25 $\n\nUse the rule that addition is compatible with reduction... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2350
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. -655x + 70 = -365"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -655x + 70 = -365 $\n\nMove all terms to the left (standard form):\n$ -655x + 435 = 0 $\n\nIsolate the $x$ term:\n$ -655x = -435 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 2351
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Prove that $f(x)=10x^2+5x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=10x^2+5x+-1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'... | {
"type": "optimization",
"seed": 1337,
"index": 2352
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. Solve for $x$ (in radians): sin(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = 1 $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(1) = 1.5708 $\n\nThe g... | {
"type": "trigonometry",
"seed": 1337,
"index": 2353
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. -43 - 141x + 56 = 8x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -43 - 141x + 56 = 8x^2 $\n\nMove all terms to the left (standard form):\n$ -8x^2 + -141x + 13 = 0 $\n\nApply the quadratic formula:\n... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2354
} |
[
{
"role": "user",
"content": "Resolve the equation provided. -92 + 206 = -995x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -92 + 206 = -995x $\n\nMove all terms to the left (standard form):\n$ 995x + 114 = 0 $\n\nIsolate the $x$ term:\n$ 995x = -114 $\n\nDivide both sides by th... | {
"type": "linear_equation",
"seed": 1337,
"index": 2355
} |
[
{
"role": "user",
"content": "Evaluate the following equation. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&-4\\\\-6&-5\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & -4 \\\\ -6 & -5 \\end{pmatrix} $\n\nCompute the determ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2356
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. -432 - 840 = -522x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -432 - 840 = -522x $\n\nMove all terms to the left (standard form):\n$ 522x + -1272 = 0 $\n\nIsolate the $x$ term:\n$ 522x = 1272 $\n\nDivide... | {
"type": "linear_equation",
"seed": 1337,
"index": 2357
} |
[
{
"role": "user",
"content": "solve: Find the modular inverse of 11 modulo 20, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $11\\cdot a^{-1} \\equiv 1 \\pmod{20}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers $x,y$ with:\n$ 11x + 2... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2358
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Find the modular inverse of 20 modulo 33, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $20\\cdot a^{-1} \\equiv 1 \\pmod{33}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2359
} |
[
{
"role": "user",
"content": "Determine the value produced by this equation. Differentiate with respect to $x$: $f(x) = \\ln(9x + 4)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(9x + 4) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\fra... | {
"type": "calculus",
"seed": 1337,
"index": 2360
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Compute the indefinite integral: $\\int -4x^3 + 6x^2 + -2x + 6\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int -4x^3 + 6x^2 + -2x + 6\\,dx $\n\nUse standard antiderivatives (and integration by pa... | {
"type": "calculus",
"seed": 1337,
"index": 2361
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation.\n\n Prove that $f(x)=6x^2+7x+-6$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+7x+-6$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'... | {
"type": "optimization",
"seed": 1337,
"index": 2362
} |
[
{
"role": "user",
"content": "solve: \n\n -8x^2 + 114 - 184x = 60"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -8x^2 + 114 - 184x = 60 $\n\nMove all terms to the left (standard form):\n$ -8x^2 + -184x + 54 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2363
} |
[
{
"role": "user",
"content": "Can you solve the equation below? Compute the indefinite integral: $\\int \\ln(4x + -9)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(4x + -9)\\,dx $\n\nUse standard antiderivatives (and integration by parts if needed):... | {
"type": "calculus",
"seed": 1337,
"index": 2364
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Find the modular inverse of 4 modulo 9, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $4\\cdot a^{-1} \\equiv 1 \\pmod{9}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2365
} |
[
{
"role": "user",
"content": "Solve the equation and show the result. Evaluate: ((119 + 360/9) * 4) + 8^4 - log_9(6561) + (345 mod 5) + ceil(-172/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((119 + 360/9) * 4) + 8^4 - log_9(6561) + (345 mod 5) + ceil(-172/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 2366
