A number cube is rolled and a coin is flipped.

A 7-column table with 2 rows. Column 1 has entries H, T. Column 2 is labeled 1 with entries H1, T1. Column 3 is labeled 2 with entries a, T2. Column 4 is labeled 3 with entries H3, T3. Column 5 is labeled 4 with entries H4, T4. Column 6 is labeled 5 with entries H5, T5. Column 7 is labeled 6 with entries H6, b.

How many possible outcomes are there?
?

What are the missing table values?

a =
b =

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