Answer:
The statement is true for every n between 0 and 77 and it is false for 
Step-by-step explanation:
First, observe that, for n=0 and n=1 the statement is true:
For n=0: 
For n=1: 
From this point we will assume that 
As we can see,
and
. Then,

Now, we will use the formula for the sum of the first 4th powers:

Therefore:

and, because
,

Observe that, because
and is an integer,

In concusion, the statement is true if and only if n is a non negative integer such that 
So, 78 is the smallest value of n that does not satisfy the inequality.
Note: If you compute
for 77 and 78 you will obtain:
Answer:
BD = 16
Step-by-step explanation:
By applying mean proportional theorem in the given right triangles,

AD × CD = BD²
8 × 32 = BD²
BD = √256
BD = 16
Therefore, measure of side BD = 16 units.
Answer:
Step-by-step explanation:
ΔΔπФ⇵β³Δ⊄⊇≡⊕⊕π⇆ω∩∨
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.
If a point A(x, y) is reflected over the x axis, the new point is at A'(x, -y). If a point B(x, y) is reflected over the y axis, the new point is at A'(-x, y).
Triangle A has vertex at (-4, -2), (-4, -5) and (-2, -5). If triangle A is reflected in the x axis to give triangle B, the vertex of triangle B is (-4, 2), (-4, 5) and (-2, 5).
If triangle B is reflected in the y axis to give triangle C, the vertex of triangle C is at (4, 2), (4, 5) and (2, 5). Hence the transformation is:
(x, y) ⇒ (-x, -y)