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Chapter 7: Problem 30
Solve each system by the addition method. Be sure to check all proposed solutions. \(\left\\{\begin{array}{l}2 x-7 y=2 \\ 3 x+y=-20\end{array}\right.\)
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a. Determine if the parabola whose equation is given opens upward or downward. b. Find the vertex. c. Find the \(x\)-intercepts. d. Find the \(y\)-intercept. e. Use (a)-(d) to graph the quadratic function. \(y=-x^{2}+2 x+3\)
A patient is not allowed to have more than 330 milligrams of cholesterol per day from a diet of eggs and meat. Each egg provides 165 milligrams of cholesterol. Each ounce of meat provides 110 milligrams. a. Write an inequality that describes the patient's dietary restrictions for \(x\) eggs and \(y\) ounces of meat. b. Graph the inequality. Because \(x\) and \(y\) must be positive, limit the graph to quadrant I only. c. Select an ordered pair satisfying the inequality. What are its coordinates and what do they represent in this situation?
In Exercises 29-30, find the vertex for the parabola whose equation is given by writing the equation in the form \(y=a x^{2}+b x+c\). \(y=(x-3)^{2}+2\)
Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{r}x+y<4 \\ 4 x-2 y<6\end{array}\right.\)
Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{r}2 x-y<3 \\ x+y<6\end{array}\right.\)
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