Karina uses the system of equations below to compare the monthly utility costs in july and december for electricity, x, and natural gas, y.

750x + 17y = 141.61
300x + 30y = 75.90
karina solves the system using linear combination and arrives at the equation 116y = 96.28. she then solves this equation for y. which statement explains karina’s solution?

the cost of electricity is $0.17 per unit.
the cost of natural gas is $0.20 per unit.
the cost of electricity is $0.72 per unit.
the cost of natural gas is $0.83 per unit.

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