Dividing the given equation by 25 we get:

Applying the natural logarithm to the above equation we get:

Finally, solving for x we get:

Answer: Option A.
Answer:
Option A. 
Step-by-step explanation:
<u><em>The complete question is</em></u>
The function g is given in three equivalent forms.
Which form most quickly reveals the vertex?
A)g(x)= 1/2(x-8)^2-8
B)g(x)= 1/2(x-12)(x-4)
C)g(x)= 1/2x^2-8x+24
we know that
The equation of a quadratic function in vertex form is equal to

where
a is the leading coefficient
(h,k) is the vertex of the function
In this problem, the option A is the equation of the function in vertex form
we have

where the vertex is the point (8,-8)
therefore
Option A
Answer: The answer is 
Step-by-step explanation: Given that Leonhard wants to place a triangular based cabinet in the corner of his room which is rectangular in shape.
The base and height of the triangular cabinet are
Therefore, area of the triangular cabinet is given by

Now, the length and breadth of the rectangular room are 30 feet and 20 feet respectively. Therefore, the area of the room is given by

According to the question,

Since the length of something cannot be negative, so the value of 'x' is

because if we take the other value of 'x', the values of (2x+3) and (3x+6) will become negative which is not possible.
Thus, (A) is the correct option.
Answer:

Step-by-step explanation:
Midpoint of a segment with the given endpoints
and
is defined by,

In this question endpoints of the segment are,
and 
Coordinates of the midpoint will be,

= 
Therefore, coordinates of the midpoint are
.
The <em><u>correct answer</u></em> is:
C. Both (house, complete mailing address) and (complete mailing address, house) are functions.
Explanation:
A function is a relation in which each element of the domain (x-values) is mapped to one element of the range (y-values).
In the set (house, complete mailing address), the values of "house" would be the domain and the values of "complete mailing address" would be the range. In order to be a function, each value of "house" would be mapped to only one value of "complete mailing address." This is true; each house will have only one complete mailing address. This means it is a function.
In the set (complete mailing address, house), the values of "complete mailing address" would be the domain and the values of "house" would be the range. In order to be a function, each value of "complete mailing address" would be mapped to only one value of "house." This is true; each complete mailing address would go with only one house. This means it is a function.