Hello!
Given the rule of V(x, y) = (x, y - 1), we can determine that it might be a horizontal or vertical shift.
Since we know that x-values are domain and y-values are range, we know that the range of the function is decreasing by 1 (y - 1), so, the entire function is shifting down one unit.
Therefore, the type of transformation given by the rule is a vertical shift/translation downwards by one unit.
Given:
The pair of composite numbers: 10 and 15
To find:
The greatest common factor (GFC) for the given pair of composite numbers.
Solution:
Two composite number are 10 and 15.
The factor forms of these two numbers are
It is clear that the common factor is 5 in both factor forms. So, the greatest common factor is
Therefore, the greatest common factor of 10 and 15 is 5.
The graph is touching the x-axis at x= 2 and is turning away.
When a graph exhibit such a behavior at a root, we say that the multiplicity of the root is 2. So the roots of the polynomial are x = 2 and x = 2. The factors of the polynomial are (x - 2) and (x - 2)
The polynomial thus can be written as product of its factors as (x-2)(x-2)
So the correct answer to this question is option B
Answer:
After expanding the polynomial 
we get 
Step-by-step explanation:
We need to expand the polynomial
Multiply the terms:
So, after expanding the polynomial we get
For either square root to exist, you require that
. This is true for all
, since
is always non-negative. This means the domain of
as a function of
is all real numbers, or
or
.
Now, because
is non-negative, and the smallest value it can take on is 7, it follows that the minimum value for the positive square root must be
, while the maximum value of the negative root must be
. This means the range is
, or
, or
![(-\infty,-\sqrt7]\cup[\sqrt7,\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C-%5Csqrt7%5D%5Ccup%5B%5Csqrt7%2C%5Cinfty%29)
.
