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Chapter 7: Problem 20
Graph each linear inequality. \(y>-2\)
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An important application of systems of equations arises in connection with supply and demand. As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The price at which supply and demand are equal is called the equilibrium price. The quantity supplied and demanded at that price is called the equilibrium quantity. Exercises 61-62 involve supply and demand. The following models describe demand and supply for threebedroom rental apartments. Demand Model Supply Model \(p=-50 x+2000\) \(p=50 x\) a. Solve the system and find the equilibrium quantity and the equilibrium price. b. Use your answer from part (a) to complete this statement: When rents are ____ per month, consumers will demand apartments and suppliers will offer _____ apartments for rent.
Describe the shape of a scatter plot that suggests modeling the data with a quadratic function.
In Exercises 65-66, let \(f\) and \(g\) be defined by the following table: $$ \begin{array}{|c|c|c|} \hline \boldsymbol{x} & \boldsymbol{f}(\boldsymbol{x}) & \boldsymbol{g}(\boldsymbol{x}) \\ \hline-2 & 6 & 0 \\ \hline-1 & 3 & 4 \\ \hline 0 & -1 & 1 \\ \hline 1 & -4 & -3 \\ \hline 2 & 0 & -6 \\ \hline \end{array} $$ Find \(|f(1)-f(0)|-[g(1)]^{2}+g(1) \div f(-1) \cdot g(2)\)
a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & -4 \\ \hline 1 & -1 \\ \hline 2 & 0 \\ \hline 3 & -1 \\ \hline 4 & -4 \\ \hline \end{array} $$
Solve each system by graphing. Check the coordinates of the intersection point in both equations. \(\left\\{\begin{array}{l}y=x+5 \\ y=-x+3\end{array}\right.\)
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