The 6th grade science teacher gives a test every 12 days and the math teacher gives a test every 9 days. Today, both the science and math are giving tests. In how many days will the science and math teachers both give tests on the same day again?

HELP

In 36 days will the science and math teachers both give tests on the same day again.

Step-by-step explanation:

Here we have , The 6th grade science teacher gives a test every 12 days and the math teacher gives a test every 9 days. Today, both the science and math are giving tests. We need to find In how many days will the science and math teachers both give tests on the same day again . Let's find out:

It's given that  science teacher gives a test every 12 days and the math teacher gives a test every 9 days . In order to find the number of days after which they'll give test at same day  , we will find LCM of 12 & 9 . i.e.

⇒       and  ,

⇒

Hence , LCM of 12 and 9 is 36 . Therefore , In 36 days will the science and math teachers both give tests on the same day again.

34

step-by-step explanation:

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.