Answer:
We need to use the mapping to find the new coordinates of X and Y.
Step-by-step explanation:
Vectorially speaking, we must look for the defintion of the translation operation such that vertex Y becomes vertex Y', which is represented by:
(1)
Where is the translation vector.
If we know that and , then the translation vector is:
If , and is the translated vector, then we obtain the following definition:
(2)
The correct answer is B.
We have to identify the transformations that take △ABC to △A"B"C".
The first transformation takes △ABC to △A'B'C'. We can see that the triangle is reflected over the x-axis (horizontal axis).
For example, as C is located on the x-axis, C' is also located on the x-axis. For A and B, its vertical coordinates change sign but mantain its absolute value.
We can write this transformation as:
This transformation shows that the horizontal coordinates are mantained and the vertical coordinates have their sign inverted.
The second transformation is a translation. The orientation stays the same but the points are translated a fixed number of units in both the horizontal and vertical direction.
We can take any point and its transformed point and compare its coordinates. For example B'' is 6 units to the right and 2 units up.
Then, we can write:
We can generalize this to the rule:
as the x-coordinate will increase 6 units and the y-coordinate will increase 2 units.
Answer: the transformations are a reflection over the horizontal axis (y=0) and a translation of (x+6,y+2) [First option].
2*10^-2 (Ten to the negative 2 power)
Answer:
60 miles.
Step-by-step explanation:
Given:
We rent a car for the day and are offered two payment options.
With option A we pay $25 flat rate plus $0.15 per mile.
With option B we pay a $10 flat rate plus $0.40 per mile.
Question asked:
For what amount of miles would the cost of option A be equal to option B ?
Solution:
<u>Let amount of miles for which the cost of option A be equal to option B = </u><u />
For option A, we pay =
For option B, we pay =
Now, to find amount of miles for which the cost of option A be equal to option B, we will equalize the equation to find the value of
By subtracting both sides by 10
By subtracting both sides by
By dividing both sides by
Therefore, for 60 miles, the cost of option A will be equal to option B.
The following subsets you can be able to create are:
{1}
{2}
{3}
{1,2}
{1,3}
{2,3}
{1,2,3}
Therefore, there are 7 subsets in all. However, we don't have to list all these possible outcomes because we could waste our time doing this but there is a formula, that is 2^n - 1 where n is a number of elements.
In the given, since there are 3 elements inside the set then we use 2^3 - 1 = 8 - 1 = 7.
See...it's easy.