} |
[
{
"role": "user",
"content": "Please calculate and resolve this equation. Compute the determinant: $A=\\begin{pmatrix}0&7\\\\2&-9\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}0&7\\\\\\2&-9\\end{pmatrix} $\n\nUse $... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2367
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. 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 $a,b\\in\\mathbb{Z... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2368
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. -23x - 16x^2 + 47 = -69"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -23x - 16x^2 + 47 = -69 $\n\nMove all terms to the left (standard form):\n$ -16x^2 + -23x + 116 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2369
} |
[
{
"role": "user",
"content": "Compute the final answer to this equation. Compute the determinant: $A=\\begin{pmatrix}-3&7\\\\-8&7\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&7\\\\\\-8&7\\end{pmatrix} $\n\nUse ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2370
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Prove that $f(x,y)=\\frac12(7x^2+6y^2)+6x+-4y+-3$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(7x^2+6y^2)+6x+-4y+-3 $\n\n$ \\frac{\\partial^... | {
"type": "optimization",
"seed": 1337,
"index": 2371
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. -7 + 43 - 182x^2 = 107x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -7 + 43 - 182x^2 = 107x $\n\nMove all terms to the left (standard form):\n$ -182x^2 + -107x + 36 = 0 $\n\nApply the quadratic formula:\n$... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2372
} |
[
{
"role": "user",
"content": "solve: 9x^2 + 182x - 113 = -150"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 9x^2 + 182x - 113 = -150 $\n\nMove all terms to the left (standard form):\n$ 9x^2 + 182x + 37 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 - 4... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2373
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Differentiate with respect to $x$: $f(x) = \\ln(4x + 7)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(4x + 7) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\fr... | {
"type": "calculus",
"seed": 1337,
"index": 2374
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. 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$ \\alpha =... | {
"type": "trigonometry",
"seed": 1337,
"index": 2375
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. -11 - 847 = -20x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -11 - 847 = -20x $\n\nMove all terms to the left (standard form):\n$ 20x + -858 = 0 $\n\nIsolate the $x$ term:\n$ 20x = 858 $\n\nDivide both sides... | {
"type": "linear_equation",
"seed": 1337,
"index": 2376
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. 13 - 39x + 154 = 175x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13 - 39x + 154 = 175x^2 $\n\nMove all terms to the left (standard form):\n$ -175x^2 + -39x + 167 = 0 $\n\nApply the quadratic formula:... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2377
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. -16 - 24 - 179x = -116x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -16 - 24 - 179x = -116x^2 $\n\nMove all terms to the left (standard form):\n$ 116x^2 + -179x + -40 = 0 $\n\nApply the quadratic fo... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2378
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. 7 + 16 - 79x = 129x^2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 7 + 16 - 79x = 129x^2 $\n\nMove all terms to the left (standard form):\n$ -129x^2 + -79x + 23 = 0 $\n\nApply the quadratic formula:\n$ x =... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2379
} |
[
{
"role": "user",
"content": "Solve the equation shown below. Compute the determinant: $A=\\begin{pmatrix}-1&4\\\\-9&8\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-1&4\\\\\\-9&8\\end{pmatrix} $\n\nUse $\\det(A)=a... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2380
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Differentiate with respect to $x$: $f(x) = -3x^3 + -7x^2 + 19x + -20$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -3x^3 + -7x^2 + 19x + -20 $\n\nApply the standard differentiation rules:\n$ f'(x... | {
"type": "calculus",
"seed": 1337,
"index": 2381
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. 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": 2382
} |
[
{
"role": "user",
"content": "Determine the correct answer to this equation. Find $A^{-1}$ for $A=\\begin{pmatrix}6&-2\\\\-5&0\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} 6 & -2 \\\\ -5 & 0 \\end{pmatrix} $\n\nCompute ... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2383
