There is an unknown amount of people at the beginning of lunch. Then Each student had 2 friends come sit with them, tripling the amount. Then the entire group divided into 5 groups, and all but one group left and went outside, so only 1/5 of the total students were left in the lunchroom 3 more people came into the lunchroom The total number of people in the lunchroom at the end of lunch was 11 Which of the following equations would represent the story above to help us find how many people were in the lunchroom at the beginning?

Ab based on the given diagram, if m_1 = 60° then m 2 = 30 60 90 180

Factor and solve to find roots x squared -x - 90 =0

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