🧮 algebra

1. **Problem statement:** Given the line equation $2y - x = 10$, find: i. The coordinates of the point where the line intersects the y-axis.

1. The problem is to understand methods for factorizing quadratic expressions. 2. A quadratic expression is generally written as $ax^2 + bx + c$ where $a$, $b$, and $c$ are constan

1. **State the problem:** Simplify the expression $$\frac{a^{\frac{1}{2}} \cdot a^{\frac{1}{3}}}{a^{\frac{1}{4}}}$$ and write the answer using only positive exponents, assuming all

1. **State the problem:** We are given the function $f(x) = \frac{1}{2}x + \frac{1}{2}$ and a set of points on the coordinate plane. We want to understand the function and verify t

1. **State the problem:** Simplify the expression $$\frac{b^{-\frac{1}{4}} \cdot b^{\frac{5}{4}}}{b^{-\frac{1}{3}}}$$ and write the answer using only positive exponents, assuming a

1. **State the problem:** Simplify the expression $$b^{\frac{1}{3}} b^{\frac{1}{2}} b^{-\frac{2}{7}}$$ and write the answer using only positive exponents, assuming all variables ar

1. نبدأ بحل السؤال الأول: انشر \((\sqrt{x} - \sqrt{y})^2\). نستخدم صيغة الفرق المربع: \((a - b)^2 = a^2 - 2ab + b^2\).

1. **Énoncé du problème :** Nous avons le système linéaire (S) :

1. **Problem Statement:** We want to find the smallest perimeter of a rectangle given that its area is 12 cm². 2. **Define variables:** Let $x$ be the length of one side of the rec

1. **State the problem:** We are given two functions $f(x) = x^2 - 7$ and $g(x) = x^2 + 3$. We need to find the value of $(f - g)(-5)$. 2. **Recall the definition of $(f - g)(x)$:*

1. **State the problem:** We are given the function $F(x) = x^2 - 7$ and want to understand its properties. 2. **Formula and rules:** This is a quadratic function of the form $ax^2

1. **State the problem:** We want to understand why $\frac{4}{5}$ is greater than $\frac{6}{10}$. 2. **Recall the rule for comparing fractions:** To compare two fractions, we can e

1. **State the problem:** Factor the expression $$\frac{123X}{756} + 125X244$$ by grouping like terms. 2. **Rewrite the expression:** The expression is $$\frac{123X}{756} + 125X244

1. **State the problem:** Hannah and Fatu shared a 50kg sack of rice in the ratio 14:11. We need to find how much rice Hannah got. 2. **Understand the ratio:** The ratio 14:11 mean

1. **Stating the problem:** We need to factorize the given algebraic expression by grouping like terms. 2. **Understanding factorization by grouping:** This method involves groupin

1. **State the problem:** The population of a school increased from 400 to 1000. We need to find the percentage increase in the population. 2. **Formula used:** The percentage incr

1. **Stating the problem:** Solve the inequality $7x^2 + 21x - 28 < 0$. 2. **Formula and rules:** This is a quadratic inequality of the form $ax^2 + bx + c < 0$. To solve it, we fi

1. El problema es resolver la inecuación cuadrática general: $$ax^2 + bx + c > 0$$ o $$ax^2 + bx + c < 0$$. 2. Primero, identificamos los coeficientes y la forma de la inecuación.

1. Planteamos el problema: Resolver la inecuación cuadrática $$4.7x^2 + 21x - 28 < 0$$. 2. Recordemos que para resolver inecuaciones cuadráticas, primero encontramos las raíces de

1. **State the problem:** We are given two linear equations: $$y = 3x + 3$$

1. The problem asks us to fill in the missing numbers in the equivalent expressions using the distributive property for the expression $5 \times \square = 5 \times (5 + 1)$. 2. The