Mariana owns and operates Stain-B-Gone Carpet Cleaners. She uses a special non-toxic cleaning solution to clean carpets. Mariana cleans 20 square yards of carpet for each quart of cleaning solution she uses. There is a proportional relationship between the amount of cleaning solution (in quarts) Mariana uses, x, and the area of carpet (in square yards) she cleans with the solution, y.

Aconstruction worker has rope 9 m long he needs to cut it in pieces that are each 3 /5 m long how many such pieces can he cut without having any rope leftover?

Segment wx is shown explain how you would construct a perpendicular bisector of wx using a compass and a straightedge

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality