🧮 algebra

1. **State the problem:** We are given the function $$y = (x^2 + x^{-2})^2$$ and want to understand its shape and properties. 2. **Rewrite the function:** Expand the square using t

1. **State the problem:** We are given the function $$y = (x^2 + x^{-2})^2$$ and want to understand its behavior and graph. 2. **Recall the formula and rules:** The function involv

1. The problem states: "The product of b and 155, added to 359 is equal to 397." We need to write this as an equation. 2. "The product of b and 155" means multiply b by 155, which

1. The problem asks us to write a quadratic equation in the form $ax^2 + bx + c = 0$ with roots 6 and 7. 2. Recall that if a quadratic equation has roots $r_1$ and $r_2$, it can be

1. **State the problem:** We need to write a quadratic equation in the form $ax^2 + bx + c = 0$ whose roots are 6 and 7. 2. **Recall the formula:** If a quadratic equation has root

1. **Problem:** Solve the quadratic equation $x^2 + 6x - 10 = 0$ using the completing the square method. 2. **Formula and rules:** To complete the square for $x^2 + bx + c = 0$, re

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