On a short road trip, if Mary spends her entire budget on gas and diner meals, Mary can afford either 35 gallons of gas or 7 diner meals. What is the opportunity cost of one diner meal?

The cost of opportunity of one diner meal is  5 gallons.

Explanation:

The cost of opportunity is the alternative that you sacrifice when you choose an option.  

It represents the benefits that you miss out on when choosing one alternative over another.  

In this case, the cost of opportunity of one diner meal is the quantity of gallons that you sacrifice.

7 diners = 35 gallons

1 diner = 35*1/7= 5 gallons

The cost of opportunity of one diner meal is  5 gallons.

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.