Consider the quadratic equation
2 answers:
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Answer:
400 megabytes of data used will make the cost from either company equal.
Step-by-step explanation:
Given that:
Per month charges of Company A = $80
Charges of 100 MB = $5 =
Let,
x be the number of MBs consumed.
y be the total charges.
y = 0.05x+80
Per month charges of Company B = $60
Charges of 100 MB = $10 = $0.1 per MB
y = 0.1x+60
For equal charges;
0.05x+80 = 0.1x + 60
80-60 = 0.1x-0.05x
20 = 0.05x
Hence,
400 megabytes of data used will make the cost from either company equal.
The standard form is pretty much the variables on the left-hand-side and the constant alone by herself on the right-hand-side, with only positive integers on the x-variable and an integers all around.
9514 1404 393
Answer:
- ratio: 2
- sum: 765
- product: 1,761,205,026,816
Step-by-step explanation:
The general term of a geometric sequence is ...
an = a1×r^(n-1)
Here, we're given that the first term is a1 = 3. From the 8th term, we can find the common ratio, r.
a8 = 384 = 3r^7
128 = r^7 . . . . . . . . divide by 3
2 = r . . . . . . . . . 7th root
The common ratio is 2.
__
The sum of the terms of a geometric series is ...
Sn = a1×(r^n -1)/(r -1)
For the known values of a1 and r, the sum o 8 terms is ...
S8 = 3×(2^8 -1)/(2 -1) = 3(255) = 765
The sum of the first 8 terms is 765.
__
The product of the first 8 terms will be ...
(3)(3×2)(3×2^2)(3×2^3)...(3×2^6)(3×2^7) = (3^8)(2^(1+2+3+...+7))
= (3^8)(2^28) = 6561 × 268,435,456
Many calculators cannot report the full value of this product. (Many spreadsheets can.)
The product of the first 8 terms is 1,761,205,026,816.
_____
In the attached, we found the value of r that made the 8th term be 384 by solving the equation 3×r^7 -384 = 0. The value is shown on the graph as the x-intercept of the exponential function. That x-intercept is 2, so r=2 (as above).
