Exam 10: Systems and Matrices

Provide an appropriate response -If the graphs of a system of two equations are a line and a parabola, what are the possible numbers of solutions (with real coordinates) of this system?

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $y \leq 2 x - x ^ { 2 }$

Perform the operation or operations when possible. - $\left[ \begin{array} { r } 3 \\- 2 \\- 4\end{array} \right] + \left[ \begin{array} { r } - 5 \\3 \\7\end{array} \right]$

Evaluate the determinant. - $\left| \begin{array} { l l l l } 5 & 2 & 1 & 6 \\5 & 4 & 5 & 7 \\8 & 6 & 8 & 1 \\7 & 2 & 9 & 8\end{array} \right|$

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. - 2x+8y+4z=-16 x+4y+2z=8 x+y+z=-2

Solve the linear programming problem. -A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400, and the average monthly salary of an aide is $1100. The camp can accommodate up to 45 staff members and needs at least 30 to run properly. The Camp must have at least 10 aides and may have up to 3 aides for every 2 counselors. How many Counselors and how many aides should the camp hire to minimize cost?

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - xy=30 x+y=-11

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Provide an appropriate response. -For a certain system of two linear equations, the solution set is $\{ 10,7 \}$ , and $D = - 27$ . Find the values of $D _ { x }$ and $D _ { y }$ .

Find the value of the determinant. - $\left| \begin{array} { l l l } 3 & 4 & 1 \\4 & 1 & 2 \\4 & 1 & 1\end{array} \right|$

The following graph shows the populations of the metropolitan areas of City X and City Y over six years. -If equations of the form y = f(t) were determined that modeled either of the two graphs, then the variable t would represent and the variable y would represent .

Use the given row transformation to change the matrix as indicated. - $\left[ \begin{array} { r r r } 3 & 5 & 12 \\ 3 & 4 & 2 \\ 6 & - 4 & 5 \end{array} \right] ; - 2$ times row 2 added to row 3

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y=(x+8) y=

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -A television manufacturing company has two different factories. The profit function for Factory I wl televisions are manufactured and sold is as follows: $P ( x ) = - 0.07 x ^ { 2 } + 25 x - 250$ The profit function for Factory II when $x$ televisions are manufactured and sold is as follows: $P ( x ) = - 0.075 x ^ { 2 } + 35 x - 1500$ For what number of televisions is the profit the same at both factories, and what is the profit?

Solve the system by elimination. - x+2y=-14 6x+3y=-21

If the system has infinitely many solutions, write the solution set with x arbitrary. - x+y-2z-8=0 3x+z+6=0 2x-y+3z+14=0

Solve the system by substitution. - x+y=-12 x-y=2

Solve the equation for x. - $\left| \begin{array} { r r r } 0 & 0 & x \\- 4 & x & - 4 \\1 & 1 & x\end{array} \right| = 4$

Find the value of the determinant. - $\left| \begin{array} { l l l } 2 & 2 & 2 \\3 & 4 & 7 \\5 & 8 & 5\end{array} \right|$