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. 560 - 913x = 550"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 560 - 913x = 550 $\n\nMove all terms to the left (standard form):\n$ -913x + 10 = 0 $\n\nIsolate the $x$ term:\n$ -913x = -10 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 2384
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Evaluate: ((-100 + 86/2) * 14) + 8^3 - log_2(16) + (39 mod 11) + ceil(8/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-100 + 86/2) * 14) + 8^3 - log_2(16) + (39 mod 11) + ceil(8/2) $\n\nCompute ... | {
"type": "arithmetic",
"seed": 1337,
"index": 2385
} |
[
{
"role": "user",
"content": "Find the solution to the following equation. Evaluate: ((144 + -384/8) * 10) + 9^4 - log_8(64) + (217 mod 10) + round(25/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((144 + -384/8) * 10) + 9^4 - log_8(64) + (217 mod 10) + round(25/2) $\n\nC... | {
"type": "arithmetic",
"seed": 1337,
"index": 2386
} |
[
{
"role": "user",
"content": "Solve the given equation and provide the solution. -845 + 410x = -815"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -845 + 410x = -815 $\n\nMove all terms to the left (standard form):\n$ 410x + -30 = 0 $\n\nIsolate the $x$ term:\n$ 410x = 30 $\n\nDiv... | {
"type": "linear_equation",
"seed": 1337,
"index": 2387
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -8 + 146x^2 + 197 = -126x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -8 + 146x^2 + 197 = -126x $\n\nMove all terms to the left (standard form):\n$ 146x^2 + 126x + 189 = 0 $\n\nApply the quadratic formula:\n$ ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 2388
} |
[
{
"role": "user",
"content": "Compute the solution for this equation. -402 + 369 = 120x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -402 + 369 = 120x $\n\nMove all terms to the left (standard form):\n$ -120x + -33 = 0 $\n\nIsolate the $x$ term:\n$ -120x = 33 $\n\nDivide both si... | {
"type": "linear_equation",
"seed": 1337,
"index": 2389
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 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 = \\... | {
"type": "trigonometry",
"seed": 1337,
"index": 2390
} |
[
{
"role": "user",
"content": "Compute the value of the following equation. Evaluate: ((-149 + 300/12) * 1) + 9^2 - log_4(4) + (187 mod 7) + ceil(-72/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-149 + 300/12) * 1) + 9^2 - log_4(4) + (187 mod 7) + ceil(-72/2) $\n\nCompu... | {
"type": "arithmetic",
"seed": 1337,
"index": 2391
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}4&7\\\\\\0&-3\\end{pmatrix},\\quad b=\\begin{pmatrix}56\\\\\\-12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}4&7\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2392
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 177 - 431 = -388x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 177 - 431 = -388x $\n\nMove all terms to the left (standard form):\n$ 388x + -254 = 0 $\n\nIsolate the $x$ term:\n$ 388x = 254 $\n\nDivide ... | {
"type": "linear_equation",
"seed": 1337,
"index": 2393
} |
[
{
"role": "user",
"content": "Determine the value of the unknown in this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}-4&0\\\\\\6&-8\\end{pmatrix},\\quad b=\\begin{pmatrix}20\\\\\\10\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}-4&0\\... | {
"type": "linear_algebra",
"seed": 1337,
"index": 2394
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Evaluate: ((-189 + -10/10) * 7) + 8^5 - log_10(100000) + (305 mod 6) + round(-75/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-189 + -10/10) * 7) + 8^5 - log_10(100000) + (305 mod 6) + round(-75/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 2395
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Compute the indefinite integral: $\\int \\ln(1x + -6)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(1x + -6)\\,dx $\n\nUse standard antiderivatives (and integration by parts ... | {
"type": "calculus",
"seed": 1337,
"index": 2396
} |
[
{
"role": "user",
"content": "Calculate the answer for this equation. Prove that $f(x)=5x^2+0x+3$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=5x^2+0x+3$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x) = 10x... | {
"type": "optimization",
"seed": 1337,
"index": 2397
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. -574x - 145 = -176"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -574x - 145 = -176 $\n\nMove all terms to the left (standard form):\n$ -574x + 31 = 0 $\n\nIsolate the $x$ term:\n$ -574x = -31 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 2398
} |
[
{
"role": "user",
"content": "Solve the following math equation. Compute $(-63+-63) \\bmod 13$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-63+-63) \\bmod 13 $\n\nUse the rule that addition is compatible with reduction modulo $n... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 2399
} |
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