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Home » Substitute into the first equation: \(2x + 3(4x - 5) = 6\). - AMAZONAWS

Substitute into the first equation: \(2x + 3(4x - 5) = 6\). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Un triangle a des côtés dans le rapport 3:4:5. Si le périmètre du triangle est de 60 unités, trouver la longueur du côté le plus long.

📌 Soit les côtés \( 3x, 4x, \) et \( 5x \).

📌 Le périmètre est :

📌 \[ 12x = 60 \]

📌 Le côté le plus long est :

📌 \[ 5x = 5 \times 5 = 25 \]

📌 Un cercle a un rayon qui est 3 unités plus long que le côté d'un carré inscrit. Si le diamètre du cercle est de 10 unités, trouver l'aire du carré.

📌 Le diamètre du cercle est de 10 unités, donc le rayon est :

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Simplify \( \frac{3 + 2i}{4 - i} \) and express in rectangular form.
Multiply numerator and denominator by conjugate \( 4 + i \):
Numerator: \( (3 + 2i)(4 + i) = 12 + 3i + 8i + 2i^2 = 12 + 11i - 2 = 1...
Denominator: \( (4 - i)(4 + i) = 16 + 1 = 17 \)
Result: \( \frac{10 + 11i}{17} = \frac{10}{17} + \frac{11}{17}i \)
#### \( \frac{10}{17} + \frac{11}{17}i \)
A rectangular prism has a volume of 108 cubic meters. Its length is tw...
Let height \( h \), then length \( l = 2h \), width \( w = h + 3 \).
Volume: \( lwh = 2h \cdot (h+3) \cdot h = 2h^2(h+3) = 2h^3 + 6h^2 = 10...
Divide by 2: \( h^3 + 3h^2 - 54 = 0 \)

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