Which two expressions are equivalent? A. 9(6 + x)
9 ⋅ 6+ 9 ⋅ x
B. x + (8 ⋅ 9)
(x + 8) ⋅ 9
C. 8⋅ 6 ÷ x
8 ⋅ x ÷ 6
D. 6 ⋅ x + 3
6 ⋅ (x + 3)

Paint color preference children adults total 0.6 0.77 liked new paint color disliked new paint color 0.4 0.15 0.23 total 1.0 1.0 1.0 which value for x completes the conditional relative frequency table by column?

Cody was 165cm tall on the first day of school this year, which was 10% taller than he was on the first day of school last year.

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