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{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Let $f(x) = \\left\\{\n\\begin{array}{cl} ax+3... |
7dbbd4a6-b06c-949a-a309-54e51079b2be | 2 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "What is the degree of the polynomial $(4 +5x^3... |
abfd1872-d78b-9465-825a-e2a8ecdc0c63 | 9 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Tim wants to invest some money in a bank which... |
243c8b79-c39e-9b75-adc1-b766ed8929b4 | 3 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Evaluate $\\left\\lceil3\\left(6-\\frac12\\rig... |
4d44961f-ab8a-9380-adfd-296abf4f2a87 | 4 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Sam is hired for a 20-day period. On days that... |
f5dd00ee-8c38-9a1b-b4ee-487e64f8b172 | 6 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "What are all values of $p$ such that for every... |
eb863988-1246-9e5d-9c1a-8bb936f15a24 | 1 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "A rectangular band formation is a formation wi... |
af6b4d2b-bd42-9182-9c58-0d9e10882752 | 5 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Find the center of the circle with equation $x... |
edd817fe-c6f1-995f-b370-d053d864fbea | 7 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "If $x = 2$ and $y = 5$, then what is the value... |
d97bfa31-fbf7-9909-adc9-e3d9eb932f0e | 17 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Let $f(x) =\n\\begin{cases}\n2x^2 - 3&\\text{i... |
38b7fde6-59cf-9dbc-af42-b511a2c47dfc | 10 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The points $(9, -5)$ and $(-3, -1)$ are the en... |
33867355-7985-9d0b-8007-c6abe7ccf8e7 | 11 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Consider the given functions: $$\\begin{array}... |
aaee8d2f-6cd9-9a6f-a600-72699f44c899 | 13 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Simplify $\\sqrt[3]{1+8} \\cdot \\sqrt[3]{1+\\... |
295393f8-7465-926b-a326-190ecc2992a4 | 12 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Berengere and her American foreign-exchange st... |
fa4fa868-f14a-9fc2-b296-b2e30e9aafd8 | 16 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The greatest integer function, $\\lfloor x\\rf... |
62b4decd-4d06-9f8d-9a62-a5f7a6efb0f3 | 15 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Let $f(x) =\n\\begin{cases}\nx/2 &\\quad \\tex... |
643d4a6b-a8e2-9610-bb8b-1d5ebf1b0acd | 18 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Let $f(x) =\n\\begin{cases}\n3x^2 + 2&\\text{i... |
f22e8bb5-076b-9a0e-8553-e523aef34873 | 14 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Let $f(x)=x^3+3$ and $g(x) = 2x^2 + 2x +1$. Wh... |
c7ec6479-187b-93bb-9863-a6ba03c6cccb | 19 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Three faucets fill a 100-gallon tub in 6 minut... |
e73799ee-2a03-9f82-9df0-9e6241fcacaa | 23 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The roots of the equation $x^2+kx+5 = 0$ diffe... |
dd87ccda-b06d-94e1-9d00-70d4ef53d31d | 20 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "At what point does the line containing the poi... |
ecf8e35c-8d0c-904d-b38c-ffea0faa2d82 | 27 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "What is the positive difference between the tw... |
e84fc014-a825-9c5e-9c94-c9d9a7bc4b39 | 21 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Find the coefficient of the $x^2$ term in the ... |
dfe7836d-41b1-9fba-a7e6-eaefffcada56 | 24 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Find the value of $x$ that satisfies $\\frac{\... |
09aab15c-91de-995a-8766-4e33d6d383ed | 22 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "If $f(3)=1$ and $f(2x)=2f(x)$ for all $x$, fin... |
b3babc2d-99f5-9186-9715-d0bb92903f9c | 25 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The points $(-1,4)$ and $(2,-3)$ are adjacent ... |
12e70b37-5832-9a47-834f-ef5399f70a4d | 28 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "For all real numbers $r$ and $s$, define the m... |
40adb77a-0f1f-9f3e-bbab-bdf6f4a19a6d | 29 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "If $(x+2)(x-3)=14$, find the sum of the possib... |
4ac8dee9-bc36-9497-aeb5-604083877146 | 26 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "What is the greatest integer $n$ such that $n^... |
c42c102a-0176-9fe0-a196-a1147d2884d2 | 33 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "What is the sum of all of the solutions of the... |
f18372af-5607-960e-a545-7cf5cbb071cb | 31 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The first and thirteenth terms of an arithmeti... |
5f7f9a08-54ef-9cc2-bc51-323b0b8c9e79 | 32 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Simplify $(2x - 5)(x + 7) - (x + 5)(2x - 1)$."... |
45dff708-c865-9c00-9bcb-150404bece8e | 30 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Rationalize the denominator: $\\frac{1}{\\sqrt... |
ba2f7162-ef3c-95c8-a054-005a9fd99f7d | 35 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Find the value of $x$ if $x$ is positive and $... |
