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\begin{document}

\begin{enumerate}

\item  Solve the equation
\[
\frac{3x-5}{2}= x+6
\]

\item  A clerk at a travel agent's can handle in 5 minutes
a customer who just demands information, and in 12 minutes a customer 
who buys a ticket. It is estimated that $70\%$ of the customers just
want information, and $30\%$ buy tickets. How many customers can a
clerk handle in a 8--hour workday?

\item  Solve the system of inequalities
\[
5< 2x-8 \le 30-x
\]

\item  Sketch the graph of the equation 
and find its intersection with the $x$--axis.
\[
3x-2y+3=0
\]

\item  A straight line goes through the points $(-1,4)$ 
and $(2,2)$. What is its slope?

\item Compute 
\[
8x^2-2x+4-(x-1)(x^2+2x+3)
\]

\item Factor the polynomial $p(x)= 2x^2+12x-14$, and
solve the equation $p(x)=0$.

\item  Compute and simplfy
\[
\frac{16-x}{x^2-2x-8}+\frac{4}{x+2}-\frac{2}{x-4}
\]

\item  Factor the polynomial $x^3-4x^2-11x+30$.

\item  Solve the equation
\[
\frac{x+8}{x-2}=3
\]

\item  Simplify the expression
\[
\left.^3 \sqrt{48y^4} \right. (64y^2)^{-\frac{1}{6}}
\]

\item  Find the points in the line $\{ y=3x-1 \}$ such that 
their distance to $(0,0)$ is 4.

\item  Find the complex solutions $z_1,z_2$ of the equation
\[
z^2+3z+\frac{25}{4}=0
\]
and compute $\frac{1}{z_1}+ \frac{1}{z_2}$.

\item  Find all real numbers $b$ such that the equation
\[
3x^2+ bx-6=0
\]
has exactly one solution.

\item  A plane nose--dives from a height of 6,000 ft. While
it does so, its height is given by the equation
\[
h(t)= 6,000 - 300t - 16t^2
\]
with $h$ the height in feet, $t$ the time in seconds. The plane must
straighten its flight at a height of 2,000 ft. For how many seconds
can it nose--dive?

\item   We have to build a rectangular playground such that
its width is 20 ft less than its length, and its total area is 4,000
square feet. What should be its length and width?

\item  Find the equation of the line that goes through
the points $(0,4)$ and $(2,-1)$. Compute the intersection of this
line with the horizontal line $y=1$.

\item  Plot the graphs of the line with equation 
$2x-2y+14=0$ and the parabolla $y=x^2-3x+2$. Compute their 
intersection points.

\item  Solve the system
\[
\left\{ 
\begin{array}{cccc}
 x & -2y & +3z & =0 \\
-x &  -y &  +z & =2 \\
2x &     & -3z & =1 
\end{array}
\right.
\]

\item  A 20--oz bag of cookies costs $\$2.20$ to produce,
and a 12--oz bag costs $\$1.40$. If the bags that we use in the 2 sizes
cost the same, what is the cost of the bag and what is the cost of
every ounce of cookies?

\item  An 80--lb sack of fertilizer has a volume of 0.32 cu ft.
We know that it contains a mix of two substances: fertilizer A, with 
density $300 \frac{\mbox{lb}}{\mbox{cu ft}}$, and fertilizer B, with 
density $200 \frac{\mbox{lb}}{\mbox{cu ft}}$. Find how much weight of
every type of fertilizer does the sack contain.

\item  A calculator seeling for $\$179.00$ cost the retailer $\$97.00$.
Find the markup rate.

\item  Determine the number of gallons of a $20\%$ alcohal solution 
and the number of gallons of a $45\%$ solution that are required
to make 10 gallons of a $35\%$ solution.

\item  If $g(x)=x(3-x)$ evaluate and simplify:
$g(5)$, $g(-2)$, $g(t+2)$.

\item  Find the time for 2 people working together to complete a task if 
it takes them 12 and 8 hours to complete the task working individually.

\item  Find the slope of the line through $(2,-4)$ and $(-10,1)$,
and find the distance between these points.

\item  Graph $f(x)=4-x^2$ and $h(x)=(x+2)^2$ on the same axes.

