The number n satisfies the n What is the value of n A205 B 305

# The number n satisfies the n what is the value of n

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The numbernsatisfies the equation80 +125 =n. What is the value ofn? (A)205(B)305(C)405(D)500(E)1000 2010 AMC 10 B, Problem #6 2010 AMC 12 B, Problem #4 “Note that 80 = 4 5 and 125 = 5 5 .” Solution Answer (C): Simplifying gives 80 + 125 = 4 5 + 5 5 = 9 5 = 405 . Hence n = 405 . Diﬃculty: Medium-easy NCTM Standard: Number and Operations Standard for Grades 9–12: understand numbers, ways of representing numbers, relationships among numbers, and number systems. The square ofxis 16 larger than the square ofy, andxis 2 larger thany. What is the productxy? 2010 AMC 10 B, Problem #7“Note thatx2y2= (xy)(x+y) = 16.” Diﬃculty: Medium-easy NCTM Standard: Algebra Standard for Grades 9–12: write equivalent forms of equations, inequalities, and systems of equations and solve them with ﬂuency-mentally or with paper and pencil in simple cases and using technology in all cases. The area of triangleEBDis one third of the area of345triangleABC. SegmentDEis perpendicularto segmentAB. What isBD?ABCDE345(A)43(B)5(C)94(D)433(E)522010 AMC 10 B, Problem #8“The area ofABCis12·3·4 = 6.” Standard: Geometry Standard for Grades 9–12: analyze properties and determine attributes of two- and three-dimensional objects. If a rectangle’s width is increased by 3, the rectanglebecomes a square and the area of the rectangle isincreased by 54.What is the area of the originalrectangle? (A)90(B)150(C)180(D)225(E)270 2010 AMC 10 B, Problem #9“Letxandybe the width and length of the originalrectangle, respectively. Form an equation to show thedifference in areas.” Standard: Geometry Standard for Grades 9–12: analyze properties and determine attributes of two- and three-dimensional objects.   • • • 