MathDB

Problems(3)

f(f(x))=6

Source:

3/27/2008
The graph of the function f f is shown below. How many solutions does the equation f(f(x)) \equal{} 6 have? [asy]size(220); defaultpen(fontsize(10pt)+linewidth(.8pt)); dotfactor=4;
pair P1=(-7,-4), P2=(-2,6), P3=(0,0), P4=(1,6), P5=(5,-6); real[] xticks={-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6}; real[] yticks={-6,-5,-4,-3,-2,-1,1,2,3,4,5,6};
draw(P1--P2--P3--P4--P5);
dot("(-7, -4)",P1); dot("(-2, 6)",P2,LeftSide); dot("(1, 6)",P4); dot("(5, -6)",P5);
xaxis("xx",-7.5,7,Ticks(xticks),EndArrow(6)); yaxis("yy",-6.5,7,Ticks(yticks),EndArrow(6));[/asy]<spanclass=latexbold>(A)</span> 2<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 5<spanclass=latexbold>(D)</span> 6<spanclass=latexbold>(E)</span> 7 <span class='latex-bold'>(A)</span>\ 2 \qquad <span class='latex-bold'>(B)</span>\ 4 \qquad <span class='latex-bold'>(C)</span>\ 5 \qquad <span class='latex-bold'>(D)</span>\ 6 \qquad <span class='latex-bold'>(E)</span>\ 7
functionLaTeXspeedospiky
System

Source:

1/2/2009
If a a, b b, and c c are positive real numbers such that a(b \plus{} c) \equal{} 152, b(c \plus{} a) \equal{} 162, and c(a \plus{} b) \equal{} 170, then abc is <spanclass=latexbold>(A)</span> 672<spanclass=latexbold>(B)</span> 688<spanclass=latexbold>(C)</span> 704<spanclass=latexbold>(D)</span> 720<spanclass=latexbold>(E)</span> 750 <span class='latex-bold'>(A)</span>\ 672 \qquad <span class='latex-bold'>(B)</span>\ 688 \qquad <span class='latex-bold'>(C)</span>\ 704 \qquad <span class='latex-bold'>(D)</span>\ 720 \qquad <span class='latex-bold'>(E)</span>\ 750
number theoryprime factorization
Area of Quadrilateral with 120 Degree Angles

Source:

4/6/2013
In quadrilateral ABCDABCD, mB=mC=120m\angle B=m\angle C=120^\circ, AB=3AB=3, BC=4BC=4, and CD=5CD=5. Find the area of ABCDABCD.
<spanclass=latexbold>(A)</span>15<spanclass=latexbold>(B)</span>93<spanclass=latexbold>(C)</span>4534<spanclass=latexbold>(D)</span>4734<spanclass=latexbold>(E)</span>153<span class='latex-bold'>(A) </span>15\qquad<span class='latex-bold'>(B) </span>9\sqrt3\qquad<span class='latex-bold'>(C) </span>\dfrac{45\sqrt3}4\qquad<span class='latex-bold'>(D) </span>\dfrac{47\sqrt3}4\qquad<span class='latex-bold'>(E) </span>15\sqrt3
geometry