Chapter 1

Express the given statement in symbols. \(d\) is not greater than 7

Solve the equation by factoring. $$2 y^{2}+5 y-3=0$$

Find the equation of the line with y-intercept b and slope \(m\). $$b=-3, m=-7$$

Express the given statement in symbols. \(c\) is at most 3

Solve the equation by factoring. $$3 t^{2}-t-2=0$$

Find the equation of the line with y-intercept b and slope \(m\). $$b=1.5, m=-2.3$$

Find the distance between the two points and the midpoint of the segment joining them. $$(a, b),(b, a)$$

Express the given statement in symbols. \(z\) is at least -17

Solve the equation by factoring. $$4 t^{2}+9 t+2=0$$

Find the equation of the line with y-intercept b and slope \(m\). $$b=-4.5, m=2.5$$

Fill the blank with \(<,=,\) or \(>\) so that the resulting statement is true. -6 ______ -2

Which of the following points is closest to the origin? $$(4,4.2),(-3.5,4.6),(-3,-5),(2,-5.5)$$

Fill the blank with \(<,=,\) or \(>\) so that the resulting statement is true. 5 ______ -3

Solve the equation by factoring. $$3 u^{2}-4 u=4$$

Which of the following points is closest to (3,2)\(?\) $$(0,0),(4,5.3),(-.6,1.5),(1,-1)$$

Fill the blank with \(<,=,\) or \(>\) so that the resulting statement is true. \(3 / 4\) ______ .75

Solve the equation by factoring. $$5 x^{2}+26 x=-5$$

Fill the blank with \(<,=,\) or \(>\) so that the resulting statement is true. 3.1416 ______ \(\pi\)

Solve the equation by completing the square. $$x^{2}-2 x=12$$

What is the perimeter of the triangle with vertices (1,1) \((5,4),\) and (-2,5)\(?\)

Fill the blank with \(<,=,\) or \(>\) so that the resulting statement is true. \(1 / 3\) ______ .33

Solve the equation by completing the square. $$x^{2}-4 x-30=0$$

Find the slope and y-intercept of the line whose equation is given. $$2 x-y+5=0$$

The consumer price index for urban consumers (CPI-U) measures the cost of consumer goods and services such as food, housing, transportation, medical costs, etc. The table shows the yearly percentage increase in the CPI-U over a decade.\(*\) $$\begin{array}{|c|c|} \hline \text { Year } & \text { Percentage change } \\ \hline 1996 & 3.0 \\ \hline 1997 & 2.3 \\ \hline 1998 & 1.6 \\ \hline 1999 & 2.2 \\ \hline 2000 & 3.4 \\ \hline 2001 & 2.8 \\ \hline 2002 & 1.6 \\ \hline 2003 & 2.3 \\ \hline 2004 & 2.7 \\ \hline 2005 & 2.5 \\ \hline \end{array}$$ Let \(p\) denote the yearly percentage increase in the CPI-U. Find the number of years in this period which satisfied the given inequality. $$p \geq 2.8$$

Solve the equation by completing the square. $$x^{2}-x-1=0$$

Find the slope and y-intercept of the line whose equation is given. $$4 x+3 y=5$$

Find the area of the triangle with vertices \((1,4),(4,3),\) and \((-2,-5) .\) You may assume that there is a right angle at vertex (1,4).

The consumer price index for urban consumers (CPI-U) measures the cost of consumer goods and services such as food, housing, transportation, medical costs, etc. The table shows the yearly percentage increase in the CPI-U over a decade.\(*\) $$\begin{array}{|c|c|} \hline \text { Year } & \text { Percentage change } \\ \hline 1996 & 3.0 \\ \hline 1997 & 2.3 \\ \hline 1998 & 1.6 \\ \hline 1999 & 2.2 \\ \hline 2000 & 3.4 \\ \hline 2001 & 2.8 \\ \hline 2002 & 1.6 \\ \hline 2003 & 2.3 \\ \hline 2004 & 2.7 \\ \hline 2005 & 2.5 \\ \hline \end{array}$$ Let \(p\) denote the yearly percentage increase in the CPI-U. Find the number of years in this period which satisfied the given inequality. $$p<2.6$$

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

Find the slope and y-intercept of the line whose equation is given. $$3(x-2)+y=7-6(y+4)$$

