Exam 7: Systems Of Equations and Inequalities

The weekly rentals for a newly released DVD of an animated film at a local video store decreased each week.At the same time, the weekly rentals for a newly released DVD of a horror film increased each week.Models that approximate the weekly rentals R for each DVD are $\left\{ \begin{array} { l l } R = 380 - 24 x & \text { Animated film } \\R = 28 + 20 x & \text { Horror film }\end{array} \right.$ where x represents the number of weeks each DVD was in the store, with x = 1 corresponding to the first week.After how many weeks will the rentals for the two movies be equal

Write the partial fraction decomposition of the improper rational expression. $\frac { x ^ { 3 } - 2 x ^ { 2 } - 14 x + 48 } { x ^ { 2 } + x - 20 }$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { c } 5 x + 7 y = 21 \\- 14 x - 18 y = - 38\end{array} \right.$

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { ( x + 1 ) ( a - x ) }$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } 3 x + 11 y = 12 \\- 2 x - 5 y = 6\end{array} \right.$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x - 4 } { x \left( x ^ { 2 } + 7 \right) ^ { 2 } }$

Select an inequality for the shaded region shown in the figure.

Find the minimum value of the objective function and where it occurs, subject to the constraints: Objective function: Z = 4x + 16y Constraints: X $\ge$ 0 Y $\ge$ 0 X + 4y $\le$ 20 X + y $\le$ 18 2x + 2y $\le$ 21

Find the minimum value of the objective function and where it occurs, subject to the indicated constraints. ​ Objective function: ​ Z = 10x + 4y ​ Constraints: ​ 0 ≤ x ≤ 60 0 ≤ y ≤ 45 5x + 6y ≤ 420 ​​ ​

Use a graphing utility to solve the system of equations.Find the solution accurate to two decimal places. $\left\{ \begin{array} { l } y = 2 e ^ { - x } \\y = \ln ( x - 2 ) + 1\end{array} \right.$

Solve the system of linear equations by the method of elimination, find (x,y). $\left\{ \begin{array} { l } - 0.06 x + 0.01 y = 0.03 \\- 0.09 x - 0.04 y = 0.09\end{array} \right.$

According to automobile association of a country, on March 27, 2009, the national average price per gallon of regular unleaded (85-octane) gasoline was $2.02, and the price of premium unleaded (93-octane) gasoline was $2.23.The cost of the blend of mid-grade unleaded gasoline (92-octane).Determine the constraints for the objective function. ​

Write the partial fraction decomposition of the rational expression. $\frac { 3 x ^ { 2 } + 3 x + 18 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$

Solve the system graphically. $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 85 \\( x - 5 ) ^ { 2 } + y ^ { 2 } & = 50\end{aligned} \right.$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { r } x + 5 y = 11 \\3 x - 10 y = 18\end{array} \right.$

Derive a set of inequalities to describe the region.

Write a set of inequalities to describe the region. Rectangle: vertices at $( 1,5 ) , ( 9,5 ) , ( 9,9 ) , ( 1,9 )$

Find the sales necessary to break even (R = C) for the cost C of producing x units and the revenue R obtained by selling x units.(Round to the nearest whole unit.) ​ C = 8630x + 264,000, R = 9950x ​

Find the maximum value of the objective function and where it occurs, subject to the constraints: Objective function: Z = 8x + 9y Constraints: X $\ge$ 0 Y $\ge$ 0 X + 4y $\le$ 20 X + y $\le$ 18 2x + 2y $\le$ 21

Solve the system by the method of elimination and check any solutions algebraically. $\left\{ \begin{array} { l } 0.05 x - 0.03 y = 0.29 \\0.07 x + 0.02 y = 0.22\end{array} \right.$