instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Let x(l) = l**3 + 6*l**2 - 8*l + 7. Suppose -3*j = 6 - 0. Let a be j*(-2 + 33/6). Is x(a) composite?\n | True\n | ibivibiv/math_instruct | |
List the prime factors of 1767441370.\n | 2, 5, 19, 9302323\n | ibivibiv/math_instruct | |
What are the prime factors of -64*(3 - (-34)/(-4))?\n | 2, 11\n | ibivibiv/math_instruct | |
Let u be (-257)/(-3) + 1 + (-6)/9. Let y(l) = -5*l**2 - 5*l**2 + 85 - 3*l**2 - u. Let p(j) = -j. Calculate y(p(q)).\n | -13*q**2 - 1\n | ibivibiv/math_instruct | |
Find the common denominator of 83/28 and (242/12)/(-15 - -22).\n | 84\n | ibivibiv/math_instruct | |
Suppose -4*y + 3*y = 4*c - 12, 5*y + 2*c = -12. Let l(i) = -i**3 - 10*i**2 - 6*i - 2. Let b be l(-8). Let s be b/36 + (-20)/90. Is y at most s?\n | True\n | ibivibiv/math_instruct | |
What is 420.57997 rounded to zero dps?\n | 421\n | ibivibiv/math_instruct | |
Let y(s) = -s**2. Let h(l) = -70*l + 20. Let g(n) = 10*n - 3. Let o(b) = -20*g(b) - 3*h(b). Calculate o(y(m)).\n | -10*m**2\n | ibivibiv/math_instruct | |
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"# What is the name of the form of the line equation $y = m(x-x0)+y0$
I have been looking everywhere for the name of this form of equation of a line $$y=m(x-x_0)+y_0$$. It's not quite point-slope. It's the same form you would... | The equation of a line in the form $y = m(x-x\_0)+y\_0$ is often referred to as the point-slope form, although the term "general point-slope form" might be more accurate. This form emphasizes the features of a line using variables $m$, $x\_0$, and $y\_0$:
* $m$ represents the slope of the line;
* $(x\_0, y\_0)$ denot... | ibivibiv/math_instruct | |
What is the value of (1008/(-240))/(392/1120)?\n | -12\n | ibivibiv/math_instruct | |
Let s(v) = -7*v + 216. Calculate s(23).\n | 55\n | ibivibiv/math_instruct | |
How many minutes are there between 9:05 PM and 2:00 AM?\n | 295\n | ibivibiv/math_instruct | |
What is the positive difference between the $2000^{\mathrm{th}}$ term and the $2005^{\mathrm{th}}$ term of the arithmetic sequence $-8,$ $-2,$ $4,$ $10,$ $\ldots$? | The common difference of this arithmetic sequence is $-2 - (-8) = 6$.
The $2000^{\mathrm{th}}$ term is $-8 + 6(2000 - 1) = -8 + 12000 - 6 = 11986$.
The $2005^{\mathrm{th}}$ term is $-8 + 6(2005 - 1) = -8 + 12030 - 6 = 12016$.
