91Ó°ÊÓ

Solve each equation by completing the square. $$-3 x^{2}+6 x+5=0$$

Solve each quadratic inequality. Write each solution set in interval notation. $$x^{2} \leq 9$$

Find each sum or difference. Write the answer in standard form. $$(2-5 i)-(3+4 i)-(-2+i)$$

Solve each equation by completing the square. $$-4 x^{2}+8 x=7$$

The table gives methane gas emissions from all sources in the United States, in millions of metric tons. The quadratic model $$y=1.493 x^{2}+7.279 x+684.4$$ approximates the emissions for these years. In the model, \(x\) represents the number of years since 2004 so \(x=0\) represents \(2004, x=1\) represents 2005 and so on. (a) According to the model, what would be the emissions in \(2010 ?\) Round to the nearest tenth of a million metric tons. (b) Find the year beyond 2004 for which this model predicts that the emissions reached 700 million metric tons. $$\begin{array}{|c|c|} \hline \text { Year } & \begin{array}{c} \text { Millions of Metric } \\ \text { Tons of Methane } \end{array} \\ \hline 2004 & 686.6 \\ \hline 2005 & 691.8 \\ \hline 2006 & 706.3 \\ \hline 2007 & 722.7 \\ \hline 2008 & 737.4 \\ \hline \end{array}$$

Solve each equation or inequality. $$|3 x+1|-1<2$$

Solve each equation. $$\sqrt{2 x+5}-\sqrt{x+2}=1$$

Solve each equation or inequality. $$|5 x+2|-2<3$$

The average cost, in dollars, for tuition and fees for in-state students at four-year public colleges over the period \(2000-2010\) can be modeled by the equation $$y=3.026 x^{2}+377.7 x+3449$$ where \(x=0\) corresponds to 2000 \(x=1\) corresponds to \(2001,\) and so on. Based on this model, for what year after 2000 was the average cost 7605 dollar (Source: The College Board, Anmual Survey of Colleges.) (IMAGE CAN NOT COPY)

Solve each quadratic inequality. Write each solution set in interval notation. $$x^{2}>16$$