In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x²+y²≤1, y−x²>0

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x²+y²<16, y≥2^x

Find the value of the objective function z = 2x + 3y at each corner of the graphed region shown. What is the maximum value of the objective function? What is the minimum value of the objective function?

Find the length and width of a rectangle whose perimeter is 36 feet and whose area is 77 square feet.

In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.

Exercises 57–59 will help you prepare for the material covered in the next section. Subtract: $\frac{3}{x - 4} - \frac{2}{x + 2}$

Exercises 57–59 will help you prepare for the material covered in the next section. Add: (5x−3)/(x²+1) + 2x/(x²+1)².

Find the length and width of a rectangle whose perimeter is 40 feet and whose area is 96 square feet.

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

$\begin{cases} x \geq 0 \\ y \geq 0 \\ 2x + 5y < 10 \\ 3x + 4y \leq 12 \end{cases}$

Exercises 57–59 will help you prepare for the material covered in the next section. Solve: $\begin{cases} A + B = 3 \\ 2A - 2B + C = 17 \\ 4A - 2C = 14 \end{cases}$

In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 3x+y≤6, 2x−y≤−1, x>−2, y<4

In Exercises 63–64, write each sentence as an inequality in two variables. Then graph the inequality. The y-variable is at least 4 more than the product of -2 and the x-variable.

Write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the x-variable and the y-variable is at most 4. The y-variable added to the product of 3 and the x-variable does not exceed 6.

Find the partial fraction decomposition of 4x²+5x-9/(x³- 6x-9)

In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the x-variable and the y-variable is no more than 2. The y-variabe is no less than the difference between the square of the x-variable and 4.

In Exercises 69–70, rewrite each inequality in the system without absolute value bars. Then graph the rewritten system in rectangular coordinates. |x|≤2, |y|≤3

Use a system of linear equations to solve Exercises 73–84. How many ounces of a 15% alcohol solution must be mixed with 4 ounces of a 20% alcohol solution to make a 17% alcohol solution?

Use a system of linear equations to solve Exercises 73–84. How many ounces of a 50% alcohol solution must be mixed with 80 ounces of a 20% alcohol solution to make a 40% alcohol solution?

Solve the systems in Exercises 79–80.

$\{\begin{array}{c}{\log }_y\text{ x=3}\\ {\log }_y\text{ (4x)=5}\end{array}$

Solve the systems in Exercises 79–80.

$\{\begin{array}{c}\text{log }{x}^2=y+3\\ \text{log }{x}^{}=y-1\end{array}$

Solve: x⁴+2x³−x²−4x−2=0

Exercises 86–88 will help you prepare for the material covered in the first section of the next chapter. a. Does (4, −1) satisfy x + 2y = 2? b. Does (4, -1) satisfy x- 2y= 6?