8ea6d7e2-969b-923f-81c5-2dd12dba264a | 36 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The perimeter of a rectangular garden is 60 fe... |
ff40d76c-3f17-91a6-9959-a4bc17f5bf86 | 34 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "What value of $x$ will give the minimum value ... |
ddadd73e-26c0-9186-81c7-de2237977492 | 38 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "A triangle has three sides of the following si... |
a91e1df2-4b72-9688-a128-def57c897546 | 37 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The function $f(x)$ is defined by $f(x)=x^{2}-... |
e903a08f-a11e-974a-8467-784e3f260d69 | 39 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The square of an integer is 182 greater than t... |
b61faa60-e2c2-9abd-8b47-3c5b4bf4198a | 40 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "A ball travels on a parabolic path in which th... |
9cef91ba-06e4-906d-9560-8339bedb490b | 43 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Express $\\frac{0.\\overline{666}}{1.\\overlin... |
37ceb601-e509-9a70-bee9-0bd93e3c349f | 42 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Find the greatest integer value of $b$ for whi... |
4ab52ce6-61d4-917b-8bb0-b5b9c0ce9b1c | 48 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Find the product of all constants $t$ such tha... |
bc9c509a-617b-9a58-91c9-b9bc0bce2434 | 45 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "A line has a slope of $-7$ and contains the po... |
488f40f8-e64e-9ff9-bbdb-dd39e0da537b | 44 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Find the coordinates of the point halfway betw... |
eb080516-64f1-9d10-a4e4-a9d5fe7c5c27 | 41 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Karen drove continuously from 9:40 a.m. until ... |
c469f13d-298a-9523-a1af-399465ee1bce | 46 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Let $C$ be the circle with equation $x^2-6y-3=... |
0ac08ee9-6e18-9dcc-8a75-add3a563034a | 47 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The functions $f(x) = x^2-2x + m$ and $g(x) = ... |
dd11460d-059c-9008-bcf5-897dcf60f796 | 49 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Factor $58x^5-203x^{11}$."
},
{
"role"... |
170582c7-2728-9594-87c3-7f0b505010be | 56 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "To calculate $31^2$, Emily mentally figures th... |
323c4db7-a45d-9853-8f2f-68d77d399a1c | 55 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Evaluate $\\log_3\\frac{1}{\\sqrt{3}}$."
},
... |
08341746-fa5e-9f26-8aaa-6535ef46620f | 50 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Evaluate the expression $ (a^2+b)^2 - (a^2-b)^... |
a0931ed7-13eb-9c34-9c33-dc0044cddc12 | 59 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Let $a$ and $b$ be the roots of the equation $... |
46f745e0-5793-95bc-b2a0-e3747d2c5081 | 58 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Solve the equation $|y-6| + 2y = 9$ for $y$."
... |
fe01e3e1-2553-93fb-b90f-9b784e10e7dc | 57 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "How many distinct solutions are there to the e... |
ad0e9a6c-f22e-93af-b997-6d5f928bb24e | 52 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The sum of two numbers is $45$. Their differen... |
76b576c4-b415-9eda-bc14-bf43906c92e4 | 54 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Krzysztof solved the quadratic equation $11x^2... |
45061777-adbc-9a02-a796-57a5ad81424a | 53 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "If $m+\\frac{1}{m}=8$, then what is the value ... |
621d08f6-ae1c-949c-981d-e806f72661b5 | 51 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Below is a portion of the graph of a function,... |
d0828af4-7c49-9444-b3d3-284eba9334eb | 62 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Wanda is trying to locate the Fermat point $P$... |
11b81e09-6521-9e02-9d4b-b0057b9aef60 | 65 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Each term of a sequence, after the first term,... |
1706d8a9-49b7-9cf0-a2a2-12f9de002f11 | 69 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "What is the value of $(2x + 5)^2$ when $x = 3$... |
72fc39ce-0955-9631-9fd4-14bec24dfab4 | 68 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "For how many integers $n$ is it true that $\\s... |
6bd80605-b7d1-97ba-b4b4-c313a265a88d | 67 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Let $p$ and $q$ be the two distinct solutions ... |
ff49b359-bb97-9a6a-8e99-b9d1c9c233bb | 61 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The center of the circle with equation $x^2+y^... |
2fc2a3f8-590c-90f4-b3c6-de85550a09cb | 63 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Simplify $(3-2i)^2$. (Your answer should be of... |
524ca074-0f11-91d8-8290-583d2fa3bc48 | 66 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The values of $f$, $g$, $h$ and $j$ are 5, 6, ... |
a7467386-9e5c-9533-b27a-9725bafcf46b | 64 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Suppose $d\\not=0$. We can write $\\left(12d+... |
