The sum of two numbers is 82. their difference is 24. write a system of equations that describes this situation. solve by elimination to find the two numbers. a. x y = 82 x – y = 24 53 and 29 b. x y = 82 x – y = 24 48 and 24 c. x y = 24 y – x = 82 48 and 30 d. x – y = 82 x y = 24 52 and 30

Which system of linear inequalities is represented by the graph? + l tv x-3y > 6 and y > 2x o x + 3y > 6 and y o x-3y > 6 and y> 2x o x + 3y > 6 and y > 2x + 4 la +

Which expression is equal to (21)(7)(3x) using the associative property? (21 · 7 · 3)x (7)(21)(3x) 32(7 + 3x) (3x)(7)(21)

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