It \$ x + 1/x = 3\$, find the value of \$ x^3 + 1/x^3 \$.

A) 18

B) 23

C) 42

D) 12

Solve the nonlinear equation:
\$x^3 − 6x^2 + 11x − 6 = 0\$

A) x = - 1, 2, 0

B) x = 1,- 2, -9

C) x = -5, 2, 2

D) x = 1, - 2, 3

Show that the following system of equations has an infinite solution:
y - 2x = 5
10x - 5y + 25 = 0

A) \$ (a_1)/(a_2) ne (b_1)/(b_2) ne (c_1)/(c_2) \$

B) \$ (a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2) \$

C) \$ (a_1)/(a_2) ne (b_1)/(b_2) = (c_1)/(c_2) \$

D) \$ (a_1)/(a_2) = (b_1)/(b_2) ne (c_1)/(c_2) \$

If there is no solution to the linear equation system 4x - ky = 13, 7x + 6y = 9, then find the value of k.

A) \$ k = - 3/7 \$

B) \$ k = 7/24 \$

C) \$ k = - 24/7 \$

D) \$ k = - 11/2 \$

If the linear system 3x + 5y = 12 and 2x - ky = 8 has no solution, find the value of k.

A) \$10/3\$

B) \$3/10\$

C) \$-3/10\$

D) \$-10/3\$

simplify the expression:
\$((3 a^2)-(12 a)+(15))/(a^2 - 4)\$

A) \$ (3(a + 1)) / (a - 2) \$

B) \$ (3(a + 1)) / (a + 2) \$

C) \$ (3(a - 1) )/ (a + 2) \$

D) \$ (3(a - 1)) / (a - 2) \$

solve the non-linear equation:
\$ 4 a^2 - 8 a + 3 \$ = 0

A) \$a = (3/2)\$ and \$a = (1/2)\$

B) \$a = (1/2)\$ and \$a = (4/2)\$

C) \$a = (1/2)\$ and \$a = (3/2)\$

D) \$a = (3/2)\$ and \$a = (4/2)\$

Solve the nonlinear equation
\$ d^4 - 5 d^2 + 6 \$ = 0

A) \$ d^2 = 4\$ and \$ d^2 = 3\$

B) \$ d^2 = 2\$ and \$ d^2 = 3\$

C) \$ d = 2\$ and \$ d = 3\$

D) \$ d^2 = 2\$ and \$ d^2 = 4\$

Determine the number of solutions for the following system of linear equations:
2a + b = 5
4a + 2b = 10

A) Inconsistent

B) Independent

C) Dependent

D) Not enough information

If the linear system ax + by = 7 and cx + dy = 5 has no solution, find the relationship between a,b,c, and d.

A) ad - bc = 35

B) ac + bd = 35

C) ab - dc = 35

D) ad - bc = - 35