🧮 algebra

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

1. **State the problem:** We have three functions: A) $f(x) = \frac{x^2 - 1}{x}$

1. The problem asks to identify which pair of given functions is not a pair, i.e., which pair does not share a characteristic or relation. 2. Let's list the functions:

1. The problem asks which of the given equalities or inequalities about the function $$f(x)=\frac{2x}{x^2 + x} - \frac{2x}{x^2 - x}$$ is true.\n\n2. Calculate $$f(-x)$$ by substitu

1. The problem asks to find the image of the point $(1,1)$ under certain replacement rules labeled as (2,3). 2. Usually, replacement rules (2,3) in a context like this refer to tra

1. The problem describes a graph with piecewise linear functions labeled as $g$, $f(x)$, $a$, $b$, $c$ on a coordinate grid with $x$-axis from $-6$ to $10$ and $y$-axis from $-6$ t

1. **State the problem:** We want to find the value of $b$ using the condition $f(2) = 3$ for the function $$f(x) = \frac{x^2 + 2x + b}{x - 1}.$$\n\n2. **Use the given point:** Sub

1. The question asks about the "map of e forming rules," which seems to involve understanding the exponential function with base $e$, the natural exponential function. 2. The expon