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Home » Even though there are four roots? Let's double-check factorization. - Dyverse

Even though there are four roots? Let's double-check factorization. - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Take the square root:

📌 When each side is increased by 2 cm, the new side length is:

📌 A' = \frac{\sqrt{3}}{4} (14)^2 = \frac{\sqrt{3}}{4} \times 196 = 49\sqrt{3}

📌 \Delta A = A' - A = 49\sqrt{3} - 36\sqrt{3} = 13\sqrt{3}

📌 \boxed{13\sqrt{3} \text{ square centimeters}}

📌 A right triangle has a hypotenuse of length \( z = 10 \) cm and an inscribed circle with radius \( c = 2 \) cm. What is the ratio of the area of the circle to the area of the triangle?

📌 A_{\text{circle}} = \pi c^2 = \pi (2)^2 = 4\pi

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\[ 7.845 + 2y = 16 \]
\[ 2y = 8.155 \]
\[ y = rac{8.155}{2} pprox 4.0775 \]
The solution is \( x pprox 2.615 \), \( y pprox 4.0775 \).
#### (2.615, 4.0775)
A companyâs profit \( P \) is given by \( P(x) = -5x^2 + 150x - 1000...
The vertex \( x \)-coordinate is \( x = -rac{b}{2a} = -rac{150}{-10}...
To maximize profit, 15 units should be sold.
The roots of the equation \( x^2 - 6x + 9 = 0 \) are:
Factor as \( (x - 3)^2 = 0 \).

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