\item  Use elimination to solve:
\[
\begin{array}{ccccc}
2x  & - & 5y & = & 18 \\
-3x & + & 4y & = & -20 \\
\end{array}
\]

\item  Simplify and factor:
\[
3y^2-(y-3(y^2-5))
\]

\item  Factor:
\[
64x^3-27
\]

\item  Simplify:
\[
\frac
{\frac{2t^2+t-15}{t^2-9}}
{\frac{4t^2-20t+25}{t^2-t-6}}
\]

\item  Simplify:
\[
\frac
{\frac{1}{x}-\frac{1}{y}}
{\frac{1}{x^2}-\frac{1}{y^2}}
\]

\item Divide:
\[
\frac{x^4+3x^2-35}{x+2}
\]

\item  Solve:
\[
\frac{7}{x+3}-\frac{6}{x-2}=6
\]

\item  Rewrite using only positive exponents and simplify:
\[
(3x^2y^{-1})^2(4x^4y^{-3})^{-\frac{1}{2}}
\]

\item  Rationalize the denominator and simplify:
\[
\sqrt[3]{
\frac{32v^7}{9u^2}
}
\]

\item  Rationalize the denominator and simplify:
\[
\frac{\sqrt{12}}{\sqrt{6}-3}
\]

\item  Write the complex number in standard form $(a+bi)$:
\[
\frac{2-\sqrt{-9}}{1+2i}
\]

\item  Solve:
\[
2x^2-6x+7
\]

\item  A little league baseball team obtains a block of tickets to a 
ball game for \$96.  When three more people decide to go to the game, 
the price per ticket is decreased by \$1.60.  How many people are going to
the game?

\item  Fid the vertex, $x$ and $y$- intercepts and graph:
\[
y=2x^2-12x+14
\]

\item  (10 points)  Solve and graph the inequality.
\[ -3 < \frac{2x-3}{2} \leq 3 \]

\item  (10 points)  Solve the equation:
\[ |x+2|=|3x-1| \]

\item  (10 points)  Find the distance between the points: (1,3) and (-2,7).

\item  (10 points)  Graph the equation, label all $x$ and $y$-intercepts.
\[ x-2y-2=0 \]

\item  Factor completely:
\[
4t^2-24t-13
\]

\item  The length of a rectangle is $\frac{3}{2}$ times the width.
The area of the rectangle is 54 cm$^2$.  
Find the length and width of the rectangle.

\item  (15 points)  Divide and simplify:
\[
\frac
{\left( \frac{5x}{x+7} \right)}
{\left(\frac{10}{x^2+8x+7}\right)}
\]

\item  (15 points)  Simplify
\[
\frac
{\left( \frac{x}{x-3} - \frac{2}{3} \right)}
{\left( \frac{10}{3x} + \frac{x^2}{x-3} \right)}
\]

\item  (15 points)  Solve the equation:
\[
\frac{3}{x-1} + \frac{6}{x^2-3x+2} = 2
\]


\item  (20 points)  Factor the polynomial.  (Hint: $(x-2)$ is a factor)
\[
x^3-5x^2-4x+20
\]

\item  (15 points)  Divide:
\[
\frac{2x^3-5x^2+x-7}{x-2}
\]


\item  (10 points)  Simplify, write your answer using only positive exponents.
\[
\left(
\frac{2x^2}{y^{-1}}
\right) ^{-2}
\]

\item  (15 points)  Rationalize the denominator.
\[
\frac{6}{7-\sqrt{7}}
\]

\item  (15 points)  Solve the equation.
\[
-6=\sqrt{x}-x
\]

\item  (15 points)  Write the complex number in standard form ($a+bi$).
\[
\frac{1+i}{1-i}
\]

\item  (15 points)  Find all solutions to the equation:
\[
x^{\frac{2}{5}}-x^{\frac{1}{5}}-2=0
\]

\item  (20 points)  Solve the equation:
\[
y^2-3y+4=0
\]

\item  (15 points)  You take a 10 mile hike.  
For the first 6 miles you travel at one speed.  
Then you pick up the pace and finish the next 4 miles 
2 miles per hour faster then the first 6 miles.  
The trip takes 4 hours.
How fast did you go in each part of the hike?

\item  (15 points)  Find the equation of the line through (1,1) and (5,-3).

\item  (15 points)  Graph the inequality:
\[
2x+3y < 9
\]










\end{enumerate}

\end{document}






