Which of the following compositions of transformations will always produce the same image, regardless of the order in which the transformations are performed?
a. translation and reflectionb. reflection and rotationc. translation and rotationd. none of the above

D. None of the above              

Step-by-step explanation:

Let us assume the transformations applied as follows:

Translation of h units to right and k units up i.e. (x,y) → (x+h,y+k).

Rotation of the figure around 90° i.e. (x,y) → (y,-x).

Reflection of the figure about x-axis i.e. (x,y) → (x,-y).

Now, we need to find the composition of transformations that gives the same image irrespective of the order.

So, let us apply the above assumed transformations on the point (x,y). Therefore, according to options:

A. Translation then reflection gives (x,y) → (x+h, y+k) → (x+h,-y-k)

or Reflection then translation will give (x,y) → (x,-y) → (x+h, -y-k).

B. Reflection then Rotation gives (x,y) → (x,-y) → (-y,-x)

or Rotation then reflection gives (x,y) → (y,-x) → (y,x)

C. Translation then rotation gives (x,y) → (x+h,y+k) → (y+k,-x-h)

Rotation then translation will give (x,y) → (y,-x) → (y+k,-(x+h) = (y+k,-x-h).

As, we can see that the resulting figure depends on the order in which the rigid transformation is applied and does not gives us the original image.

So, option D is correct.

the answer is somewhere there guys it really . there im just not gonna answer

step-by-step explanation:

but i'm guessing ur first option tho

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.