🧮 algebra

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

1. **State the problem:** Find the value of $b$ such that the line passing through points $(0,b)$ and $(2,0)$ is collinear with the line given by the equation $$x - 2y + 1 = 0.$$ 2

1. You asked to solve an unspecified problem by showing all formulas involved. 2. Since you did not provide a specific problem, I will demonstrate the process of solving a quadrati

1. Let's start with a simple algebra problem: Solve for $x$ in the equation $2x + 3 = 7$. 2. To isolate $x$, subtract 3 from both sides: $$2x + 3 - 3 = 7 - 3$$ which simplifies to

1. Stating the problem: We are given the system of equations: $$X + \sqrt{Y} = 11$$

1. **Stating the problem:** Determine which among the sets A, B, or C have points that lie on the same straight line. 2. **Approach:** Points are collinear if the slope between any