Exam 10: Systems and Matrices

Solve the problem. -Linda invests $\$ 25,000$ for one year. Part is invested at $5 \%$ , another part at $6 \%$ , and the rest at $8 \%$ . The total income from all 3 investments is $\$ 1600$ . The combined income from the $5 \%$ and $6 \%$ investments is the same as the income from the $8 \%$ investment. Find the amount invested at each rate.

Solve the problem. -The following table shows the number of dog collars, in thousands, produced by Allied Pet Products in the three years considered. Find a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ that fits this data. Using this function, what would you predict the dog collar production of Allied Pet Product: to be in year 27 ? Year Number of dog collars (in thousands) 0 20 6 14 18 23.6

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - 4x-3y+6z=-5 8x+4y-8z=-5 20x-15y+30z=-1

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - $y \geq x^{2}+4$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - +=13.85 x=3y-1

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { r r r } - 3 & 7 & - 6 \\1 & \mathrm {~m} & - 2\end{array} \right] = \left[ \begin{array} { l l l } \mathrm { x } & \mathrm { y } & - 6 \\1 & 1 & - 2\end{array} \right]$

Provide an appropriate response -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 7. What does this indicate to you about the system of equations?

Provide an appropriate response -The solution set of the system $y _ { 1 } = - x + 5$ and $y _ { 2 } = - 2 x + 7$ is $\{ ( 2,3 ) \}$ . Using slopes and $y$ -intercept: determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - x+y-3=0 x-y-=0

Evaluate the determinant. - $\left| \begin{array} { r r r r } 3 & - 2 & 2 & - 1 \\4 & 1 & 1 & 6 \\- 3 & 2 & - 2 & 1 \\5 & 0 & 3 & - 2\end{array} \right|$

Perform the operation or operations when possible. - $\left[ \begin{array} { r r } - 4 & 1 \\2 & 5\end{array} \right] + \left[ \begin{array} { r r } 6 & 2 \\1 & - 1\end{array} \right]$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - y=10|x|-25 y=

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - $x^{2}-x y+y^{2}=3$ $2 x^{2}+x y+2 y^{2}=12$

Find the value of the determinant. - $\left| \begin{array} { l l l } 0 & 1 & 2 \\2 & 0 & 6 \\3 & 6 & 2\end{array} \right|$

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

If the system has infinitely many solutions, write the solution set with x arbitrary. - +-=- -+=- --+=

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[\begin{array}{rr|r}-3 & -7 & -2 \\3 & -2 & 3\end{array}\right]$

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - -2x+8y-z=-15 x-2y+7z=68 -4x+y+z=-18

Find the value of the determinant. - $\left| \begin{array} { l l } - 5 & - 3 \\b & a\end{array} \right|$

A nonlinear system is given, along with the graphs of both equations in the system. Determine if the points of intersection specified on the graph are solutions of the system by substituting directly into both equations. - y=(4x+2) y=