A student concludes that for all values of x,x^2+x+1 produces a prime number. Which value of x serves as counterexample to prove
this conclusion false?
1 answer:
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The equation which gives the correct value of n, the number of GB, for which Plans A and B cost the same is 8n = 20 + 6(n-2)
To determine which equation gives the correct value of n, the number of GB, for which Plans A and B cost the same, we will first solve the equations.
- For the first equation
8n = 20 + 6n
Collect like terms
8n - 6n = 20
2n = 20
Then, n = 20 ÷ 2
n = 10 GB
For Plan A
No initial fee and $8 for each GB
Here, 10GB will cost 10 × $8 = $80
For Plan B
$20 for the first 2GB and $6 for each additional GB after the first 2
Here, 10GB will cost $20 + (8 × $6) = $20 + $48 = $68
∴ Plans A and B do not cost the same here.
- For the second equation
8n = 20(2n) + 6
First, clear the bracket
8n = 40n + 6
Now, collect like terms
40n - 8n = 6
42n = 6
∴ n = 6 ÷ 42
n = 1/7 GB
For Plan A
No initial fee and $8 for each GB
Here, 1/7GB will cost 1/7 × $8 = $1.14
For Plan B
$20 for the first 2GB and $6 for each additional GB after the first 2
Here, 1/7GB will cost $20 (Since the lowest cost is $20)
∴ Plans A and B do not cost the same here.
- For the third equation
8n = 20 + 6(n-2)
First, clear the brackets
8n = 20 + 6n - 12
Now, collect like terms
8n - 6n = 20 - 12
2n = 8
n = 8 ÷ 2
n = 4 GB
For Plan A
No initial fee and $8 for each GB
Here, 4GB will cost 4× $8 = $32
For Plan B
$20 for the first 2GB and $6 for each additional GB after the first 2
Here, 4GB will cost $20 + (2 × $6) = $20 + $12 = $32
Plans A and B do not cost the same here.
∴ Plans A and B do cost the same here
- For the fourth equation
8n = 20 + 2n + 6
Collect like terms
8n - 2n = 20 + 6
6n = 26
n =
n = GB or
GB
For Plan A
No initial fee and $8 for each GB
Here, GB will cost
× $8 = $34.67
For Plan B
$20 for the first 2GB and $6 for each additional GB after the first 2
Here, GB will cost $20 + (
× $6) = $20 + $14 = $34
∴ Plans A and B do not cost the same here.
Hence, the equation which gives the correct value of n, the number of GB, for which Plans A and B cost the same is 8n = 20 + 6(n-2)
Learn more here: brainly.com/question/9371507