Trying to find the missing segment to the triangle in the attached image.

36 units.

Step-by-step explanation:

we will use concept of basic proportionality theorem,

it states that , when a line is drawn parallel to one side of the triangle and intersect the other two sides then the two sides are divided in the same ratio.

Example:

In a triangle ABC

If  DE is  parallel to BC

D is a point on line AB and E is  point on AC, then

by basic proportionality theorem)

AD/DB = AE/EC

in the problem  given one side has a parallel line drawn to it

Hence we can use basic proportionality theorem in it

20/30 = 24/?

2/3 = 24/?

=> ? = 24*3/2 = 36

Hence, missing segment value is 36 units.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )