The goal programming problem with the objective function min p1(d1+) +p2(d2–) is initially solved by the computer and the objective function value is 0. what constraint should be added for the second problem? a) d1+ ≤ 0b) –d1+ + d2– = 0c) d1+ = 0d) d1+ + d2– = 0

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

1. avoid them

2. a talk with them

3. ask someone you trust

4. ignore

5. call police

false is correct i hope.

i might be