\hfill \hfill } %} \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{case}[theorem]{Case} \newtheorem{claim}[theorem]{Claim} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} \newenvironment{proof}[1][Proof]{\noindent\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \input{tcilatex} \geometry{left=0.4in,right=0.5in,top=0.5in,bottom=0.4in} \pagestyle{fancy} \lhead{\color{blue} \Large Math 207} \cfoot{} \chead{\LARGE Worksheet 1} \rhead{\large page \thepage} \textwidth 7.6in \textheight 9.6in \setlength{\headheight}{28pt} \setlength{\parindent}{-6pt} \begin{document} \begin{enumerate} \item Expand each of the following.% %TCIMACRO{\TeXButton{3col begin}{\begin{multicols}{3}}}% %BeginExpansion \begin{multicols}{3}% %EndExpansion a) \ $\left( x+5\right) \left( x-5\right) $ b) \ $\left( x-3\right) ^{2}$ c) $\ \left( 2x-1\right) ^{2}$ d) \ $\left( 2x-1\right) ^{3}$ e) \ $\left( 3x-5\right) \left( 9x^{2}+15x+25\right) $ f) \ $\left( x-3\right) ^{2}-\left( x-1\right) \left( 3x+5\right) $% %TCIMACRO{\TeXButton{multicol end}{\end{multicols}}}% %BeginExpansion \end{multicols}% %EndExpansion \item Solve each of the following equations. \ Make sure to check your solution(s).% %TCIMACRO{\TeXButton{2col begin}{\begin{multicols}{2}}}% %BeginExpansion \begin{multicols}{2}% %EndExpansion a) \ $\left( 2x-1\right) ^{2}-3x\left( x-2\right) =8+\left( x-3\right) ^{2}$ b) \ $\dfrac{3x+1}{4}-\dfrac{2x-1}{3}=x-4$ c) \ $\left( x+7\right) \left( 2x-1\right) \left( 5x-8\right) =0$ d) \ $\left( 2x-1\right) ^{5}=0$ e) \ $6x^{3}=3x^{2}$ %TCIMACRO{\TeXButton{multicol end}{\end{multicols}}}% %BeginExpansion \end{multicols}% %EndExpansion \item Completely factor each of the following over the real numbers. a) \ $a^{5}+a^{4}\qquad \qquad $b) \ $3x^{2}-48\qquad \qquad $c) \ $4a^{5}-4a $ \item Factor each of the following over the real numbers by completing the square.% %TCIMACRO{\TeXButton{3col begin}{\begin{multicols}{3}}}% %BeginExpansion \begin{multicols}{3}% %EndExpansion a) \ $126x+4x^{2}-2x^{3}$ b) \ $4x^{2}-24x-64$ c) \ $2x+x^{2}+26$ d) \ $12x-2x^{2}-4$ e) \ $2x^{2}+x-15$ \ %TCIMACRO{\TeXButton{multicol end}{\end{multicols}}}% %BeginExpansion \end{multicols}% %EndExpansion \item Simplify each of the following expressions. a) \ $\sqrt{50}-3\sqrt{18}+\sqrt{200}$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ c) \ Rationalize $\ \dfrac{3}{\sqrt{10}-4}$ b) \ $\left( 8-\sqrt{5}\right) ^{2}$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d) \ Find the exact value of \ $x^{2}-4x+7$ \ if \ $x=5-\sqrt{2}$ \item a) \ Solve the equation $x^{2}+7=6x$. b) \ Use exact values to check your solutions. \item Graph the straight lines $y=-\dfrac{2}{3}x+1$ and $x+2y=0$ in the same coordinate system. Use your graph to find the coordinates of the point where the lines intersect.\newline \FRAME{itbpF}{2.4933in}{2.5054in}{0in}{}{}{10by10w.bmp}{\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display "USEDEF";valid_file "F";width 2.4933in;height 2.5054in;depth 0in;original-width 12.7603in;original-height 12.8226in;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename '../../../../../Math143/math143_sp16/exams/exam4/exam4/10by10w.bmp';file-properties "XNPEU";}% } \pagebreak \item Graph the parabola $y=8x+x^{2}+12$. Clearly label the coordinates of five points on the parabola, including vertex and intercepts.\newline \FRAME{itbpF}{2.4933in}{2.5054in}{0in}{}{}{10by10w.bmp}{\special{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display "USEDEF";valid_file "F";width 2.4933in;height 2.5054in;depth 0in;original-width 12.7603in;original-height 12.8226in;cropleft "0";croptop "1";cropright "1";cropbottom "0";filename '../../../../../Math143/math143_sp16/exams/exam4/exam4/10by10w.bmp';file-properties "XNPEU";}% } \item Find the distance between $\left( 7,-2\right) $ \ and $\left( 3,3\right) $. \item Compute the exact value of the area of the triangle with sides $10% \unit{cm},$ $10\unit{cm},$ and $8\unit{cm}$ long. \item Write an equation for the line that is\newline a) \ parallel to $2x-5y=17$ and passes through $P\left( 10,-2\right) $.% \newline b) \ perpendicular to $2x-5y=17$ and passes through $P\left( 10,-2\right) $.% \newline c) \ passes through the points $\left( -2,4\right) $ and $\left( 6,0\right) $% . \item We have $72$ coins in a jar, all dimes and nickels. \ How many of each coin do we have if the total value of all coins is $\$4.75$? \item We are standing on the top of a $912$ feet tall tower and throw a small object upward. \ We measure and record the vertical location of the object. \ (Location is measured in feet, time in seconds.) \ $t$ seconds after we threw it, the vertical position of the object is% \begin{equation*} h\left( t\right) =-16t^{2}+256t+912 \end{equation*} a) \ Where is the object $6$ seconds after we threw it?\newline b) \ How long does it take for the object to be at a height of $1360$ feet above the ground?\newline c) \ How long does it take until the obejct hits the ground? \end{enumerate} \end{document}