Raj and Aditi like to play chess against each other. Aditi has won 12 of the 20 games so far. They decide to play more games. How many more games will Aditi have to win to have a 70% winning record?

12 + x = 0.70(20 + x)
x = x equals StartFraction 20 Over 3 EndFraction is approximately 6.67. ≈ 6.67
She will have to win 7 more games to have a 70% winning record.

How many more games will Aditi have to win to have an 80% winning record?

The linear equation that models this is
.

Aditi would have to win
more games to have an 80% winning record.

Amir wants to proportionally increase the size of a photo to create a poster for his room. the size of the original photo is shown. complete the statement and then answer the question to represent ways that amir can increase the size of his photo.

Is a square always, sometimes, or never a parallelogram

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