Filling a Vase Leah has a flower vase in the shape of a rectangular prism with a square base. The vase has a height of 12 inches.

There are flowers and some water in the vase. The water is getting low, so Leah takes the vase to the sink and begins to add water.

After 5 seconds, the height of the water in the vase is 3.85 inches.

After 10 seconds, the height of the water in the vase is 5.7 inches.

Part A Write a linear function that models the relationship between the number of seconds the water has been running and the height of the water in the vase. Enter your answer and explanation in the box.



Part B Identify the rate of change and the initial value of your function, and explain the meaning of each in terms of the situation. Enter your answers and explanation in the box.

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