Exam 7: Systems Of Equations and Inequalities

Select the region determined by the constraints.Then find the maximum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. ​ Objective function: ​ Z = 3x + 2y ​ Constraints: ​ X ≥ 0 ​y ≥ 0 5x + 2y ≤ 20 5x + y ≥ 10 ​ ​

A small fast-food restaurant invests $5,951 to produce a new food item that will sell for $3.81.Each unit can be produced for $2.50.How many items must be sold to break even? ​

Select the correct graph of the inequality. $( x - 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } > 4$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } 3 x + 2 y = 10 \\2 x + 5 y = 3\end{array} \right.$

Solve the system of linear equations by the method of elimination.Find (u,v) and check your solution algebraically. $\left\{ \begin{array} { l } 5 u + 6 v = 28 \\3 u + 5 v = 20\end{array} \right.$

The perimeter of a triangle is 170 feet.The longest side of the triangle is 5 feet shorter than twice the shortest side.The sum of the lengths of the two shorter sides is 36 feet more than the length of the longest side.Find the lengths of the sides of the triangle. ​

Determine whether the ordered triple is a solution of the system of equations. $\left\{ \begin{array} { c l } 6 x - y + 2 z & = 26 \\4 x - 3 z & = 26 \\2 x + 5 z & = 0\end{array} \right.$ $( 5,0 , - 2 )$

According to automobile association of a country, on March 27, 2009, the national average price per gallon of regular unleaded (88-octane) gasoline was $2.08, and the price of premium unleaded (93-octane) gasoline was $2.27.Write an objective function that models the cost of the blend of mid-grade unleaded gasoline (89-octane).What is the optimal cost? ​

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 4 } { x ^ { 2 } - 3 x }$

Solve the system of equations by graphing. $\left\{ \begin{aligned}x + y & = 0 \\6 x - 7 y & = 13\end{aligned} \right.$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 7 x ^ { 2 } + 6 } { ( x - 6 ) ^ { 3 } }$

Use back-substitution to solve the system of linear equations. $\left\{ \begin{array} { c c } 2 x + y - 3 z & = 10 \\y + z & = 6 \\z & = 4\end{array} \right.$

Select the correct graph of the inequality. $10 x ^ { 2 } - y - 11 > 0$

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. ​ Objective function: ​ Z = 7x + 6y ​ Constraints: ​ X ≥ 0 ​y ≥ 0 5x + 2y ≤ 20 5x + y ≥ 10 ​

Find the equilibrium point (x,p) of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. Demand Supply p=150-0.07x p=65+0.1x

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 2 x } { ( x - 2 ) ^ { 2 } }$

Select the correct graph of the inequality. $y < \ln 13 x$

Use a graphing utility to graph the inequality. $y \geq \frac { 5 } { 9 } x - 4$

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. $\left\{ \begin{array} { c } x - y = 2 \\- 2 x + 2 y = 9\end{array} \right.$

Derive a set of inequalities to describe the region. Triangle: vertices at (0, 0), (4, 0), (4, 5)