Chapter 1

Determine whether the lines whose equations are given are parallel, perpendicular, or neither. \(3 x+y-3=0 \quad\) and \(\quad 6 x+2 y+17=0\)

Use interval notation to denote the set of all real numbers \(x\) that satisfy the given inequality. $$x \geq 12$$

Solve the equation by any method. $$2 x^{2}=6 x+3$$

Determine whether the lines whose equations are given are parallel, perpendicular, or neither. \(y=2 x+4\) and \(\quad .5 x+y=-3\)

Express the given numbers (based on 2006 estimates) in scientific notation. Population of the world: 6,506,000,000

Solve the equation by any method. $$t^{2}+4 t+13=0$$

Determine whether the lines whose equations are given are parallel, perpendicular, or neither. Do the points \((-4,6),(-1,12),\) and (-7,0) all lie on the same straight line? [Hint: Use slopes.]

Express the given numbers (based on 2006 estimates) in scientific notation. Population of the United States: 298,400,000

Solve the equation by any method. $$5 x^{2}+2 x=2$$

Express the given numbers (based on 2006 estimates) in scientific notation. Average distance from Earth to Pluto: 5,910,000,000,000 meters

Solve the equation by any method. $$\frac{7 x^{2}}{3}=\frac{2 x}{3}-1$$

Express the given numbers (based on 2006 estimates) in scientific notation. Radius of a hydrogen atom: .00000000001 meter

Solve the equation by any method. $$x^{2}+\sqrt{2} x-3=0$$

Express the given numbers (based on 2006 estimates) in scientific notation. Width of a DNA double helix: .000000002 meter

Use a calculator to find approximate solutions of the equation. $$4.42 x^{2}-10.14 x+3.79=0$$

Express the given number in normal decimal notation. Speed of light in a vacuum: \(2.9979 \times 10^{8}\) miles per second

Use a calculator to find approximate solutions of the equation. $$8.06 x^{2}+25.8726 x-25.047256=0$$

Find the equation of the perpendicular bisector of the line segment joining the two given points. $$(2,-3),(4,7)$$

Find the equation of the circle with given center and radius \(r\). $$(-3,4) ; \quad r=2$$

Express the given number in normal decimal notation. Average distance from the earth to the sun: \(1.50 \times 10^{11}\) meters

Use a calculator to find approximate solutions of the equation. $$3 x^{2}-82.74 x+570.4923=0$$

Find the equation of the perpendicular bisector of the line segment joining the two given points. $$(-6,2),(6,-7)$$

Find the equation of the circle with given center and radius \(r\). $$(-3,-5) ; \quad r=3$$

Express the given number in normal decimal notation. Electron charge: \(1.602 \times 10^{-27}\) coulomb

Use a calculator to find approximate solutions of the equation. $$7.63 x^{2}+2.79 x=5.32$$

Find an equation for the line satisfying the given conditions. Through (-2,1) with slope 3.

Find the equation of the circle with given center and radius \(r\). $$(0,0) ; \quad r=\sqrt{3}$$

Find all real solutions of the equation exactly. $$y^{4}-7 y^{2}+6=0$$

Find an equation for the line satisfying the given conditions. \(y\) -intercept -7 and slope 1.

Find the equation of the circle with given center and radius \(r\). $$(5,-2) ; \quad r=1$$

Express the given number in normal decimal notation. One light-year is the distance light travels in a 365 -day year. The speed of light is about 186,282.4 miles per second. (a) How long is 1 light-year (in miles)? Express your answer in scientific notation. (b) Light from the North Star takes 680 years to reach the earth. How many miles is the North Star from the earth?

Find all real solutions of the equation exactly. $$x^{4}-2 x^{2}+1=0$$

Find an equation for the line satisfying the given conditions. Through (2,3) and parallel to \(3 x-2 y=5\).

Sketch the graph of the equation. Label the \(x\) - and y-intercepts. $$(x-5)^{2}+(y+2)^{2}=5$$

The gross federal debt was about 8365 billion dollars in 2006 , when the U.S. population was approximately 298.4 million people. (a) Express the debt and the population in scientific notation. (b) At that time, what was each person's share of the federal debt?

Find all real solutions of the equation exactly. $$x^{4}-2 x^{2}-35=0$$

Find an equation for the line satisfying the given conditions. Through ( 1,-2 ) and perpendicular to \(y=2 x-3\).

Apple reported that it had sold 28 million iPods through the end of 2005 and that 14 million iPods were sold in the first quarter of \(2006 .\) If the rate in the first quarter of 2006 continues through the end of \(2008,\) how many iPods will be sold? Express your answer in scientific notation.

Find all real solutions of the equation exactly. $$x^{4}-2 x^{2}-24=0$$

Find an equation for the line satisfying the given conditions. \(x\) -intercept 5 and \(y\) -intercept -5.

Sketch the graph of the equation. Label the \(x\) - and y-intercepts. $$(x+1)^{2}+(y-3)^{2}=9$$

Simplify the expression without using a calculator. Your answer should not have any radicals in it. $$\sqrt{2} \sqrt{8}$$

Find all real solutions of the equation exactly. $$2 y^{4}-9 y^{2}+4=0$$

Sketch the graph of the equation. Label the \(x\) - and y-intercepts. $$(x-2)^{2}+(y-4)^{2}=1$$

Simplify the expression without using a calculator. Your answer should not have any radicals in it. $$\sqrt{12} \sqrt{3}$$

Find all real solutions of the equation exactly. $$6 z^{4}-7 z^{2}+2=0$$

Find an equation for the line satisfying the given conditions. Through (-1,3) and perpendicular to the line through (0,1) and (2,3).

Find the center and radius of the circle whose equation is given. $$x^{2}+y^{2}+8 x-6 y-15=0$$

Simplify the expression without using a calculator. Your answer should not have any radicals in it. $$\sqrt{\frac{3}{5}} \sqrt{\frac{12}{5}}$$

Find the center and radius of the circle whose equation is given. $$15 x^{2}+15 y^{2}=10$$