f5adf82a-ecfa-9b12-a17c-7f10044c9cfb | 60 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Let $f(x)=3x-2$, and let $g(x)=f(f(f(f(x))))$.... |
f61bcecf-dd1d-9ead-bbf4-ec914f3e3013 | 76 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Simplify and rationalize the denominator: $\\f... |
f71e5701-05fe-9117-8eab-febd70bcbd1e | 71 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The product of two consecutive page numbers is... |
6a4dff68-0941-9c38-aa6f-5d1e2d481934 | 77 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The first three terms of an arithmetic sequenc... |
e623bba0-263e-9df7-b664-ad030b8c4d48 | 73 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Solve for $x$: $\\dfrac{1}{2} + \\dfrac{1}{x} ... |
b6df6557-2623-9c45-a5d9-a8eaa72d985f | 78 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "How many integers $n$ satisfy $(n+3)(n-7) \\le... |
384724f9-c484-97b8-8e49-098644eaa312 | 79 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The graph of $y=ax^2+bx+c$ is given, with inte... |
19ed55b1-b232-90d5-b662-da29c185f99c | 75 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "What is the sum of the values of $x$ that sati... |
3980d5c3-e681-9d13-9d09-565bf4957964 | 74 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "A portion of the graph of a quadratic function... |
ca45b5e6-b7a8-9591-9de7-4bfda069a269 | 70 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "What is the value of $x$ in the equation $16^{... |
5a5d4a3f-4e71-9b07-9188-00b884242230 | 72 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Find the absolute value of the difference of t... |
45f42601-161e-9d4b-8981-04b34b0503f6 | 86 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "A geometric sequence of positive integers is f... |
0e7fa91b-f3fb-9e2e-9592-ffa3f15a346c | 85 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "For $y=\\frac{x+2}{5x-7}$, at what $x$-value i... |
522c477a-f9cc-995c-b788-b9f45dfe847d | 84 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "A geometric sequence of positive integers is f... |
1523da37-a26f-9bf4-b056-482489fd936d | 83 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "What is the distance between the center of the... |
820e5bb9-d697-9c05-8e9c-af9cb658f2b0 | 81 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Compute $\\frac{x^8+12x^4+36}{x^4+6}$ when $x=... |
81bb77db-f71b-98fc-819e-dea097812df9 | 89 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Let $f(x) = \\left\\lceil\\dfrac{1}{x+2}\\righ... |
7d7698f8-4f39-9760-bf57-3fe829679882 | 88 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "A $33$-gon $P_1$ is drawn in the Cartesian pla... |
87d31e83-7f83-9165-a9ee-dc610b6e6e95 | 82 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "If $x-y=15$ and $xy=4$, what is the value of $... |
ab7f42ba-4231-91c1-ad22-7bee27576bd3 | 80 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "I have the following terms of an arithmetic se... |
43cbce8a-3d30-9ee8-a6e6-7e7c59629b16 | 87 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The points $(0,4)$ and $(1,3)$ lie on a circle... |
a6f19608-781f-991d-9fa7-a1becd85bd77 | 96 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Solve for $x>0$ in the following arithmetic se... |
3e027e89-48b9-98c7-966b-15ba55da0236 | 94 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Solve for $x$: $$5^{x + 4} = 125^x.$$"
},
... |
d8404b21-b67a-9c63-96ce-d9c5c4399433 | 98 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Simplify the following expression in $x$: \n$$... |
f5094628-33f3-9737-a03d-ed7e79bd5c59 | 91 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Rationalize the denominator of $\\displaystyle... |
9b665514-d4c6-9083-9713-f3ee5fca6571 | 92 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Compute the range of $y=|x+7|-|x-2|$."
},
... |
e566f665-0041-9fb2-98a3-a3553a3fcf30 | 97 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "On a particular day in Salt Lake, UT, the temp... |
20ecbb91-3abd-9e0d-b80e-85493205b5b4 | 95 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Solve for $x$: $(x-4)^3=\\left(\\frac18\\right... |
871f217e-a827-9b95-80c0-bceef633b1cc | 99 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "If the system of equations \n\\begin{align*}\n... |
0a825aec-c24e-9f70-82e0-74c81b0060d3 | 93 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Suppose that $a^2$ varies inversely with $b^3$... |
8198a96a-e104-980e-9640-cc17ac4c8f38 | 90 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "The values of a function $f(x)$ are given in t... |
8e8c6b5c-7836-995e-8fb0-c97e1792ef7b | 106 | [
{
"role": "system",
"content": "You are a helpful math assistant. You have access to mathematical tools to help solve problems. Always think through problems step by step, and use tools when calculations are needed."
},
{
"role": "user",
"content": "Evaluate $\\left\\lceil-\\sqrt{\\frac{49}{4}}\... |
End of preview. Expand in Data Studio
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