HELP ASAP the points K, L,M and N all lie on the same line segment, in that order, such that the ratio of KL : LM : MN is equal to 4 : 3 : 4. if KN = 33, find MN

Step-by-step explanation:

Given that points K, L, M, and N are collinear, and the ratio of the segments, KL:LM:MN = 4:3:4, we can find the lenght of MN as follows, since we are also given the total lenght of the whole segment, KN = 33.

Length of MN = the individual ratio value of MN ÷ the total ratio value of the 3 segments × lenght of the whole segment

Individual ratio value of MN = 4

Total ratio value = 4 + 3 + 4 = 11

Length of whole segment, KN = 33

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is