🧮 algebra

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

1. **State the problem:** Solve the system of equations: $$3x - 6y = 15$$

1. مسئله را بیان می‌کنیم: باید مقدار عبارت $$-\left| - \sqrt{\sqrt{6} - 4} \right|$$ را محاسبه کنیم. 2. ابتدا به یاد داشته باشیم که قدر مطلق هر عددی همیشه غیرمنفی است، یعنی:

1. **Problem statement:** A number is increased by 20% and then decreased by 20%. We need to find the net increase or decrease percent. 2. **Formula and rules:**

1. **State the problem:** Rationalise the denominator of the fraction $$\frac{1}{5 + \sqrt{3}}$$ and simplify the result. 2. **Formula and rule:** To rationalise a denominator with

1. **State the problem:** Rationalise the denominator of $$\frac{3\sqrt{5}}{\sqrt{6}}$$ and simplify the expression. 2. **Formula and rule:** To rationalise a denominator containin

1. **State the problem:** Rationalise the denominator of $\frac{\sqrt{7}}{\sqrt{3}}$ and simplify the expression. 2. **Formula and rule:** To rationalise a denominator containing a

1. **State the problem:** Rationalise the denominator of the fraction $$\frac{11}{\sqrt{5}}$$ and simplify the result. 2. **Formula and rule:** To rationalise a denominator contain

1. The problem is to rationalise the denominator of the expression $\frac{1}{\sqrt{7}}$ and express the answer in its simplest form. 2. To rationalise the denominator means to elim

1. **State the problem:** Expand and fully simplify the expression $$(7 + \sqrt{3})(1 + \sqrt{3})$$. 2. **Formula used:** Use the distributive property (FOIL method) for multiplyin