et k(s) = s. Let f(x) = x**2 + 2*x + 2. Let i(v) = g*k(v) + f(v). What is the units digit of i(3)?
2
Let t = -7 + 16. Suppose -g = 3*c - t, -4*g - c + 15 + 65 = 0. What is the units digit of g?
1
Suppose -3*k = 3*w - 5*w + 129, 5*k - 25 = 0. Let t = w + -49. What is the tens digit of t?
2
Let q = -17 - -27. Let x = -6 + q. Suppose x*b - 3*y = -0*y + 71, -4*y = 3*b - 22. What is the units digit of b?
4
Suppose 4*v = v + 18. Suppose -a = -x + v, -2*x = 2*a - 3*a - 13. What is the units digit of x?
7
Let f(c) = -c**3 - 5*c**2 + 3*c + 1. What is the tens digit of f(-6)?
1
What is the units digit of (7 + -5)/(0 + 1)?
2
Let d(q) = q - 5. Let y be d(5). What is the units digit of y + 1 - (0 - 4)?
5
Let p(z) = -z - 10. Let x be p(-10). Suppose 3*w + 3*n - 51 = x, 0*w + 5*n + 65 = 5*w. What is the units digit of w?
5
What is the units digit of ((-5136)/(-32))/(3/4)?
4
Let h(p) be the first derivative of -p**3/3 + 3*p**2 - 7*p - 4. Let u be h(5). Let s(k) = -k**3 + 2*k**2 + 2*k + 3. What is the units digit of s(u)?
5
Suppose -c - 3*d + 235 = 0, 4*c - 13*d + 12*d = 979. What is the hundreds digit of c?
2
What is the units digit of ((-8)/12)/((-1)/9)?
6
Let u = 22 - 16. What is the units digit of u?
6
Let q(f) = f**2 + 3*f - 2. Let l be q(-4). Suppose -2 = i - l*i. What is the units digit of i?
2
Let k = -59 + 163. What is the hundreds digit of k?
1
Suppose 0 = -0*s + 3*s + 12. What is the units digit of 2/s - 19/(-2)?
9
Suppose 0 = -5*u + 448 - 118. Let o be (4/(-12))/((-2)/u). Suppose 2*s = 41 - o. What is the units digit of s?
5
What is the hundreds digit of (-2)/(-6)*-3*(5 - 114)?
1
Suppose -d - 3*v = -0*d - 9, 5*v - 23 = d. Suppose 0*q - 2*q = 8. Let j = d - q. What is the units digit of j?
1
Let i(k) = k**3 + 26*k**2 - 36*k - 63. What is the hundreds digit of i(-27)?
1
Let s(q) = 2*q**2 - q + 22. What is the units digit of s(10)?
2
Let u = 11 + -9. What is the units digit of u + 4/(8/18)?
1
Let g(h) = h**3 + 8*h**2 + 5*h - 11. Let o be g(-7). Suppose -8*l + 195 = -o*l. What is the units digit of l?
9
Suppose -3*u - 2*u = -2*g + 438, -5*g = 5*u + 410. Let j = -8 + 0. What is the units digit of u/j + (-3)/(-12)?
1
Suppose -4*d = -2*d - 22. Let c = d + -4. What is the units digit of c?
7
Let u(w) = -w + 3*w**3 + w**3 - 3*w**3 + w**2. Let h be u(-2). Let d = 6 - h. What is the units digit of d?
8
Let h = -9 + 30. Suppose -3*j = -h - 3. Suppose 0 = w + o - j, 5*w - 3*o + 4*o - 24 = 0. What is the units digit of w?
4
Let w = 8 - 0. Suppose -5*m + 2*y + 93 = 0, 3*m - 55 + w = -y. What is the units digit of m?
7
Suppose -3*i - 8 = i. Let k(x) = 3 - 2*x - 6 + 0*x. What is the units digit of k(i)?
1
Suppose -9 = -8*q + 119. What is the units digit of q?
6
Let s be (18/4)/(6/8). Suppose 4*h = 102 - s. Suppose -f = -5*q - h, 4 = -3*f + 2*f - 2*q. What is the units digit of f?
