Exam 5: Systems of Equations and Inequalities

Graph the solution set of the system of inequalities or indicate that the system has no solution. - +\leq81 3x+4y\leq12

Solve Nonlinear Systems By Addition Solve the system by the addition method. - $2 x ^ { 2 } + x y - y ^ { 2 } = 3$ $x ^ { 2 } + 2 x y + y ^ { 2 } = 3$

Graph the inequality. -x + y < -4

Decompose P/Q, Where Q Has Only Distinct Linear Factors Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. 1) $\frac { 6 x - 4 } { ( x + 6 ) ( x + 2 ) }$ A) $\frac { A } { x + 6 } + \frac { B } { x + 2 }$ B) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ( x + 2 ) }$ C) $\frac { \mathrm { A } } { x + 6 } + \frac { \mathrm { B } } { \mathrm { x } + 2 } + \frac { \mathrm { Cx } + \mathrm { D } } { ( \mathrm { x } + 6 ) ( \mathrm { x } + 2 ) }$ D) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }$ - $\frac { 16 x ^ { 2 } + 68 x + 30 } { x ( x + 3 ) ( x + 5 ) }$

Solve Nonlinear Systems By Addition Solve the system by the addition method. - 4-4=-48 3+2=44

Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. - $\frac { 7 x ^ { 2 } + 13 x - 10 } { ( x + 6 ) \left( x ^ { 2 } + 5 \right) }$

Solve the problem. -The area of a garden is 2160 square feet, and the length of its diagonal is 78 feet. Find the dimensions of the garden.

Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. - $\frac { 5 x ^ { 2 } + 7 x + 11 } { x ^ { 3 } + 4 x ^ { 2 } + 5 x + 20 }$

Determine if the given ordered triple is a solution of the system. - (-3,-1,5) 5x+4y+z=-14 2x-2y-z=-9 3x+y+5z=15

Graph the solution set of the system of inequalities or indicate that the system has no solution. - y\geq2x-4 x+2y\leq7 y\geq-2 x\leq1

Use Linear Programming to Solve Problems Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. -Objective Function: z = -x - 5y Find maximum.

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - x+8y=37 5x+7y=20

Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. - $\frac { 5 x ^ { 3 } + 30 x - 6 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. - $\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$

Solve Nonlinear Systems By Addition Solve the system by the addition method. - -3-1=0 4+3-19=0

Solve the problem. -Find the values of $a , b$ , and $c$ such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 1 , - 5 ) , ( 2,13 )$ , and $( 3,23 )$ .

Solve the system of equations by the substitution method. - $- 4 x + 7 y = 59$ $2 x - 5 y = - 43$

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - 5x-6y=2 -20x+24y=-4

Determine whether the given ordered pair is a solution of the system. - (5,-1) 3x+y=14 2x+3y=7

Decompose P/Q, Where Q Has Only Distinct Linear Factors Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. 1) $\frac { 6 x - 4 } { ( x + 6 ) ( x + 2 ) }$ A) $\frac { A } { x + 6 } + \frac { B } { x + 2 }$ B) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ( x + 2 ) }$ C) $\frac { \mathrm { A } } { x + 6 } + \frac { \mathrm { B } } { \mathrm { x } + 2 } + \frac { \mathrm { Cx } + \mathrm { D } } { ( \mathrm { x } + 6 ) ( \mathrm { x } + 2 ) }$ D) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }$ - $\frac { x } { ( x - 3 ) ( x - 4 ) }$