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Chapter 8: Problem 91
What does a dashed line mean in the graph of an inequality?
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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?
Determine the amplitude, period, and phase shift of \(y=-2 \cos \left(2 x-\frac{\pi}{2}\right) .\) Then graph one period of the function. (Section 5.5, Example 6)
An objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of \(x\) and \(y\) for which the maximum occurs. Objective Function Constraints $$ \begin{aligned} &z=x+6 y\\\ &\left\\{\begin{array}{l} {x \geq 0, y \geq 0} \\ {2 x+y \leq 10} \\ {x-2 y \geq-10} \end{array}\right. \end{aligned} $$
When using the addition or substitution method, how can you tell if a system of linear equations has infinitely many solutions? What is the relationship between the graphs of the two equations?
will help you prepare for the material covered in the next section. Solve by the addition method: $$\left\\{\begin{array}{l}{2 x+4 y=-4} \\\\{3 x+5 y=-3}\end{array}\right.$$
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