🧮 algebra

1. **Nyatakan masalah:** (a) Permudahkan ekspresi $\frac{8\sqrt{h} + 5\sqrt{k}}{\sqrt{h} - \sqrt{k}}$.

1. **Problem 22:** Given a rectangle with length $x + 4$ and width $x - 2$, we need to: a) Write the expression for the perimeter.

1. Тодорхойлолт: f(x) функц нь хоёр хэсэгтэй өгөгдсөн: $$f(x) = \begin{cases} x+1, & \text{хэрэв } x \leq -1 \\ x^2, & \text{хэрэв } x > -1 \end{cases}$$

1. The problem asks to identify which equations represent inverse variation. Inverse variation means $y$ varies inversely as $x$, so $y = \frac{k}{x^n}$ for some $n > 0$.

1. **State the problem:** Simplify the expression $\frac{1}{3} U_n + 1 - U_n + 3$. 2. **Rewrite the expression:** Combine like terms involving $U_n$ and constants separately:

1. **State the problem:** Simplify the expression $$\frac{1}{3} (U_n + 1) - U_n + 3$$. 2. **Write the expression clearly:** $$\frac{1}{3} (U_n + 1) - U_n + 3$$.

1. **State the problem:** Find the slope of the line passing through the points $(2,3)$ and $(5,9)$. 2. **Formula:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_

1. **State the problem:** Simplify the expression $$\frac{\frac{1}{3}U_n + 1}{U_n + 3}$$ where $U_n$ is a variable or sequence term. 2. **Write the expression clearly:**

1. **Problem Statement:** We have two lines intersecting at point $(0, 2)$ dividing the plane into 4 sections. We want to determine which section is shaded based on the given point

1. The problem is to analyze the system of inequalities: $$y \geq 4x + 2$$

1. **State the problem:** Simplify the expression $$\frac{\frac{1}{3}U_n + 1}{U_n + 3}$$ where $U_n$ is a variable. 2. **Rewrite the numerator:** The numerator is $$\frac{1}{3}U_n

1. **State the problem:** Find the equation of the line parallel to the given line and passing through the given point for each part (a to h). 2. **Formula and rules:**

1. **Stating the problem:** We need to solve the fraction and ratio calculations given: - Calculate $\frac{13}{2} \times \frac{5}{3}$

1. (a) Subtract the fractions $\frac{3}{4} - \frac{1}{7}$. Step 1: Find a common denominator, which is $28$.

1. The problem is to simplify and evaluate $$(\sqrt{2} - 4\sqrt{3})^2$$. 2. We use the formula for the square of a binomial: $$(a - b)^2 = a^2 - 2ab + b^2$$.

1. **State the problem:** We are given three points $P(-1, n-1)$, $Q(n, n-3)$, and $R(n-6, 3)$, and we need to find the value of $n$ such that these points are collinear. 2. **Form

1. The problem is to solve the given information, but no specific equation or expression was provided. 2. To solve an algebraic problem, we need a clear equation or expression to w

1. **Problem Statement:** Find the equation of the straight line passing through each pair of points using the formula $y = mx + c$ where $m$ is the slope and $c$ is the y-intercep

1. La oss løse et enkelt algebraisk problem: Finn løsningen for ligningen $$2x + 3 = 7$$. 2. Formelen vi bruker er å isolere variabelen $x$. Det gjør vi ved å først trekke fra 3 på

1. **State the problem:** Find the equation of the line passing through points (-5, 3) and (2, 4). 2. **Formula:** The slope (gradient) $m$ of a line through points $(x_1, y_1)$ an

1. The problem is to solve a linear equation using the formula $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. 2. The formula $y = mx + c$ represents a straight li