Function h models an object's height in feet after x seconds have passed. Which equation shows that the object's height increased by 100 feet over the first 15-second period? A. h(15) 100

B. h(100) = 15

C. h(15) - h(0) = 100

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C

Step-by-step explanation:

We know that function h represents an object's height in feet after x seconds.

In that case, option A) h(15) = 100 means that after 15 seconds, the object's height is 100 feet.

Option B) h(100) = 15 means that after 100 seconds, the object's height is 15 meters.

Therefore, neither A nor B are correct.

Option C) h(15) - h(0) = 100 means that between the zeroth and 15th second, their difference is 100 feet.

In other words, the object's height increased by 100 feet over the first 15-second period.

Option C is correct.

For Option D), it gives us the average rate of change. (h(15) - h(0)) / (15) = 100 means that for the first fifteen seconds, the height of the object increased at an average rate of 100 feet per second.

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