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Home » ‘Open Mouth’ Secrets Revealed—Ex periodo of Transformation You Can’t Ignore! - DNSFLEX

‘Open Mouth’ Secrets Revealed—Ex periodo of Transformation You Can’t Ignore! - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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Using Vieta's formulas:
Sum of roots \( = -rac{b}{a} = 3 + (-2) = 1 \).
Product of roots \( = rac{c}{a} = 3 imes (-2) = -6 \).
Therefore, \( b = -1 \) and \( c = -6 \).
The expression is \( b^2 - 4ac = (-1)^2 - 4(1)(-6) = 1 + 24 = 25 \).
\( S_{n-1} = 3(n-1)^2 + 5(n-1) = 3(n^2 - 2n + 1) + 5n - 5 = 3n^2 - 6n...
\( a_n = S_n - S_{n-1} = (3n^2 + 5n) - (3n^2 - n - 2) = 6n + 2 \)
The 10th term is \( a_{10} = 6(10) + 2 = 60 + 2 = 62 \).
A circle is inscribed in a right triangle with legs of 8 and 15. Find...
The hypotenuse \( c = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289}...

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Thus, the area decreases by $ \boxed{20\sqrt{3}} $.
Question: A triangle has side lengths 13 cm, 14 cm, and 15 cm. Find th...
Use Heron’s formula to compute the area. Semi-perimeter $ s $:
Area $ A $:
= \sqrt{21 \cdot 8 \cdot 42} = \sqrt{7056} = 84 \text{ cm}^2
The shortest altitude corresponds to the longest side, which is 15 cm....
= \frac{1}{2} \cdot 15 \cdot h \Rightarrow 168 = 15h \Rightarrow h = \...
Thus, the shortest altitude is $ \boxed{11.2} $.Question: Find the vec...
Solution: Let $\mathbf{v} = \langle v_1, v_2, v_3 \rangle$. Compute $\...
\mathbf{v} \times \mathbf{b} = \begin{vmatrix}

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