Exam 10: Systems and Matrices

Solve the problem. -Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 132$ for 3 days and 300 miles, while Mary was charged $\$ 241$ for 5 days and 600 miles. What does Best Rental charge per day and per mile?

Solve the problem using matrices. -Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 106 g protein, 98 g fat, and 144 g carbohydrate. According to the health-conscious hostess, The marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs Have 14 g protein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, And 6 g carbohydrate. How many of each snack can he eat to obtain his goal?

Find the value of the determinant. - $\left| \begin{array} { r r r } 8 & - 6 & 5 \\0 & 3 & 6 \\0 & 0 & - 4\end{array} \right|$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $y \leq 3 \left( x ^ { 2 } + 3 \right) - 2$

Solve the problem. -A grain dealer sold to one customer 9 bushels of wheat, 3 of corn, and 5 of rye for $\$ 40.90$ ; to another, 3 of wheat, 5 of corn, and 9 of rye for $\$ 47.30$ ; and to a third, 5 of wheat, 9 of corn, and 3 of rye for $\$ 46.10$ . What was the price per bushel for corn?

Find the partial fraction decomposition for the rational expression. - $\frac { - 4 x ^ { 2 } - 2 x - 42 } { ( x - 3 ) \left( x ^ { 2 } + 3 \right) }$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l } \mathrm { a } \\9 \\8\end{array} \right] = \left[ \begin{array} { l } 8 \\\mathrm { x } \\8\end{array} \right]$