Chapter 1

Solve each equation or inequality. $$|6-2 x|+1=3$$

Carbon monoxide (CO) combines with the hemoglobin of the blood to form carboxyhemoglobin (COHb), which reduces transport of oxygen to tissues. Smokers routinely have a \(4 \%\) to \(6 \%\) COHb level in their blood, which can cause symptoms such as blood flow alterations, visual impairment, and poorer vigilance ability. The quadratic model $$T=0.00787 x^{2}-1.528 x+75.89$$ approximates the exposure time in hours necessary to reach this \(4 \%\) to \(6 \%\) level, where \(50 \leq x \leq 100\) is the amount of carbon monoxide present in the air in parts per million (ppm). (Source: Indoor Air Quality Environmental Information Handbook: Combustion Sources.) (a) A kerosene heater or a room full of smokers is capable of producing 50 ppm of carbon monoxide. How long would it take for a nonsmoking person to start feeling the above symptoms? (b) Find the carbon monoxide concentration necessary for a person to reach the \(4 \%\) to \(6 \%\) COHb level in 3 hr. Round to the nearest tenth.

Solve each formula for the indicated variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples \(4(a)\) and \((b)\). \(S=2 \pi r h+2 \pi r^{2}, \quad\) for \(h \quad\) (surface area of a right circular cylinder)

Solve each equation. $$\sqrt{x+7}+3=\sqrt{x-4}$$

Solve each equation by completing the square. $$-2 x^{2}+4 x+3=0$$

Solve each equation or inequality. $$|4-4 x|+2=4$$

Refer to Exercise \(45 .\) High concentrations of carbon monoxide (CO) can cause coma and death. The time required for a person to reach a COHb level capable of causing a coma can be approximated by the quadratic model $$T=0.0002 x^{2}-0.316 x+127.9$$ where \(T\) is the exposure time in hours necessary to reach this level and \(500 \leq x \leq 800\) is the amount of carbon monoxide present in the air in parts per million (ppm). (Source: Indoor Air Quality Environmental Information Handbook: Combustion Sources.) (a) What is the exposure time when \(x=600\) ppm? (b) Estimate the concentration of CO necessary to produce a coma in \(4 \mathrm{hr}\).

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

Solve each quadratic inequality. Write each solution set in interval notation. $$x(x+1)<12$$

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

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

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

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. $$\begin{array}{|c|c|} \hline \text { Year } & \begin{array}{c} \text { Millions of Metric } \\ \text { Tons of Methane } \end{array} \\ \hline 2004 & 686.6 \\ \hline 2005 & 691.8 \\ \hline 2006 & 706.3 \\ \hline 2007 & 722.7 \\ \hline 2008 & 737.4 \\ \hline \end{array}$$

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

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

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

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

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)

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

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

Solve each equation. $$\sqrt{4 x+1}-\sqrt{x-1}=2$$

Solve each equation by completing the square. $$-3 x^{2}+9 x=7$$

Solve each equation or inequality. $$\left|5 x+\frac{1}{2}\right|-2<5$$

Estimated revenue from Internet publishing and broadcasting in the United States during the years 2004 through 2008 can be modeled by the equation $$y=318.4 x^{2}+1612 x+8596$$ where \(x=0\) corresponds to the year \(2004, x=1\) corresponds to \(2005,\) and so on, and \(y\) is in millions of dollars. Approximate the revenue from Internet publishing and broadcasting in 2006 to the nearest million. (Source: U.S. Census Bureau.)

Find each sum or difference. Write the answer in standard form. $$-i \sqrt{2}-2-(6-4 i \sqrt{2})-(5-i \sqrt{2})$$

Solve each equation for \(x\). $$2(x-a)+b=3 x+a$$

Solve each equation. $$\sqrt{3 x}=\sqrt{5 x+1}-1$$

Francisco claimed that the equation \(x^{2}-8 x=0\) cannot be solved by the quadratic formula since there is no value for \(c .\) Is he correct?

Solve each equation or inequality. $$\left|2 x+\frac{1}{3}\right|+1<4$$

The number of U.S. households subscribing to cable TV for the period 2000 through 2010 can be modeled by the equation $$y=-0.0746 x^{2}+3.146 x+79.52$$ where \(x=0\) corresponds to \(2000, x=1\) corresponds to \(2001,\) and so on, and \(y\) is in millions. Based on this model, approximately how many U.S. households, to the nearest tenth of a million, subscribed to cable TV in 2008? (Source: Nielsen Media Research.)

Find each sum or difference. Write the answer in standard form. $$3 \sqrt{7}-(4 \sqrt{7}-i)-4 i+(-2 \sqrt{7}+5 i)$$

Solve each equation for \(x\). $$5 x-(2 a+c)=4(x+c)$$

Solve each quadratic inequality. Write each solution set in interval notation. $$4 x^{2}+3 x+1 \leq 0$$

Solve each equation. $$\sqrt{2 x}=\sqrt{3 x+12}-2$$

Solve each equation or inequality. $$|10-4 x|+1 \geq 5$$

If p units of an item are sold for \(x\) dollars per unit, the revenue is \(R=p x\). Use this idea to analyze the following problem. Number of Apartments Rented The manager of an 80-unit apartment complex knows from experience that at a rent of \(\$ 300,\) all the units will be full. On the average, one additional unit will remain vacant for each \(\$ 20\) increase in rent over \(\$ 300 .\) Furthermore, the manager must keep at least 30 units rented due to other financial considerations. Currently, the revenue from the complex is \(\$ 35,000 .\) How many apartments are rented? Suppose that \(x\) represents the number of \(\$ 20\) increases over \(\$ 300 .\) Represent the number of apartment units that will be rented in terms of \(x .\)

Find each product. Write the answer in standard form. $$(2+i)(3-2 i)$$

Solve each quadratic inequality. Write each solution set in interval notation. $$x^{2}-2 x \leq 1$$

Solve each equation. $$\sqrt{x+2}=1-\sqrt{3 x+7}$$

Solve each equation using the quadratic formula. $$x^{2}-x-1=0$$

Solve each equation or inequality. $$|12-6 x|+3 \geq 9$$

Find each product. Write the answer in standard form. $$(-2+3 i)(4-2 i)$$

Solve each equation for \(x\). $$4 a-a x=3 b+b x$$

Solve each quadratic inequality. Write each solution set in interval notation. $$x^{2}+4 x>-1$$

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

Solve each equation using the quadratic formula. $$x^{2}-3 x-2=0$$

Find each product. Write the answer in standard form. $$(2+4 i)(-1+3 i)$$

Which one of the following inequalities has solution set \((-\infty, \infty) ?\) A. \((x-3)^{2} \geq 0\) B. \((5 x-6)^{2} \leq 0\) C. \((6 x+4)^{2}>0\) D. \((8 x+7)^{2}<0\)

Solve each equation. $$\sqrt{2 \sqrt{7 x+2}}=\sqrt{3 x+2}$$