Point m is on line segment ln . given ln=3x+3,ln=3x+3, lm=4x, lm=4x, and mn=2x, mn=2x, determine the numerical length of mn .

MN = 2

This question is dealing with division of line segments.

The line segment is Line LN.

A point M is on the line segment such that;

LN = (3x + 3)

LM = 4x

MN = 2x

Thus;

LM + MN = LN

Plugging in the relevant values;

4x + 2x = (3x+3)  

6x = 3x + 3  

rearranging, gives;

6x - 3x = 3

3x = 3

x = 3/3

x = 1

MN = 2x

Thus; MN = 2(1)

MN = 2

Read more at;

2 units.

Step-by-step explanation:

Given : LN = (3x + 3)

            LM = 4x

and MN = 2x

To find : (Length of MN)

Point M lies on a line segment LN.

As shown in the figure m(LN) = m(MN)

Now we plug in the values.

(3x+3) = 4x + 2x

3x + 3 = 6x

3 = 6x - 3x

3 = 3x

x = (  = 1

Since MN = 2x

               = 2 × 1

               = 2 units.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47