Jonas jogged up the hill at an average rate of of a mile per minute and then walked down the hill at an average rate of StartFraction 1 Over 16 EndFraction left-parenthesis 42 minus x right-parenthesis. of a mile per minute. The round trip took him 42 minutes. What is the missing value in the table that represents the distance of the trip down the hill? A table showing Rate in miles per minute, Time in minutes, and Distance in miles. The first row has Up the Hill, and has StartFraction 1 Over 12, x, and StartFraction 1 Over 12 x. The second shows, Down the Hill, and has StartFraction 1 Over 16 EndFraction, 42 minus x, and question mark.

x
StartFraction 1 Over 16 EndFraction minus x. – x
42 – 42 minus StartFraction 1 Over 16 EndFraction x. x
StartFraction 1 Over 16 EndFraction left-parenthesis 42 minus x right-parenthesis. (42 – x)

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Simplify the following expression 48^1/2

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