Stoplight a changes color every 30 seconds and stoplight b changes every 40 seconds. after how many seconds will the stoplights change colors at the same time again?

After 120 seconds

Step-by-step explanation:

Here, we want to know the number of seconds after which both spotlights will change colors at the same time again.

Basically, what we want to do here is to

calculate the value with which 30 and 40 have the same multiples or we want to

calculate the lowest common multiple of 30 and 40

The multiples of 30 are 30,60,90,120 etc

The multiples of 40 are 40,80,120 etc

We can see that the lowest common multiple of both is 120

So therefore the spotlights will change colors at the same time after 120 seconds

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

step-by-step explanation:

mean or average is 40.6