A music store is having a clearance sale on all of its vinyl records, CDs, and electronic downloads. For the sale, each item (vinyl, CD, and electronic download) costs the same regardless of the artist, with the price including the tax. Sarah, Jamie, and Frank decide to make the most of this sale, and they each purchase several items. Sarah buys 3 vinyl records, 4 CDs, and 1 electronic download for a total of $32. Jamie buys 2 vinyl records, 5 CDs, and 7 electronic downloads for a total of $37. Frank buys 6 CDs, and 6 electronic downloads for a total of $30.

What is the price of each vinyl, CD, and electronic download?

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