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Home » \[ \frac39210000 = 0.0392 \text liters \] - Groen Casting

\[ \frac39210000 = 0.0392 \text liters \] - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 #### 70.69

📌 A quadratic equation is given by \( 3x^2 - 12x + 9 = 0 \). Find the roots using the quadratic formula.

📌 Here, \( a = 3 \), \( b = -12 \), and \( c = 9 \).

📌 \[ b^2 - 4ac = (-12)^2 - 4 \times 3 \times 9 = 144 - 108 = 36 \]

📌 \[ x = \frac{12 \pm \sqrt{36}}{6} = \frac{12 \pm 6}{6} \]

📌 \[ x = 3 \quad \text{or} \quad x = 1 \]

📌 A piece of wire is 24 meters long and is bent to form a rectangle with a length twice its width. What are the dimensions of the rectangle?

📌 Let the width be \( w \) and the length \( 2w \).

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The area \(A\) of the triangle is:
A = \frac{1}{2} \times 9 \times 12 = 54 \text{ cm}^2
The semi-perimeter \(s\) of the triangle is:
s = \frac{9 + 12 + 15}{2} = 18 \text{ cm}
The radius \(r\) of the inscribed circle is given by:
r = \frac{A}{s} = \frac{54}{18} = 3 \text{ cm}
Thus, the radius of the inscribed circle is \(\boxed{3}\).
A circle is inscribed in a triangle with sides measuring 7 cm, 24 cm,...
First, verify that the triangle is a right triangle using the Pythagor...
25^2 = 7^2 + 24^2 \quad \Rightarrow \quad 625 = 49 + 576 \quad \Righta...

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