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Which number is a solution of the inequality?

6 greater than z left-parenthesis 10 minus z right-parenthesis
A. 0
B. 1
C. 2
D. 3

I'm super confused on this question. Awarding Brainiest for Answer and Step By Step Explanation. Thanks!

Respuesta :

mhanifa

Answer:

  • A. 0

Step-by-step explanation:

Given inequality:

  • 6 > z(10 - z)

Solution:

  • 6 > 10z - z²
  • z² - 10z + 6 > 0
  • z² - 10z + 25 > 19
  • (z - 5)² > 19
  • z - 5 > √19 ⇒ z > 5 + √19 ⇒ z > 9.35
  • z - 5 < - √19 ⇒ z < 5 - √19 ⇒ z < 0.64

The only number satisfying this inequality is 0.

Correct choice is A

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