🧮 algebra

1. The problem is to simplify the expression \( \frac{4}{\sqrt{5} - \sqrt{2} - \sqrt{6}} \).\n\n2. First, identify the denominator: \( \sqrt{5} - \sqrt{2} - \sqrt{6} \). The goal i

1. The problem asks to simplify the expression $$\frac{\frac{y}{\sqrt{5}} - \sqrt{2} - \sqrt{6}}{\sqrt{5} - \sqrt{2} - \sqrt{6}}$$ and express it clearly. 2. First, rewrite the num

1. The problem states a cyclist travels 20 km at an average speed of $x$ km/h. 2. (a) The time taken for this journey is distance divided by speed, which is $$\frac{20}{x}$$ hours.

1. Énonçons le problème : Simplifier l'expression $$\frac{y}{\sqrt{y^{2}-16}} - \frac{x}{\sqrt{x^{2}-16}}$$ et comparer avec $$\frac{2y}{\sqrt{y^{2}-16}} - \frac{2x}{\sqrt{x^{2}-16

1. **Problem a:** Write the scientific form of 0.006237 and find the characteristic of its logarithm. - First, write 0.006237 in scientific notation. Move the decimal 3 places righ

1. Stating the problem: Solve the system:

1. The problem states two functions. First, \( f(x) = \sqrt{x+1} - 1 \) with its inverse \( g(x) = x+1 \). 2. The domain of \( f \) is \( x \geq -1 \) because the expression under

1. State the problem: Simplify the expression $$-\frac{7}{4} + \frac{7}{16} \times \frac{1}{8} \times 384 \times \frac{3}{28}$$. 2. First, calculate the product part $$\frac{7}{16}

1. Stating the problem: Simplify the expression $$\frac{3}{2} - \frac{153}{4} \times 4 \left(4 - \frac{503}{126}\right)$$ and give the answer as an integer or simplified fraction.

1. Énonçons le problème : Trouver l'opposé de $a$ dans la fraction $\frac{16}{9}$.\n\n2. Rappelons que l'opposé d'un nombre $a$ est $-a$.\n\n3. Ici, la fraction $\frac{16}{9}$ repr

1. समस्या: दो व्यक्ति चाय बेचते हैं। पहला व्यक्ति सालाना 150 क्विंटल चाय 60 रुपए प्रति क्विंटल बेचता है। दूसरा व्यक्ति 100 क्विंटल चाय 300 रुपए प्रति क्विंटल बेचता है। हमें दूसरा व

1. We are given the equation $x^2 \sqrt{x} = 3$. 2. Recall that $\sqrt{x} = x^{1/2}$.

1. The problem is to solve the equation $$x^2 \sqrt{x} = 3$$ for $x$. 2. Rewrite the square root using fractional exponents: $$\sqrt{x} = x^{1/2}$$.

1. نبدأ بتحديد المطلوب: مثال على مصفوفة حجم 3×3 يعني مصفوفة تحتوي على 3 صفوف و3 أعمدة. 2. يمكن تمثيل المصفوفة على الشكل التالي:

1. نبدأ بتعريف مصفوفة بسيطة كمثال. لنأخذ المصفوفة $$A = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}$$. 2. لإيجاد القيم الذاتية لمصفوفة $$A$$، نستخدم المعادلة $$\det(A - \lambda I)

1. Problem: Multiply each pair of binomials/trinomials. (a) Multiply \((3x - 2y)(4x + 3y)\)

1. First, write down the expression: $$108 - [72 - 6 \times 10 + \frac{100}{4} - 5] + [4 - 3 \times 4 - \frac{12}{2} + 14]$$ 2. Simplify inside the first bracket:

1. Énoncé du problème : Résoudre l'expression $$45-[4\times8-23+6\times4]+[(3\times10\div25)-25]$$. 2. Calculer les opérations à l'intérieur des crochets et parenthèses en respecta

1. Statement of the problems. (a) Simplify the expression $ (x + y')(x + z) $ using the laws of Boolean algebra.

1. Start by stating the problem: Simplify the expression $2x + 3y - 5x + 4y + 2y - 3x$. 2. Group like terms together: Combine the terms with $x$ and the terms with $y$ separately.

1. **State the problem:** Solve the equation $$\frac{2x}{x^2 - 4} + \frac{x}{x+3} = \frac{2}{3}$$ for $x$. 2. **Factor denominators and find a common denominator:** Note that $x^2