and F lie on a second line parallel to the first with EF 1 A triangle with

And f lie on a second line parallel to the first with

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andFlie on asecond line, parallel to the first, withEF= 1.Atriangle with positive area has three of the six pointsas its vertices. How many possible values are there forthe area of the triangle? (A)3(B)4(C)5(D)6(E)7 2009 AMC 10 B, Problem #12“The area of a triangle is determined by the base andheight of the triangle.” Difficulty:Medium-hardNCTM Standard:Geometry Standard: analyze properties and determine attributes of two- andthree-dimensional objects.Mathworld.com Classification:Geometry>Plane Geometry>Triangles>Triangle Properties> Triangle Area
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As shown below, convex pentagonABCDEhas sidesAB= 3,BC= 4,CD= 6,DE= 3, andEA= 7.The pentagon is originally positioned in the plane withvertexAat the origin and vertexBon the positivex-axis. The pentagon is then rolled clockwise to theright along thex-axis. Which side will touch the pointx= 2009on thex-axis?ABCDEx34637(0,0)(A)AB(B)BC(C)CD(D)DE(E)EA2009 AMC 10 B, Problem #13“After a full rotation,Awill be at point(23,0).”SolutionAnswer (C):Define a rotation of the pentagon to be a sequence thatstarts withABon thex-axis and ends whenABis on thex-axis thefirst time thereafter. Because the pentagon has perimeter 23 and2009 =23·87+8, it follows that after 87 rotations, pointAwill be atx= 23·87 =2001and pointBwill be atx= 2001 + 3 = 2004. PointsCandDwillnext touch thex-axis atx= 2004 + 4 = 2008andx= 2008 + 6 = 2014,respectively. Therefore a point onCDwill touchx= 2009.Difficulty:MediumNCTM Standard:Algebra Standard: understand patterns, relations, and functions.Mathworld.com Classification:Number Theory>Sequences>Sequence
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On Monday, Millie puts a quart of seeds, 25% of whichare millet, into a bird feeder.On each successiveday she adds another quart of the same mix of seedswithout removing any seeds that are left. Each daythe birds eat only 25% of the millet in the feeder, butthey eat all of the other seeds.On which day, justafter Millie has placed the seeds, will the birds findthat more than half the seeds in the feeder are millet?(A)Tuesday(B)Wednesday(C)Thursday(D)Friday(E)Saturday2009 AMC 10 B, Problem #142009 AMC 12 B, Problem #11“Generalize a sequence of the number of quarts ofmillet find on dayn.”
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