Answer:
<h2>The Possible range for x is : ]8 , 18[</h2>
Step-by-step explanation:
To can draw this triangle if:
4x - (2x - 6) < 42 < 4x + (2x - 6)
solve inequality 1 :
4x - (2x - 6) < 42 ⇔ 2x + 6 < 42 ⇔ 2x < 36 ⇔ x < 18 (1)
Solve inequality 2 :
42 < 4x + (2x - 6) ⇔ 42 < 6x - 6 ⇔ 48 < 6x ⇔ 8 < x (2)
from (1) and (2) we deduce that : 8 < x < 18
F(x) = x^2/2 + 2x + 1f(x) = 1/2 * (x^2 + 4x) + 1f(x) = 1/2 * (x^2 + 4x + 4) - 1/2 * (4) + 1f(x) = 1/2 * (x + 2)^2 - 1
The vertex is (-2, -1). The axis of symmetry is x = -2. The minimum value is -1. The maximum value is infinity.
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