Hans has $27 which he decides to spend on x and y. commodity x costs $16 per unit and commodity y costs $10 per unit. he has the utility function u(x, y) = 2x^2 + 2y^2 and he can purchase fractional units of x and y. hans will choose
(a) only x item.
(b) only y item.
(c) both x and y.

Solve the equation x/4 - 5= -8 -27 -12 -7 12

Statements reasons 1. ab ? cd; ad ? bc 1. given 2. ac ? ac 2. reflexive property 3. ? adc ? ? cba 3. ? 4. ? dac ? ? bca; ? acd ? ? cab 4. cpctc 5. ? dac and ? bca are alt. int. ? s; ? acd and ? cab are alt. int. ? s 5. definition of alternate interior angles 6. ab ? cd; ad ? bc 6. converse of the alternate interior angles theorem 7. abcd is a parallelogram 7. definition of parallelogram what is the missing reason in step 3?

In the diagram, a building cast a 35-ft shadow and a flagpole casts an 8-ft shadow. if the the flagpole is 18 ft tall, how tall is the building? round the the nearest tenth.