In Problem given below, use the inverses found in Problems mentioned to solve each system of equations.

$$\left\{\begin{aligned} x+2 z & =2 \\ -x+2 y+3 z & =-\frac{3}{2} \\ x-y & =2\end{aligned}\right.$$

Given f(x) = x + 4 and g(x) = x$^2$ - 3x, find $(g \circ f)(-3)$.

A store that specializes in selling nuts has available 72 pounds (lb) of cashews and 120 lb of peanuts. These are to be mixed in 12-ounce (oz) packages as follows: a lower-priced package containing 8 oz of peanuts and 4 oz of cashews, and a quality package containing 6 oz of peanuts and 6 oz of cashews. (a) Use x to denote the number of lower-priced packages, and use y to denote the number of quality packages. Determine a system of linear inequalities that describes the possible numbers of each kind of package.

(b) Plot the system and label the corner points.

Solve the following system of equations. If the system has no solution, say that it is inconsistent.

$$\left\{\begin{aligned} x+4 y-3 z & =-8 \\ 3 x-y+3 z & =12 \\ x+y+6 z & =1\end{aligned}\right.$$

Solve each system. Use any method you wish.

$$\left\{\begin{array}{c}{\ln x=5 \ln y} \\ {\log _{2} x=3+2 \log _{2} y}\end{array}\right.$$

Nick has a credit card balance of $ 4200. If the credit card company charges 18 % interest compound daily, and Nick does not make any payments on the account, state how long will it take for his balance to double. Round to two decimal places.

The length of fence required to enclose a rectangular field is 3000 meters.What are the dimensions of the field if it is known that the difference between its length and width is 50 meters?

Four large cheeseburgers and two chocolate shakes cost a total of 7.90 dollars. Two shakes cost 15% more than one cheeseburger. What is the cost of a cheeseburger? A shake?

Solve the following system of equations. If the system has no solution, say that it is inconsistent.

$$\left\{\begin{aligned} x+2 y-z & =-3 \\ 2 x-4 y+z & =-7 \\ -2 x+2 y-3 z & =4\end{aligned}\right.$$

Mike's Toy Truck Company manufactures two models of toy trucks, a standard model and a deluxe model. Each standard model requires 2 hours (h) for painting and 3 h for detail work; each deluxe model requires 3 h for painting and 4 h for detail work. Two painters and three detail workers are employed by the company, and each works 40 h per week.

(a) Using x to denote the number of standard-model trucks and y to denote the number of deluxe-model trucks, determine a system of linear inequalities that describes the possible numbers of each model of truck that can be manufactured in a week.

(b) Plot the system and label the corner points.

The following problem is based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Nick has a credit card balance of $\$ 4200$. If the credit card company charges $18 \%$ interest compound daily, and Nick does not make any payments on the account, how long will it take for his balance to double? Round to two decimal places.

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$$\left\{\begin{array}{rr}{x-y-z=} & {1} \\ {-x+2 y-3 z=} & {-4} \\ {3 x-2 y-7 z=} & {0}\end{array}\right.$$

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

$$\left\{\begin{aligned}-x+y+z=&-1 \\-x+2 y-3 z=&-4 \\ 3 x-2 y-7 z=& 0 \end{aligned}\right.$$

In Problem given below, use the inverses found in Problems mentioned to solve each system of equations.

$$\left\{\begin{aligned} x-y+z & =2 \\ -2 y+z & =2 \\ -2 x-3 y & =\frac{1}{2}\end{aligned}\right.$$