🧮 algebra

1. **Problem:** Find the Least Common Multiple (LCM) or KPK of 8, 12, and 18. 2. **Formula and rules:**

1. **Problem:** Find the Cartesian equation for the parametric curve given by $$x = \frac{t}{t - 1}, \quad y = \frac{t - 2}{t + 1}, \quad -1 < t < 1.$$\n\n2. **Goal:** Eliminate th

1. **State the problem:** Simplify the expression $15x + 5x$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part the same.

1. **State the problem:** Simplify the expression $2x + 3x$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part the same.

1. **State the problem:** Solve the system of linear equations: $$6x - 11y = -83.8$$

1. **State the problem:** Solve the equation $$\frac{1}{\tanh(x)} - \frac{0.5}{\tanh(x)} - \frac{0.95}{x} = 0$$ for $x$. 2. **Combine like terms:** Since the first two terms have t

1. **State the problem:** We want to find a common denominator for the expression $$\frac{2x}{6x+6} + \frac{x-8}{12x-12}$$. 2. **Factor each denominator:**

1. **State the problem:** Find the permissible values of $x$ for the expression $$\frac{2x}{6x+6} + \frac{x-8}{12x-12}.$$\n\n2. **Identify restrictions:** The denominators cannot b

1. The problem asks to find the equation of a line in the form $y = mx + c$ given two points on the line. 2. The general form is $y = mx + c$, where $m$ is the slope and $c$ is the

1. **State the problem:** Find the equation of the line passing through the points $(-3,0)$ and $(0,2)$ in slope-intercept form $y=mx+b$. 2. **Formula:** The slope $m$ of a line th

1. **بيان المسألة:** لدينا مجموعتان I و J معطاة بمجالات وشروط مختلفة، ونريد إيجاد تقاطع المجموعتين $I \cap J$ واتحادهما $I \cup J$.

1. **Problem Statement:** We need to find a polynomial function that matches the given graph. 2. **Observations:** The graph has roots approximately at $x = -6$, $x = 0$, and $x =

1. The problem is to understand what complex numbers are and their basic properties. 2. A complex number is a number that can be expressed in the form $a + bi$, where $a$ and $b$ a

1. **State the problem:** We have a straight line drawn on a centimeter grid. Tina assumes the scale is 1 cm = 1 unit and wants to find the gradient of the line. 2. **Formula for g

1. **Problem statement:** We have a straight line graph showing the cost (£) against units used. The line passes through points (0,0) and (100,10).

1. The problem is to graph the linear function $y = -6 + x$. 2. This is a linear equation in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. The problem is to understand and simplify surds. 2. A surd is an expression containing a root, such as a square root, that cannot be simplified to remove the root.

1. The problem is to graph the system of equations and find their solution: $$y = -6 + x$$

1. **State the problem:** Solve the equation $3^x = x$ for $x$. 2. **Understand the problem:** We want to find the value(s) of $x$ such that the exponential function $3^x$ equals t

1. **State the problem:** Simplify the expression $2x\sqrt{2}$. 2. **Recall the rules:** The square root of 2, $\sqrt{2}$, is an irrational number approximately equal to 1.414. Whe

1. مسئله: اگر \(\left( -\infty, 2 - \frac{m-1}{3} \right) \cap [m-3, +\infty)\) مجموعه‌ای تک‌عضوی باشد، مقدار \(m\) را بیابید. 2. ابتدا تعریف کنیم: دو بازه \(\left( -\infty, 2 - \f