How many equal sections divide a directed line segment if it is to be partitioned with a 5: 7 ratio

 The line segment can be divided into 12 equal sections.

Step-by-step explanation:  We are given to find the number of equal sections that divide a directed line segment if it is to be partitioned with a 5 : 7 ratio.

We know that

if a line directed line segment is partitioned in the ratio a : b, then we can divide the line segment in (a + b) equal sections.

So, the number of equal sections in which the given line segment can be divided is given by

Thus, the line segment can be divided into 12 equal sections.

you have 6 cupcakes

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.