4
Let n be 5/2 + 1/2. Suppose -n*v = 2 - 8. What is the units digit of v/4*(-1 + 3)?
1
Let l(a) = -a**3 - a**2 + a + 2. Let s be l(0). Suppose 281 = 5*t + 2*y, -s*y - 3*y = 2*t - 104. What is the units digit of t?
7
Let v(j) = j**2 + 2. Let y be (-3)/(-1*(-3 - -2)). What is the tens digit of v(y)?
1
Let j(v) be the second derivative of v**5/20 - 11*v**4/12 + 7*v**3/3 - 6*v**2 - 10*v. What is the units digit of j(10)?
8
Let x(j) be the third derivative of -j**4/4 - j**3/3 + j**2. Let i be x(-4). Suppose i = 3*z + 4. What is the units digit of z?
6
Let w(h) = -h - 7. Let q be w(-10). Suppose q*b - 33 = 54. What is the units digit of b?
9
Let c(v) = 2*v + 3. Let f(x) = 2*x + 4. Let t(j) = -7*c(j) + 6*f(j). What is the units digit of t(-3)?
9
Suppose -12 = -4*q - 4. Let p(a) = a**3 - 3*a**2 - a. Let w be p(q). Let g = w + 10. What is the units digit of g?
4
Suppose 4*x + 0*w + 3*w = 31, -2*x = w - 17. What is the tens digit of x?
1
Let b(k) = -3*k + 4. Let m(r) = -13*r + 17. Let o(d) = -9*b(d) + 2*m(d). Let a be o(0). What is the units digit of 7/(1/(-2)*a)?
7
What is the units digit of ((-2)/12 + (-18)/12)*-54?
0
What is the tens digit of (-1710)/(-14) - 1/7?
2
Suppose 4*k + 74 = -4*l - 6, -5*l + 10 = 0. Let h = k - -23. What is the units digit of h?
1
Let z(v) = -4*v - 3. What is the units digit of z(-6)?
1
Let a(d) = 6*d**2 + 1. Let k be a(1). Let j(n) = -5*n + 0*n - k + 2*n. What is the units digit of j(-5)?
8
Let f(n) = -9*n**3 + 0*n**2 + 2*n + 5*n**3 + 1 - n**2. Let u be f(-2). Let k = u + -15. What is the units digit of k?
0
Suppose 0 = 3*t - j - 43, -j + 4*j + 12 = 0. What is the tens digit of t?
1
Let v(w) = -2*w - 4. Suppose -3*l + 3*f = 0, 0*f - 2*f - 18 = 4*l. What is the units digit of v(l)?
2
Let u(t) = t**2 - 3. Let v be u(4). Suppose -6 = -l + v. What is the tens digit of l?
1
Let m be (-156)/18 + (-2)/6. Let h be (m/(-6))/(3/16). Suppose -r + h = -8. What is the units digit of r?
6
What is the tens digit of 2 + (-3540)/(-26) + (-6)/39?
3
Suppose 3*b - 5*f - 587 = 0, -4*b + 4*f - 8*f = -836. What is the hundreds digit of b?
2
Suppose -11*o = -1228 - 312. What is the hundreds digit of o?
1
Let s = 47 + -18. What is the tens digit of s?
2
Let w(o) = o**2 + 7*o + 4. Let n be w(-7). Suppose -135 = -f - n*f. What is the tens digit of f?
2
What is the tens digit of 24/12*2/(-2) - -49?
4
Let v be (-2)/5 - 48/(-20). Suppose -4*o + 11 = 3*b, -o + 3 = 2*b - 1. Suppose 0 = -o*p + 20 - v. What is the units digit of p?
9
Suppose 5*g + 28 + 17 = 0. Let n = 18 + g. What is the units digit of n?
9
Suppose -4*g - 1 = -3*v, -3*g - 3*v - 10 = -4. Let t(s) be the first derivative of -s**2 - s - 20. What is the units digit of t(g)?
