Answer:
The explicit form is ![a_{n}=162(2/3)^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3D162%282%2F3%29%5E%7Bn-1%7D)
Step-by-step explanation:
The explicit form of a geometric sequence is given by:
![a_{n}=ar^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Dar%5E%7Bn-1%7D)
where an is the nth term, a is the first term of the sequence and r is the common ratio.
In this case:
a=162
The value of the common ratio is obtained by dividing one term by the previous term.
For the first and second terms:
108/162=2/3
For the second and third terms (In order to prove that 2/3 is the common ratio)
72/108=2/3
Therefore:
r=2/3
Replacing a and r in the formula:
![a_{n}=162(2/3)^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3D162%282%2F3%29%5E%7Bn-1%7D)
The area here is 2 triangles and 3 rectangularso the total area is the sum of all areas area of triangle = 0.5 * base * height = 0.5 * 4 * 3 = 6 ft^2 the area of the rectangular 1 = 5 * 7 = 35 ft^2 the area of rectangular 2 = 4 * 7 = 28 ft^2 the area of rectangular 3 = 3 * 7 = 21 ft^2 so the total surface area = 2(6) + 35 + 28 + 21 = 96 ft^2
The answer is
P= -20
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3
Hope this helps:)
*GilmoreGirl01*
The equation of the line in its generic form is:
y = mx + b
Where,
m = (y2-y1) / (x2-x1)
For (-1, 3) and (0, 1):
We look for the value of m:
m = (1-3) / (0 - (- 1))
m = (- 2) / (0 + 1)
m = -2
We look for the value of b:
1 = m (0) + b
b = 1
The line is:
y = -2x + 1
For (1, 4) and (0, 2):
We look for the value of m:
m = (2-4) / (0-1)
m = (- 2) / (- 1)
m = 2
We look for the value of b:
2 = m (0) + b
b = 2
The line is:
y = 2x + 2
The system of equations is:
y = -2x + 1
y = 2x + 2
Answer:
the system has one solution