The positive difference between these two terms is $12016 - 11986 = \boxed{30}$.The answer is:... | ibivibiv/math_instruct | |
What is -3500639 divided by 7?\n | -3500639/7\n | ibivibiv/math_instruct | |
Let q(d) = 5*d**2 + 4*d - 4. Let r(i) = 21*i**2 + 18*i - 9. Let x(n) = 43*n**2 + 37*n - 22. Let c(m) = 5*r(m) - 3*x(m). What is 4*c(b) + 21*q(b)?\n | 9*b**2\n | ibivibiv/math_instruct | |
-294 divided by -670\n | 147/335\n | ibivibiv/math_instruct | |
Let o(q) = -72*q**3 - 28*q. Let l(z) = -13*z**3 - 5*z. Let w be (3 - -12)/(7/329). Let i be (-3)/(-30)*2 - w/25. Determine i*l(j) + 5*o(j).\n | 4*j**3\n | ibivibiv/math_instruct | |
What is the highest common divisor of 660 and 32835?\n | 165\n | ibivibiv/math_instruct | |
Let a(i) = -i**2 - 10*i - 7. Let u be (9 + (4 - 5 - -1))*-1. Let v be a(u). Solve -7 = -k - 2, 3*k = v*z + 17 for z.\n | -1\n | ibivibiv/math_instruct | |
Is 17924981527 composite?\n | True\n | ibivibiv/math_instruct | |
Let c be -2 + (-5)/2*-4. Let m = c - 2. Let x be -2 - -4*57/m. What is the greatest common divisor of x and 6?\n | 6\n | ibivibiv/math_instruct | |
Let m(b) be the second derivative of b**4/12 + 4*b**3/3 - 7*b**2/2 - 7*b + 5. Calculate the remainder when m(-12) is divided by 22.\n | 19\n | ibivibiv/math_instruct | |
Solve 5*g - 30*l + 34*l - 5 = 0, 2*g + 10 = -4*l for g.\n | 5\n | ibivibiv/math_instruct | |
What is -0.0001002 rounded to five dps?\n | -0.0001\n | ibivibiv/math_instruct | |
Expand (-94 + 5*s + 94)*((4 - 1 + 5)*(2 - 2 + s) + s + s - 2 + 1)*(s**2 + 5 - 5).\n | 50*s**4 - 5*s**3\n | ibivibiv/math_instruct | |
List the prime factors of 32861568.\n | 2, 3, 85577\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) 2/9 (b) -1/4 (c) -3 (d) -1.162\n | a\n | ibivibiv/math_instruct | |
Let u(p) = -3*p - 2. Let d be u(-4). Suppose 2*n = -4*z - n + 40, 3*n + d = z. Suppose 5*b - 133 = -33. Calculate the highest common factor of z and b.\n | 10\n | ibivibiv/math_instruct | |
Collect the terms in -7480*o + o**2 + 22453*o + 2*o**2 - 7489*o - 7484*o.\n | 3*o**2\n | ibivibiv/math_instruct | |
In base 8, what is -11 - 6057?\n | -6070\n | ibivibiv/math_instruct | |
What is 87273000 rounded to the nearest one million?\n | 87000000\n | ibivibiv/math_instruct | |
b"What is the tth term of 4975, 4854, 4655, 4378, 4023, 3590, 3079?\n" | -39*t**2 - 4*t + 5018\n | ibivibiv/math_instruct | |
What is 7935 divided by 15?\n | 529\n | ibivibiv/math_instruct | |
What is the value of ((-4)/(-12))/(24/(-9))?\n | -1/8\n | ibivibiv/math_instruct | |
Which is bigger: 654 or 487?\n | 654\n | ibivibiv/math_instruct | |
Let s(m) = m**3 + 7*m**2 + m + 2. Does 34 divide s(6)?\n | True\n | ibivibiv/math_instruct | |
Let d(u) = u**2 + 15*u + 9. Determine d(-15).\n | 9\n | ibivibiv/math_instruct | |
Let m(p) = 4*p**2 + 255*p + 256. Calculate m(-1).\n | 5\n | ibivibiv/math_instruct | |
Let g = -75.1 - -75. Which is the second biggest value? (a) -35 (b) -2/9 (c) g (d) -0.4\n | b\n | ibivibiv/math_instruct | |
List the prime factors of 8221386.\n | 2, 3, 31, 44201\n | ibivibiv/math_instruct | |
How many minutes are there between 4:06 AM and 5:43 AM?\n | 97\n | ibivibiv/math_instruct | |
Let h(n) = -2*n**3 - 7*n**2 + n + 4. What is the remainder when h(-5) is divided by ((39/4)/(50/40))/((-3)/(-10))?\n | 22\n | ibivibiv/math_instruct | |
Solve c - 3*c = -4*c for c.\n | 0\n | ibivibiv/math_instruct | |
