Ella makes a smoothie for breakfast every morning. Today, she wants to use melon, apple, orange, and peach. In how many different ways (orders) can she add these fruits to her blender?

24 different ways

Step-by-step explanation:

( 1 ) We can apply factorial in this case. We have 4 elements, melon, apple, orange, and peach. The number of ways with which we have to arrange these fruits should be 4! ( again, there are 4 elements ).

4! = 4 3 2 1

4 3 2 1 = 12 2 1

12 2 = 24 different ways

( 2 ) The first method was the simpler approach. You can confirm this answer through another method...simply list out the different possibilities, altering their order in a specified manner.

{ melon, apple, orange, peach }

{ melon, apple, peach, orange }

{ melon, peach, apple, orange }...and keep on trying different combinations!

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