In order to determine which number is a solution of the inequality, we need to solve the inequality and see which numbers satisfy it.
Starting with the inequality: 6 > z(10-z)
Expanding the expression on the right side: 6 > 10z - z^2
Rearranging the terms: z^2 - 10z + 6 < 0
To solve this quadratic inequality, we can find the roots of the equation: z^2 - 10z + 6 = 0
Using factoring or the quadratic formula, the roots of the equation are approximately 0.386 and 9.614.
Now, we need to determine the sign of the quadratic expression for different values of z.
For z < 0.386, the quadratic expression is positive, so it does not satisfy the inequality.
For 0.386 < z < 9.614, the quadratic expression is negative, so it satisfies the inequality.
For z > 9.614, the quadratic expression is positive, so it does not satisfy the inequality.
Therefore, the solution to the inequality 6 > z(10-z) is 0.386 < z < 9.614.
Which number is a solution of the inequality?
6 > z(10-z)
1 answer