Let r(f) = 74629*f - 108. Let i(z) = -5*z. What is r(i(q))?\n | -373145*q - 108\n | ibivibiv/math_instruct | |
Let v(y) = 6*y**3 - y**2 - y - 1. What is v(3)?\n | 149\n | ibivibiv/math_instruct | |
Let r(y) be the third derivative of -y**6/24 - y**5/12 + 8*y**2. Determine n, given that r(n) = 0.\n | -1, 0\n | ibivibiv/math_instruct | |
Solve -3 = 2*d + l, -4*d - l = -7*d + 8 for d.\n | 1\n | ibivibiv/math_instruct | |
Let j be (-6 + 24/4)/(2/(-2)). Suppose 11*z - 12 - 21 = j. Let o(x) = 0 + 31*x - z + 3. Let t(k) = 2*k**2. What is o(t(g))?\n | 62*g**2\n | ibivibiv/math_instruct | |
Is 9907239451 a prime number?\n | False\n | ibivibiv/math_instruct | |
What is the thousands digit of -6 + 2901 + -1 + -12?\n | 2\n | ibivibiv/math_instruct | |
Solve 2894*j + 15 = 2890*j + 3*s, 2 = j + 5*s for j.\n | -3\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 310288910?\n | 2\n | ibivibiv/math_instruct | |
What is the second derivative of -9*k**4 - 1769*k**3 - 86*k + 19?\n | -108*k**2 - 10614*k\n | ibivibiv/math_instruct | |
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"# Prove Trig Identity
sorry if this question isn't high quality. I don't understand #11 here:http://imgur.com/QQ5cmOb This is what I've tried http://m.imgur.com/3keNf1o
I know it's basically turning sum into product and I p... | To prove the trigonometric identity in question, we will delve into two main concepts: Sum-to-Product Identities and Double Angle Formulas. Familiarity with these identities is essential for manipulating trigonometric expressions. We will then apply these concepts step by step to establish the desired identity.
Sum-t... | ibivibiv/math_instruct | |
Let b(r) = r**3 - 3*r**2 - 4*r. Let v be b(4). Suppose -5*d = -2*p + 15, v = 5*d - 8 + 3. Suppose -4*z - 5 = 4*g - 3*z, p = -2*z. Solve q - 4 = -g for q.\n | 4\n | ibivibiv/math_instruct | |
Simplify (1*(sqrt(1053) + 1)**2 - ((sqrt(208) - sqrt(208)*-2) + -5)**2)*5.\n | -4215 + 690*sqrt(13)\n | ibivibiv/math_instruct | |
Find h, given that -4*h + 5*h + 7685*h**2 - 7686*h**2 - 5*h = 0.\n | -4, 0\n | ibivibiv/math_instruct | |
In base 15, what is -c016 + -3?\n | -c019\n | ibivibiv/math_instruct | |
Let h(a) = -a - 6. Let d(u) = -u - 11. Let l(r) = 3*d(r) - 5*h(r). List the prime factors of l(3).\n | 3\n | ibivibiv/math_instruct | |
What are the prime factors of 1360461?\n | 3, 439, 1033\n | ibivibiv/math_instruct | |
Let n(d) = -10 + 11 + 2*d + d - 2. Let t(f) = 5. Let k(p) = p - 14. Let z(s) = 4*k(s) + 11*t(s). Let m be (-78)/21 - 4/14. Calculate m*z(x) + 5*n(x).\n | -x - 1\n | ibivibiv/math_instruct | |
Let l = -12 + 9. Put 3, l, 0 in increasing order.\n | l, 0, 3\n | ibivibiv/math_instruct | |
What is the least common multiple of 1365756 and 2800?\n | 136575600\n | ibivibiv/math_instruct | |
What is the sixth root of 51482557 to the nearest integer?\n | 19\n | ibivibiv/math_instruct | |
Is 70 a factor of 320965552?\n | False\n | ibivibiv/math_instruct | |
b"What is the cth term of -24631182, -49262376, -73893570?\n" | -24631194*c + 12\n | ibivibiv/math_instruct | |
Let w be ((-4)/(-10))/(18/27630). Let q(y) = w - 339 + 9*y - 325. Let m be q(9). Is m smaller than 31?\n | False\n | ibivibiv/math_instruct | |
Let b = -283397/22 - -12884. Calculate the common denominator of b and -61/4.\n | 44\n | ibivibiv/math_instruct | |