1
Let h be (15/(-12))/((-2)/8). Suppose -10 = 5*i + 2*z, -2*z = -h*i + 3*z + 25. Suppose i = -2*w - 5*s + 10, 0 = 4*w + 2*s - 20. What is the units digit of w?
5
Suppose h + 2*h + 3*i = 135, h + 3*i - 51 = 0. Suppose n - h = -2*n. What is the units digit of n?
4
Suppose 2*k - 52 = -4*m - 2*k, -1 = k. What is the units digit of m?
4
Let w = -85 - -148. What is the units digit of w?
3
Let x(b) = b**2 - 20*b + 14. What is the tens digit of x(29)?
7
Let q(g) = 5*g**2 + g + 9. Let h(w) = 9*w**2 + 2*w + 17. Let u(b) = 4*h(b) - 7*q(b). Let p be u(0). Suppose 3*r - 14 = -p. What is the units digit of r?
3
Suppose 0*u = -2*u + 6. What is the units digit of -1 + (u - 1) + 0?
1
Suppose -5*n + 3*s = -9, 4*s - 3 = n - 15. Suppose n = -4*c + 150 - 38. What is the tens digit of c?
2
Let h = 12 - 7. Suppose -p - 2*k = -3*p + 30, 0 = -2*p - h*k + 30. What is the tens digit of p?
1
Let f = 14 + 23. Suppose -5 = -5*w, -w - f = -3*h + 22. What is the units digit of h?
0
Let r(o) = 18*o. What is the hundreds digit of r(9)?
1
Let g = 7 + -3. Suppose 3 = -2*r + 3*k, -2*r + r + g*k = 14. What is the units digit of r?
6
Let z(i) = 16*i**3 - i**2. Let n be z(1). Let f be 1 + -1 + 4/2. Suppose f*u = -c + n, 5*c = -3*u - u + 69. What is the tens digit of c?
1
Let z = -22 - -38. Suppose -3*a = -56 - z. Suppose -2*x - x = -a. What is the units digit of x?
8
Suppose 582 = 55*l - 52*l. What is the hundreds digit of l?
1
Let o(g) be the first derivative of g**4 - 2*g**3/3 + g - 1. Let i(z) = z**3 + 4*z**2 + z + 5. Let j be i(-4). What is the units digit of o(j)?
3
Let s(f) = 2*f**3 - f**2 + f. Let r be s(1). Suppose 3*x - 44 = -2*u, -2*u + 34 + 6 = r*x. Suppose -4*k - 4 = -u. What is the units digit of k?
3
Suppose -2*d + 7 = -d. Let g = 12 - d. What is the units digit of g?
5
Let h(m) = -2*m**3 - 8*m**2 + 17*m. Let g(z) = -3*z**3 - 7*z**2 + 18*z + 1. Let x(w) = -3*g(w) + 4*h(w). What is the tens digit of x(10)?
3
Let n be (6/4)/(2/4). Suppose 43 = i - n*d, -6 + 79 = 3*i + 5*d. Suppose 5*u + 3*z = -0*z + 52, -i = -3*u - 2*z. What is the tens digit of u?
1
Let n(d) = d**3 + 9*d**2 + 4. Let x be n(-9). Suppose -x*k + 6*k - 4 = 0. Suppose 5*i - k - 8 = 0. What is the units digit of i?
2
What is the hundreds digit of 191 + 1 - (-12)/3?
1
Let z be 14 + (-4 + 2 - 0). Suppose -z = 2*h - 2. Let r(k) = -k**2 - 7*k - 3. What is the units digit of r(h)?
7
Suppose -51 = 13*u - 14*u. What is the units digit of u?
1
Suppose -2*t + 7 = -3*t. Let z = -5 - t. Suppose -d + z = -2. What is the units digit of d?
4
Suppose 0 = -x - 4*o - 18, -3*x + 11 = -5*x - 3*o. Suppose i = 2*i - x. Suppose 5*m - 12 = -i. What is the units digit of m?
2
Let g(c) be the second derivative of c**5/20 + c**4/6 - c**3/6 - c**2/2 + c. Wha