The chart below shows an expression evaluated for four different
values of x
x: x2+x+5:
1 7
2 11
6 47
7 61
Josiah concluded that for all positive values of x, x2+x+5 produces a prime number. Which value of x serves as a counterexample to prove Josiah’s conclusion false?
A: 5
B: 11
C: 16
D: 21
Try each one see which one isn't prime. You won't have to go far down the list.
To find the counterexample, we need to check each value of x and see if x^2 + x + 5 is a prime number.
Plugging in x = 5, we get:
5^2 + 5 + 5 = 25 + 5 + 5 = 35
Since 35 is not a prime number (it can be divided by 5 and 7), x = 5 is a counterexample.
Therefore, the correct answer is A: 5.
To find the counterexample that disproves Josiah's conclusion, we need to evaluate the expression x^2 + x + 5 for each of the given values of x and check if the result is a prime number.
The given values of x are 1, 2, 6, and 7. Let's evaluate the expression for each of these values:
For x = 1: 1^2 + 1 + 5 = 7
For x = 2: 2^2 + 2 + 5 = 11
For x = 6: 6^2 + 6 + 5 = 47
For x = 7: 7^2 + 7 + 5 = 61
Looking at the results, we can see that the expression produces prime numbers for all the given values of x. However, to find the counterexample, we need to check the options A, B, C, and D.
Option A: For x = 5: 5^2 + 5 + 5 = 35
Option B: For x = 11: 11^2 + 11 + 5 = 157
Option C: For x = 16: 16^2 + 16 + 5 = 277
Option D: For x = 21: 21^2 + 21 + 5 = 487
From the given options, the value of x = 16 (Option C) is the counterexample because the result, 277, is not a prime number. Therefore, the answer is option C: 16.