Chapter 1

Solve the equation. $$3 x+2=26$$

Find the coordinates of the point \(P .\). \(P\) lies 4 units to the left of the \(y\) -axis and 5 units below the \(x\) -axis.

Use your calculator to determine which of the following rational numbers is the best approximation of the irrational number \(\pi\) $$\frac{22}{7}, \quad \frac{355}{113}, \quad \frac{103,993}{33,102}, \quad \frac{2,508,429,787}{798,458,000}$$ If your calculator says that one of these numbers equals \(\pi\) it's lying. All you can conclude is that the number agrees with \(\pi\) for as many decimal places as your calculator can handle (usually \(12-14\) ).

Solve the equation. $$\frac{y}{5}-3=14$$

Find the slope of the line through the given points. $$(1,2)$;(3,7)$$

Find the coordinates of the point \(P .\). \(P\) lies 3 units above the \(x\) -axis and on the same vertical line as (-6,7).

\(b, c,\) and \(d\) are real numbers such that \(b<0\) \(c>0,\) and \(d<0 .\) Determine whether the given number is positive or negative. $$-b$$

Solve the equation. $$3 x+2=9 x+7$$

Find the slope of the line through the given points. $$(-1,-2)$;(2,-1)$$

Solve the equation. $$-7(t+2)=3(4 t+1)$$

Find the slope of the line through the given points. $$(1 / 4,0) ;(3 / 4,2)$$

Find the coordinates of the point \(P .\). \(P\) lies 4 units to the right of the \(y\) -axis, and its \(y\) -coordinate is half its \(x\) -coordinate.

\(b, c,\) and \(d\) are real numbers such that \(b<0\) \(c>0,\) and \(d<0 .\) Determine whether the given number is positive or negative. $$b c d$$

Solve the equation. $$\frac{3 y}{4}-6=y+2$$

Find the slope of the line through the given points. $$(\sqrt{2},-1) ;(2,-9)$$

Solve the equation. $$2(1+x)=3 x+5$$

Find a number t such that the line passing through the two given points has slope -2. $$(0, t) ;(9,4)$$

Sketch a scatter plot and a line graph of the given data. The table shows sales of personal digital video recorders.* Let \(x=0\) correspond to \(2000,\) and measure \(y\) in thousands. $$\begin{array}{|c|c|}\hline \text { Year } & \text { Number Sold } \\\\\hline 2000 & 257,000 \\\\\hline 2001 & 129,000 \\ \hline 2002 & 143,000 \\\\\hline 2003 & 214,000 \\\\\hline 2004 & 315,000 \\\\\hline 2005 & 485,000 \\\\\hline \end{array}$$

\(b, c,\) and \(d\) are real numbers such that \(b<0\) \(c>0,\) and \(d<0 .\) Determine whether the given number is positive or negative. $$b c-b d$$

Solve the equation for the indicated variable. $$x=3 y-5 \text { for } y$$

Sketch a scatter plot and a line graph of the given data. The maximum yearly contribution to an individual retirement account (IRA) was \(\$ 3000\) in \(2003 .\) It changed to \(\$ 4000\) in 2005 and will change to \(\$ 5000\) in \(2008 .\) Assuming \(3 \%\) inflation, however, the picture is somewhat different. The table shows the maximum IRA contribution in fixed 2003 dollars. Let \(x=0\) correspond to 2000. $$\begin{array}{|c|c|}\hline \text { Year } & \text { Maximum Contribution } \\\\\hline 2003 & 3000 \\\\\hline 2004 & 2910 \\\\\hline 2005 & 3764 \\\\\hline 2006 & 3651 \\\\\hline 2007 & 3541 \\\\\hline 2008 & 4294 \\\\\hline\end{array}$$

Find a number t such that the line passing through the two given points has slope -2. $$(1, t) ;(-2,4)$$

Solve the equation for the indicated variable. $$5 x-2 y=1 \text { for } x$$

(a) If the first coordinate of a point is greater than 3 and its second coordinate is negative, in what quadrant does it lie? (b) What is the answer in part (a) if the first coordinate is less than \(3 ?\)

Find a number t such that the line passing through the two given points has slope -2. $$(t+1,5) ;(6,-3 t+7)$$

Use a calculator and list the given numbers in order from smallest to largest. $$\frac{189}{37}, \frac{4587}{691}, \quad \sqrt{47}, \quad 6.735, \quad \sqrt{27}, \quad \frac{2040}{523}$$

Solve the equation for the indicated variable. $$A=\frac{h}{2}(b+c) \quad \text { for } b$$

In what quadrant(s) does a point lie if the product of its coordinates is (a) positive? (b) negative?

Use a calculator and list the given numbers in order from smallest to largest. $$\frac{385}{177}, \quad \sqrt{10}, \quad \frac{187}{63}, \quad \pi, \quad \sqrt{\sqrt{85}}, \quad 2.9884$$

Solve the equation for the indicated variable. $$V=\pi b^{2} c \quad \text { for } c$$

Let \(L\) be a nonvertical straight line through the origin. \(L\) intersects the vertical line through (1, 0) at a point P. Show that the second coordinate of \(P\) is the slope of \(L\).

Express the given statement in symbols. -4 is greater than -8

Solve the equation for the indicated variable. $$V=\frac{\pi d^{2} h}{4} \text { for } h$$

(a) Plot the points \((5,3),(4,-2),(-1,4),\) and (-3,-5) (b) Change the sign of the \(x\) -coordinate in each of the points in part (a), and plot these new points. (c) Explain how the points \((a, b)\) and \((-a, b)\) are related graphically. [Hint: What are their relative positions with respect to the \(y\) -axis?]

Express the given statement in symbols. -17 is less than 6

Solve the equation for the indicated variable. $$\frac{1}{r}=\frac{1}{s}+\frac{1}{t} \quad \text { for } r$$

Find the distance between the two points and the midpoint of the segment joining them. $$(-3,5),(2,-7)$$

Express the given statement in symbols. \(\pi\) is less than 100

Solve the equation by factoring. $$x^{2}-8 x+15=0$$

Find the distance between the two points and the midpoint of the segment joining them. $$(2,4),(3,6)$$

Express the given statement in symbols. \(x\) is nonnegative.

Solve the equation by factoring. $$x^{2}-5 x+6=0$$

Find the distance between the two points and the midpoint of the segment joining them. $$(-2,5),(-1,2)$$

Express the given statement in symbols. \(z\) is greater than or equal to -4

Solve the equation by factoring. $$x^{2}-5 x=14$$

Find the distance between the two points and the midpoint of the segment joining them. $$(-2,3),(-3,2)$$

Express the given statement in symbols. \(t\) is negative.

Solve the equation by factoring. $$x^{2}+x=20$$

Find the equation of the line with y-intercept b and slope \(m\). $$b=5, m=4$$

Find the distance between the two points and the midpoint of the segment joining them. $$(\sqrt{2}, 1),(\sqrt{3}, 2)$$