Which shows the correct way to use the rule "multiply by the reciprocal" for the expression below? 7 divided by StartFraction 5 Over 8 EndFraction StartFraction 1 Over 7 EndFraction times StartFraction 5 Over 8 EndFraction = StartFraction 5 Over 56 EndFraction StartFraction 7 Over 1 EndFraction times StartFraction 5 Over 8 EndFraction = StartFraction 35 Over 8 EndFraction StartFraction 1 Over 7 EndFraction times StartFraction 8 Over 5 EndFraction = StartFraction 8 Over 35 EndFraction StartFraction 7 Over 1 EndFraction times StartFraction 8 Over 5 EndFraction = StartFraction 56 Over 5 EndFraction

Is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis.

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

Astrid spent $36 on new shoes. this was $12 less than twice what she spent on a new skirt. part a: which equation would solve for how much she spent on the skirt? part b: solve the equation in the workspace provided below. how much did astrid spend on her skirt?