Show that the three points are the vertices of a right triangle, and state the length of the hypotenuse. I You may assume that a triangle with sides of lengths \(a, b, c\) is a right triangle with hypotenuse c provided that \(a^{2}+b^{2}=c^{2} .1\). $$(0,0),(1,1),(2,-2)$$

The consumer price index for urban consumers (CPI-U) measures the cost of consumer goods and services such as food, housing, transportation, medical costs, etc. The table shows the yearly percentage increase in the CPI-U over a decade.\(*\) $$\begin{array}{|c|c|} \hline \text { Year } & \text { Percentage change } \\ \hline 1996 & 3.0 \\ \hline 1997 & 2.3 \\ \hline 1998 & 1.6 \\ \hline 1999 & 2.2 \\ \hline 2000 & 3.4 \\ \hline 2001 & 2.8 \\ \hline 2002 & 1.6 \\ \hline 2003 & 2.3 \\ \hline 2004 & 2.7 \\ \hline 2005 & 2.5 \\ \hline \end{array}$$ Let \(p\) denote the yearly percentage increase in the CPI-U. Find the number of years in this period which satisfied the given inequality. $$p>2.3$$

Find the number of real solutions of the equation by computing the discriminant. $$x^{2}+4 x+1=0$$

Find the slope and y-intercept of the line whose equation is given. $$2(y-3)+(x-6)=4(x+1)-2$$

Show that the three points are the vertices of a right triangle, and state the length of the hypotenuse. I You may assume that a triangle with sides of lengths \(a, b, c\) is a right triangle with hypotenuse c provided that \(a^{2}+b^{2}=c^{2} .1\). $$(3,-2),(0,4),(-2,3)$$

The consumer price index for urban consumers (CPI-U) measures the cost of consumer goods and services such as food, housing, transportation, medical costs, etc. The table shows the yearly percentage increase in the CPI-U over a decade.\(*\) $$\begin{array}{|c|c|} \hline \text { Year } & \text { Percentage change } \\ \hline 1996 & 3.0 \\ \hline 1997 & 2.3 \\ \hline 1998 & 1.6 \\ \hline 1999 & 2.2 \\ \hline 2000 & 3.4 \\ \hline 2001 & 2.8 \\ \hline 2002 & 1.6 \\ \hline 2003 & 2.3 \\ \hline 2004 & 2.7 \\ \hline 2005 & 2.5 \\ \hline \end{array}$$ Let \(p\) denote the yearly percentage increase in the CPI-U. Find the number of years in this period which satisfied the given inequality. $$p \leq 3.0$$

Find the number of real solutions of the equation by computing the discriminant. $$4 x^{2}-4 x-3=0$$

Find the equation of the line with slope \(m\) that passes through the given point. $$m=1 ;(4,7)$$

Find the number of real solutions of the equation by computing the discriminant. $$9 x^{2}=12 x+1$$

Find the equation of the line with slope \(m\) that passes through the given point. $$m=2 ;(-2,1)$$

Fill the blank so as to produce two equivalent statements. For example, the arithmetic statement "a is negative" is equivalent to the geometric statement "the point a lies to the left of the point \(0 . "\) Arithmetic Statement \(a \geq b\) Geometric Statement ______

Find the number of real solutions of the equation by computing the discriminant. $$9 t^{2}+15=30 t$$

Find the equation of the line with slope \(m\) that passes through the given point. $$m=-1 ;(6,2)$$

Find the number of real solutions of the equation by computing the discriminant. $$25 t^{2}+49=70 t$$

Find the equation of the line with slope \(m\) that passes through the given point. $$m=0 ;(-4,-5)$$

Find the number of real solutions of the equation by computing the discriminant. $$49 t^{2}+5=42 t$$

Find the equation of the line through the given points. $$(0,-5) and (-3,-2)$$

The number of passengers annually on U.S. commercial airlines was 650 million in 2002 and is expected to be 1.05 billion in 2016 . (a) Represent this data graphically by two points. (b) Find the midpoint of the line segment joining these two points. (c) How might this midpoint be interpreted? What assumptions, if any, are needed to make this interpretation?

Draw a picture on the number line of the given interval. $$(0, \infty)$$

Use the quadratic formula to solve the equation. $$x^{2}-4 x+1=0$$