Asix-foot-tall person is standing next to a flagpole. the person is casting a shadow 1 1/2 feet in length, while the flagpole is casting a shadow 5 feet. how tall is the flagpole?

20 ft

This problem can be solved by the Thales’s theorem, which states:

Two triangles are similar when they have equal angles and proportional sides  

It should be noted that to apply Thales' Theorem, it is necessary to establish the two triangles are similar, that is, that they have the corresponding angles equal or that their sides are proportional to each other.  

Now, if we measure the shadow of the flagpole and the shadow of the person, at the same moment, we can use the first Thales' Theorem to calculate the height of the flagpole, knowing the height of the person.

In this case we have two similar triangles (Figure attached) where is the height of the flagpole, is the height of the person, is the length of the shadow of the flagpole and is the length of the shadow of the person.

Having this clear, we can write the following relation with both similar triangles:

  (1)

We know all these lengths except , which is the value we want to to find.  

So, in order to approach this problem we have to find from equation (1):  

Then:

>>>>>This is the height of the flagpole

81 seats

step-by-step explanation:

if you multiply 0.65 times 125 then you get 81.5 seats. well since you can't have half of a seat you have to round down and get 81 seats in the no children zones. that leave 44 seats outside of the no children zone.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.