Your friend is trying to calculate the height of a nearby oak tree. you tell him that you learned how to use similar triangles in geometry class. you tell your friend to measure his height (75 inches) and you measure the length of his shadow (48 inches). both of you measure the length of the tree’s shadow (38 feet). how tall is the tree (in feet)? round to the nearest hundredth.

The height of the tree is 59.38 feet.

Step-by-step explanation:

It is given that the height of friend is 75 inches and the length of his shadow is 48 inches.

The ratio of height and shadow of friend is

Let the length of the tree in feet is x.

The length of the tree’s shadow is 38 feet. The ratios of height and shadow of tree is

Using similar triangles property the ratio of height and shadow is same for both objects.

Multiply both sides by 38.

Therefore the height of the tree is 59.38 feet.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be