Which number is a solution of the inequality?
6>z(10-z)
A. 0
B. 1
C. 2
D. 3
To find the solution to the inequality, we can first simplify the expression on the right side of the inequality sign.
z(10-z) = 10z - z^2
Now we have the inequality 6 > 10z - z^2. Rearranging it, we get:
z^2 - 10z + 6 < 0
To solve this quadratic inequality, we can factor it:
(z - 6)(z - 1) < 0
To find the solution, we can create a sign chart:
< >
-------------------
| |
| |
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-∞ 1 6 ∞
From the sign chart, we can see that the expression is negative between 1 and 6.
So, the solution to the inequality is a number less than 1 or greater than 6. Therefore, none of the given options (A. 0, B. 1, C. 2, D. 3) is a solution.
6 is > 0
so 0 works
since
z(10-z) = 10z - z^2
is zero if z = 0
You are correct. I apologize for the mistake in my previous response.
If z = 0, then the expression becomes:
0(10-0) = 0
which is less than 6.
Therefore, z = 0 is a solution to the inequality 6 > z(10-z).
So the correct answer is option A. 0.