🧮 algebra

1. **Stating the problem:** We are given a pattern of equations: $1 + 4 = 5$

1. **Stating the problem:** We are given the equation $0 = 5k_n$ and need to find the value of $k_n$. 2. **Formula and rules:** The equation is a simple linear equation. To solve f

1. **State the problem:** Simplify the expression $$\frac{x^{2} - 16}{x^{2} - 8x + 16} - \frac{x^{2}}{x^{2} + 4x} = \lambda$$ and express it in simplest form. 2. **Factor all polyn

1. **State the problem:** Solve the system of linear equations: $$3kx - 4y = 2$$

1. The problem is to understand the expression "it is not d/a b/c or q/b?" and clarify its meaning. 2. This looks like a question about fractions or ratios, possibly comparing or c

1. مسئله: حل معادله $$|2x+3| = -1$$. 2. قانون مهم: مقدار قدر مطلق $$|a|$$ همیشه بزرگتر یا مساوی صفر است، یعنی $$|a| \geq 0$$ برای هر عدد حقیقی $$a$$.

1. The problem is to analyze the ellipse given by the equation $$\frac{(x+5)^2}{100} + \frac{(y-5)^2}{49} = 1.$$\n\n2. This is the standard form of an ellipse centered at $(-5, 5)$

1. **State the problem:** We are given the ellipse equation $$\frac{(x + 11)^2}{25} + \frac{(y - 2)^2}{9} = 1$$ and need to analyze its properties.

1. The problem is to find the domain and range of a function. 2. The domain of a function is the set of all possible input values (x-values) for which the function is defined.

1. **State the problem:** We need to simplify and understand the function given as $Y = \frac{1}{1 + \sqrt{x}}$. 2. **Formula and rules:** The function involves a square root in th

1. **Stating the problem:** Create a word problem involving a linear equation in one variable relevant to student life. 2. **Example problem:** "A student saves 50 units of money e

1. **State the problem:** We need to find $Z^6$ where $Z=\frac{4i}{1 - i\sqrt{3}}$. 2. **Simplify the denominator:** Multiply numerator and denominator by the conjugate of the deno

1. The problem is to evaluate the expression $\frac{n \times n + n}{n}$ when $n = 10$. 2. The expression can be written as $\frac{n^2 + n}{n}$.

1. The original expression is $\frac{n \times n + n}{n}$. 2. The term $n \times n$ is the multiplication of $n$ by itself, which is defined as $n^2$.

1. The problem is to evaluate the expression $\frac{n \times n + n}{n}$ when $n=10$. 2. The expression can be written as $\frac{n^2 + n}{n}$.

1. **State the problem:** We need to find $Z^6$ where $Z=\frac{4i}{1 - i\sqrt{3}}$. 2. **Simplify the denominator:** Multiply numerator and denominator by the conjugate of the deno

1. The problem asks how the expression $\frac{2}{x}+1$ came about in the composition of functions. 2. Given functions $f(x)$ and $g(x)$, the composition $(f \circ g)(x) = f(g(x))$

1. **Problem Statement:** Given $$L= \frac{xy + zx - x^2}{(\log_g k)}, \quad M= \frac{yz + xy - y^2}{(\log_g k)}, \quad N= \frac{zx + yz - z^2}{(\log_g k)}$$ and the condition $$L

1. Problem: Determine which ordered pairs belong to the given relations. **a)** Relation $R = \{(x, y) \mid y < x\}$

1. Stating the problem: Solve the equation $$\frac{n \times n + n}{n} = 10$$ for $n$. 2. Write the expression clearly: $$\frac{n^2 + n}{n} = 10$$.

1. **State the problem:** We need to translate the equation "square root of (x + 4) + square root of (x + 2) = 6" into a mathematical equation and then solve for $x$. 2. **Write th