Exam 5: Systems of Equations and Inequalities

Solve the problem. -The equation that represents the proper traffic control and emergency vehicle response availability in a small city is $2 \mathrm { P } + 3 \mathrm {~F} \leq 23$ , where $\mathrm { P }$ is the number of police cars on active duty and $\mathrm { F }$ is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation $2 \mathrm { P } + \mathrm { F } \leq 17$ is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so $\mathrm { P } \geq 0$ and $\mathrm { F } \geq 0$ . Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for $\mathrm { P }$ and the vertical axis for F. If 5 police cars are on active duty and 5 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied?

Solve the system by the addition method. - 2y=-22-7x 2x=8-2y

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. - 2x-7y=5 -6x+21y=-20

Graph the inequality. - $2 x + 4 y \leq 8$

Determine if the given ordered triple is a solution of the system. - (3,-1,-2) x+2y+2z=-3 5y+3z=-11 z=-2

Graph the solution set of the system of inequalities or indicate that the system has no solution. - 2x+y<2 2x+y>1

Solve the problem. -The area of a rectangular piece of cardboard shown is 860 square inches. The cardboard is used to make an open box by cutting a 4-inch square from each corner and turning up the sides. If the box is to have a Volume of 1680 cubic inches, find the dimensions of the cardboard that must be used.

Solve the system of equations. - -13+4z=3(x-2y) 3(x-4y-z)=-18 -3(2x+y)+3z=6

Solve Nonlinear Systems By Addition Solve the system by the addition method. - +=40 -13x+=82

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. -Objective Function $\quad \mathrm { z } = 17 \mathrm { x } - 24 \mathrm { y }$ Constraints $0 \leq \mathrm { x } \leq 5$ $0 \leq y \leq 8$ $4 x + 5 y \leq 30$ $4 x + 3 y \leq 20$

Decompose P/Q, Where Q Has Repeated Linear Factors Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. - $\frac { 9 x ^ { 2 } - 9 x + 6 } { ( x - 1 ) ^ { 3 } }$

Solve the problem. -A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 2 hot dogs, 4 bags of potato chips, and 3 soft drinks for $9.00. The price of a hot dog is $1.50 more than the price of a bag of Potato chips. The cost of a soft drink is $3.00 less than the price of two hot dogs. Find the cost of each item.

Graph the solution set of the system of inequalities or indicate that the system has no solution. - y\geq3x y\leq8

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. - Objective Function z=7x-6y Constraints x\geq0 0\leqy\leq5 x-y\leq9 x+2y\leq12

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) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }$ - $\frac { 7 x + 5 } { x ^ { 2 } - 8 x + 15 }$

Solve the system of equations by the substitution method. - $2 y = x + 8$ $2 x + 4 y = 0$

Graph the solution set of the system of inequalities or indicate that the system has no solution. -

Decide if the system of equations in two variables is linear or nonlinear. - $\left\{ \begin{array} { l } x y = - 7 \\x + 9 y = 5\end{array} \right.$

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. - y=x+6 x-2y=-12

Solve the problem. -In 1985, in the town of Appleby, 20.4% of Hispanics were overweight, increasing by an average of 0.45% per year. In 1985, in the town of Appleby, 0.18% of whites were overweight, increasing by an average of 30.4% per year. If these trends continue, in which year will the percentage of Hispanics who are Overweight be the same as the percentage of whites who are overweight? Round to the nearest year. What Percentage of Hispanics (to the nearest whole percent)will be overweight at that time?