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Chapter 5: Problem 103
If \(x=3, y=2,\) and \(z=-3,\) does the ordered triple \((x, y, z)\) satisfy the equation \(2 x-y+4 z=-8 ?\)
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In Exercises 106-109, determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing a linear inequality, I should always use \((0,0)\) as a test point because it's easy to perform the calculations when 0 is substituted for each variable.
The group should write four different word problems that can be solved using a system of linear equations in two variables. All of the problems should be on different topics. The group should turn in the four problems and their algebraic solutions.
You are about to take a test that contains computation problems worth 6 points each and word problems worth 10 points each. You can do a computation problem in 2 minutes and a word problem in 4 minutes. You have 40 minutes to take the test and may answer no more than 12 problems. Assuming you answer all the problems attempted correctly, how many of each type of problem must you answer to maximize your score? What is the maximum score?
In \(1978,\) a ruling by the Civil Aeronautics Board allowed Federal Express to purchase larger aircraft. Federal Express's options included 20 Boeing 727 s that United Airlines was retiring and/or the French-built Dassault Fanjet Falcon \(20 .\) To aid in their decision, executives at Federal Express analyzed the following data: $$\begin{array}{lcc}\hline & \text { Boeing 727 } & \text { Falcon 20 } \\\\\hline \text { Direct Operating cost } & \$ 1400 \text { per hour } & \$ 500 \text { per hour } \\\\\text { Payload } & 42,000 \text { pounds } & 6000 \text { pounds }\end{array}$$ Federal Express was faced with the following constraints: \(\cdot\) Hourly operating cost was limited to \(\$ 35,000 .\) \(\cdot\) Total payload had to be at least \(672,000\) pounds. \(\cdot\) Only twenty 727 s were available. Given the constraints, how many of each kind of aircraft should Federal Express have purchased to maximize the number of aircraft?
Exercises 116-118 will help you prepare for the material covered in the next section. a. Graph the solution set of the system: $$\left\\{\begin{aligned} x & \geq 0 \\ y & \geq 0 \\ 3 x-2 x & \leq 6 \\ y & \leq-x+7 .\end{aligned}\right.$$ b. List the points that form the corners of the graphed region in part (a). c. Evaluate \(2 x+5 y\) at each of the points obtained in part (b).
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