🧮 algebra

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

1. The problem is to convert a given equation into standard form. 2. Standard form for a linear equation is usually written as $$Ax + By = C$$ where $A$, $B$, and $C$ are integers,

1. **Problem Statement:** Find the roots and factored form of the function $f(x)$ given its roots and graph description. 2. **Roots of $f(x)$:** The roots are the values of $x$ whe

1. The problem involves analyzing the graph of the piecewise function $$f(x) = \begin{cases} -x + 1 & x < 0 \\ x - 2 & 0 \leq x \end{cases}$$ and identifying the error in the graph

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} -x + 1, & x < 0 \\ x - 2, & x \geq 0 \end{cases}$$

1. **State the problem:** Francis is hiking up Killington Hill. After 1 hour, his elevation is 100 feet, and after 5 hours, it is 360 feet. We need to find the slope of the line re

1. **Problem:** Given $3^s = \sqrt{3} \times 3\sqrt{7} \sqrt{9}$, find the value of $(13 + 24x)^4$. 2. **Step 1: Simplify the right side of the equation for $3^s$**

1. **State the problem:** Simplify the expression $$\frac{\sqrt[5]{\frac{1}{10000}} \times \sqrt[5]{-0.00032}}{\sqrt[4]{(-4)^4}}.$$ 2. **Recall the rules:**

1. The problem states that Francis is hiking up Killington Hill and we know two points on his elevation path: after 1 hour, elevation is 100 feet, and after 5 hours, elevation is 3

1. The problem asks to identify the order of transformations applied to the function $f(x) = x^2$ to get $f(-x + 4) + 3$. 2. The original function is $f(x) = x^2$.

1. **State the problem:** Solve the inequality $ (x-2)(x+1) \leq 3(x+1) $. 2. **Rewrite the inequality:** Expand the left side and keep the right side as is:

1. **State the problem:** Calculate the average rate of change of the function $f(x) = \sqrt{x} + 2$ over the interval $[2,7]$. 2. **Formula:** The average rate of change of a func

1. The problem states that we have a parabola passing through the points $(-2,9)$, $(-1,3)$, $(0,1)$, $(1,3)$, and $(2,9)$. We want to create a table of values for the function ref