Acollege is currently accepting students that are both in-state and out-of-state. they plan to accept three times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students. let x = the number of out-of-state students and y = the number in-state students. write the constraints to represent the incoming students at the college.
0 < x ≤ 100 and 0 < y ≤ 300
x > 0 and y > 0
0 < x ≤ 100 and y > 300
0 < x and y < 100

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4