Maximize the function f(x, y) = 8x + 9y in the region determined by the following constraints. 3x + 2y ≤ 18 3x + 4y ≥ 12 x ≥ 0 y ≥ 0

Ahighway between points a and b has been closed for repairs. an alternative route between there two locations is to travel between a and c and then from c to b what is the value of y and what is the total distance from a to c to b?

Apyramid fits exactly inside a cube. the cube and the pyramid share the same square base, and they are both exactly the same height. the volume of the cube is 66 cubic inches. what is the volume of the pyramid? explain your answer. answer asap

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