🧮 algebra

1. **مشكلة:** تقاسم ثلاثة إخوة أرباح تجاراتهم \n- الأول أخذ \( \frac{1}{5} \) من الأرباح \n- الثاني أخذ \( \frac{3}{10} \) من الأرباح \n- الثالث أخذ \( \frac{1}{4} \) مما أخذ الأول

1. **Definición del logaritmo:** El logaritmo de un número $x$ en base $b$ se define como el exponente al que hay que elevar $b$ para obtener $x$. Esto se expresa como: $$\log_b x

1. State the problem: Express $$\frac{(\log m)^p \sqrt{3 - n}}{m n^2}$$

1. **State the problem:** Express $$\frac{\log m^p \sqrt{3-n}}{mn^2}$$ in terms of $$\log m$$, $$\log n$$, and $$\log p$$. 2. **Rewrite the numerator:**

1. Stating the problem: We are given the function $F(x) = x^2 - 6x + 5$ and need to analyze it. 2. Identify the type of function: This is a quadratic function in standard form $F(x

1. **State the problem:** Find the domain and range of the function $$y=\frac{\sqrt{x^2 - 5x + 6}}{\sqrt{x^2 - x + 6}}.$$\n\n2. **Domain analysis:** The domain consists of all $x$

1. The problem is to analyze the quadratic function $F(x) = x^2 - 6x + 5$. 2. First, find the vertex to understand the function's shape. The vertex formula for $x$ is given by $x =

1. **State the problem:** Express $$\frac{(\log m)^p \sqrt{3 - n}}{m n^2}$$ in terms of \(\log m\), \(\log n\), and \(\log p\). 2. **Analyze each part:**

1. Resuelve la ecuación $\log 2 + \log(11 - x^2) = 2 \log(5 - x)$ Usamos propiedades de los logaritmos: $\log a + \log b = \log(ab)$ y $n \log a = \log(a^n)$.

1. Énoncé du problème : Soit la suite $(s_n)$ définie par

1. We are given the quadratic function $F(x) = x^2 - 6x + 5$. 2. To analyze this function, let's find its vertex by completing the square.

1. Resolver la ecuación \(\log 2 + \log(11 - x^2) = 2 \log(5 - x)\) Usamos la propiedad de logaritmos \(\log a + \log b = \log(ab)\) y \(2 \log c = \log c^2\):

1. The problem is to solve the quadratic equation $$3x^2 - 4x + 9 = 0$$. 2. Use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$, where $$a=3$$, $$b=-4$$, and $$c=

1. Problem 14(a): Simplify $\sqrt{32} + \sqrt{98}$. - $\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$.

1. The first equation is given as $3. (3x - 1) + 1) (1 - 3x) = 0$. Likely, the intended expression is $(3x - 1 + 1)(1 - 3x) = 0$. Simplify inside the parentheses: $3x - 1 + 1 = 3x$

1. Stating the problem: Solve the quadratic equation $x^2 - 3x + 2 = 0$ using factorization. 2. To factorize, look for two numbers that multiply to the constant term $2$ and add up

1. The problem is to solve the system of linear equations $$\begin{cases} a_1 x + b_1 y = c_1 \\ a_2 x + b_2 y = c_2 \end{cases}$$

1. The problem is to solve the quadratic equation $$x^2 - 5x + 6 = 0.$$\n\n2. To solve this quadratic equation, we can factor it. We look for two numbers that multiply to $6$ and a

1. Stating the problem: We want to solve the inequality $$5^{\frac{x^2 - 3x}{2x - 4}} \leq 5.$$\n\n2. Since the base 5 is positive and greater than 1, the exponential function is i

1. The problem is to solve the equation $$\left| \frac{9 - x^2}{x - 1} \right| = \frac{x^2 - 9}{x - 1}$$. 2. Notice that $$x^2 - 9 = (x - 3)(x + 3)$$ and $$9 - x^2 = -(x^2 - 9) = -

1. সমস্যাটি হলো, আমরা অনুসন্ধান করবো কতগুলি পাথর বার করা হয়েছে, যেখানে নিচের শর্তগুলি দেওয়া আছে: ৮ ফল সামনে, ১ ০ ফল পূর্ণ হলে পাথর পারলে ৬ ফল আর \(x\) ফল বাদলে \(x+6\) ফল হবে। 2.