Atree cast a 25-foot shadow. at the same time of the day, a 6-foot man standing near the tree casts 9-foot shadow. what is the height of the tree, to the nearest foot?

The height of the tree is 16.67 feet.

Step-by-step explanation:

Refering the figure, let the height be "x" feet.

It is evident that triangles ABC and triangle EDC are similar.

(as both man and tree are perpendicular to the ground)

thus,

hence,

Thus, .

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form