Answer:
The transformation of to
consists in a vertical translation. The new equation is
.
Step-by-step explanation:
Let . We proceed to make the required transformations on
, which consists in one vertical translation, 3 units in the -y direction. That is to say:
(1)
Then, the transformation of to
consists in a vertical translation. The new equation is
.
A.
If she will choose 8 from 12 photos, the total number of ways she can choose is given by a combination of 12 choose 8, since the order of the photos doesn't matter.
The formula for a combination of n choose p is:
For n = 12 and p = 8, we have:
So there are 495 ways.
B.
If she wants to arrange the 12 photos, the total number of ways is given by the factorial of 12:
There are 479,001,600 ways.
C.
Since 10 photos already have specific places, we need to calculate the number of ways to arrange the other two photos in the two remaining places.
In this case, there are only 2 ways of organizing the remaining two photos:
Photo 1 first, photo 2 last, or photo 1 last and photo 2 first.
Answer:
6
Step-by-step explanation:
Using the sine ratio in the right triangle
let x = hypotenuse and sin45° = , then
sin45° = =
and
=
( cross- multiply )
× x = 6
Divide both sides by
x = 6