Multiply both sides of your equation bye the denominator
Answer:
80 < 93 < 121 < 127
Step-by-step explanation:
For a geometric series,
Formula to be used,
Sum of t terms of a geometric series = 
Here t = number of terms
a = first term
r = common ratio
1). 
First term of this series 'a' = 3
Common ratio 'r' = 2
Number of terms 't' = 5
Therefore, sum of 5 terms of the series = 
= 93
2). 
First term 'a' = 1
Common ratio 'r' = 2
Number of terms 't' = 7
Sum of 7 terms of this series = 
= 127
3). 
First term 'a' = 1
Common ratio 'r' = 3
Number of terms 't' = 5
Therefore, sum of 5 terms = 
= 121
4). 
First term 'a' = 2
Common ratio 'r' = 3
Number of terms 't' = 4
Therefore, sum of 4 terms of the series = 
= 80
80 < 93 < 121 < 127 will be the answer.
The root is the x intercepts or the zeros of the problem
If I were to graph
(x-5)(x+4)=0
We need a number for x which makes this equation 0
The numbers are 5 or -4
These are the x intercepts of the parabola or roots
Well, I'm not completely sure, because I don't know the formal definition
of "corner" in this work. It may not be how I picture a 'corner'.
Here's what I can tell you about the choices:
A). (0, 8)
This is definitely a corner of the feasible region.
It's the point where the first and third constraints cross.
So it's not the answer.
B). (3.5, 0)
This is ON the boundary line between the feasible and non-feasible
regions. But it's not a point where two of the constraints cross, so
to me, it's not what I would call a 'corner'.
C). (8, 0)
Definitely not a corner, no matter how you define a 'corner'.
This point is deep inside the non-feasible zone, and it doesn't
touch any point in the feasible zone.
So tome, this looks like probably the best answer.
D). (5, 3)
This is definitely a corner. It's the point of intersection (the solution)
of the two equations that are the first two constraints.
The feasible region is a triangle.
The three vertices of the triangle are (0,8) (choice-A),
(0,-7) (not a choice), and (5,3) (choice-D) .
region is a triangle
The area of the triangle is 60.
12 x 10 = 120
120/2 = 60
