Students observing a caterpillar crawl on a tree noticed that the caterpillar crawled upwards 38 of an inch every minute. the caterpillar was already 4.5 feet off the ground when the students began observing.
which function represents the total number of inches the caterpillar crawls after x minutes?
f(x) = 4.5x + 3/8
f(x) = 54x + 3/8
f(x( = 3/8x + 54
f(x) = 3/8x + 4.5

Third Option

Step-by-step explanation:

We want to propose an equation that models the distance traveled by the caterpillar as a function of time, we have a constant initial quantity of 4.5 feet and then we know that every minute the caterpillar advances 3/8 of an inch

Then the distance that the caterpillar to advanced after x minutes is:

Then we know that initially the caterpillar was at a distance of 4.5 feet or 54 inch

Then the equation for the distance in inch is:

my discord name is kinglilcliff12#7776

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