Solve -239*r + 237*r = 10 for r.\n | -5\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 3869827 and 26.\n | 13\n | ibivibiv/math_instruct | |
Product of -3.605 and 0.5.\n | -1.8025\n | ibivibiv/math_instruct | |
Let s = -12 - -4. Let z = s + 8.4. Let m = 0.1 - z. What is the smallest value in -5, -4, m?\n | -5\n | ibivibiv/math_instruct | |
Suppose -5*i + 13 = -i + 3*x, 3*x = i - 7. Suppose 5*v - 7*s + 2*s = 400, 328 = i*v + 4*s. What is the greatest common factor of 27 and v?\n | 27\n | ibivibiv/math_instruct | |
Convert -51b (base 16) to base 12.\n | -90b\n | ibivibiv/math_instruct | |
Let p = -17405 - -17597. Sort 3, p, 0, 4, 5.\n | 0, 3, 4, 5, p\n | ibivibiv/math_instruct | |
Let i(x) be the third derivative of -3*x**4/4 - 47*x**3/6 + 152*x**2. Calculate the least common multiple of i(-3) and 18.\n | 126\n | ibivibiv/math_instruct | |
Does 7 divide 93003933?\n | False\n | ibivibiv/math_instruct | |
Let q(h) = 139*h**2 - 3*h - 2. Suppose 4*i - k = -7, -5*i + 10 = -9*i - 2*k. List the prime factors of q(i).\n | 2, 5, 7\n | ibivibiv/math_instruct | |
Suppose 0*n - 5*n + 283 = 3*a, 147 = 3*n - 2*a. Solve -20*y = 33*y - n for y.\n | 1\n | ibivibiv/math_instruct | |
Find the third derivative of 2*c**4 + 53248813*c**3 + 16*c**2 - 102657*c - 4.\n | 48*c + 319492878\n | ibivibiv/math_instruct | |
Which is the third biggest value? (a) 2/261 (b) -0.08 (c) 5 (d) -3/5 (e) 2\n | a\n | ibivibiv/math_instruct | |
Solve r - r = -4*r for r.\n | 0\n | ibivibiv/math_instruct | |
Let z(y) = -13*y**3 + y**2 + y - 1. Does 11 divide z(-1)?\n | False\n | ibivibiv/math_instruct | |
What is a in -5*a**3/4 + 205*a**2/2 - 8405*a/4 = 0?\n | 0, 41\n | ibivibiv/math_instruct | |
(-8)/68 + (21/18)/(340/(-330))\n | -5/4\n | ibivibiv/math_instruct | |
Solve 1769 = -g - 15*z + 1744, 5*g - 17 = -4*z for g.\n | 5\n | ibivibiv/math_instruct | |
4*-2727.99\n | -10911.96\n | ibivibiv/math_instruct | |
What is the square root of 47361 to the nearest integer?\n | 218\n | ibivibiv/math_instruct | |
Round 27581012.2 to the nearest one thousand.\n | 27581000\n | ibivibiv/math_instruct | |
Let v(n) = n**3 - 2*n**2 - 6*n + 4. Let d be v(4). Solve -l + 2 = -g, -4*l - 2*g + d = -2*l for l.\n | 4\n | ibivibiv/math_instruct | |
Simplify (h**(-1/2)/(h*h**(-3/7)))**(-26) assuming h is positive.\n | h**(195/7)\n | ibivibiv/math_instruct | |
Put 5, 17, 3 in descending order.\n | 17, 5, 3\n | ibivibiv/math_instruct | |
What is -596424 times 7?\n | -4174968\n | ibivibiv/math_instruct | |
Suppose 3*n = -4*i + 27, -3*i + 11*n - 15*n + 22 = 0. Suppose 246 - 96 = 5*x. Let h be (-16)/70 - i/x. Is h at least -1?\n | True\n | ibivibiv/math_instruct | |
Suppose h - 4*n + 3 = 0, h - 3*h + 5 = 3*n. Is -3/7 greater than h?\n | False\n | ibivibiv/math_instruct | |
Two letters picked without replacement from ojojjjjjjjjjojjjjj. Give prob of picking 1 o and 1 j.\n | 5/17\n | ibivibiv/math_instruct | |
What is the least common multiple of 1113 and 428346?\n | 2998422\n | ibivibiv/math_instruct | |
What is the units digit of 7016?\n | 6\n | ibivibiv/math_instruct | |
b"What is the uth term of 303, 611, 933, 1275, 1643, 2043?\n" | u**3 + u**2 + 298*u + 3\n | ibivibiv/math_instruct | |
Let a(u) = -u**2 - 3*u + 22. Let x be a(-14). Let j = -115 - x. What is the remainder when 592 is divided by j?\n | 14\n | ibivibiv/math_instruct |
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