A geometry teacher asked Charlene to define “acute triangle.” Charlene said that an acute triangle is a triangle whose three interior angles have measures less than 90°90°. Is Charlene’s definition valid?A.Yes, because no right triangles fit this definition.B.No, because some scalene triangles fit this definition.C.Yes, because this definition fits all acute triangles and does not fit triangles that are not acute.D.No, because not all acute triangles fit this definition.

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general 11 months ago 5547

Frank is constructing the circumscribed circle for △XYZ. He has already used his compass and straightedge to complete the part of the construction shown in the figure.Which construction could be his next step?Place the point of the compass on point Y and draw an arc intersecting the two arcs.Place the point of the compass on point X and draw an arc intersecting the two arcs.Place the point of the compass on point Z and draw an arc through points X and Y.Place the point of the compass on one of the arcs and draw an arc through point X.

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general 11 months ago 8450

PLEASE HELP AND SHOW ALL WORK7.04Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.(4 points each.)1. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = quantity four times quantity four n plus one times quantity eight n plus seven divided all divided by six2. 12 + 42 + 72 + ... + (3n - 2)2 = quantity n times quantity six n squared minus three n minus one all divided by twoFor the given statement Pn, write the statements P1, Pk, and Pk+1.(2 points)2 + 4 + 6 + . . . + 2n = n(n+1)

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general 11 months ago 4505