🧮 algebra

1. **State the problem:** Simplify and analyze the quadratic expression $-x^{2} + 2x - \frac{3}{4}$. 2. **Recall the standard form:** A quadratic expression is generally written as

1. **State the problem:** We are given two points on a coordinate plane and need to find the equation of the line passing through these points. 2. **Identify the points:** From the

1. **Problem:** Find the gradient of the straight line joining points A (-4, -1) and B (4, 2). 2. **Formula:** The gradient $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$

1. **Problem statement:** Find the gradient of the straight line joining points A and B. 2. **Formula for gradient:** The gradient $m$ of a line joining points $A(x_1,y_1)$ and $B(

1. **State the problem:** Given two functions $f(x) = 5 - x$ and $g(x) = x^3$, find the composition $fg(x)$, which means $f(g(x))$. 2. **Recall the composition formula:** The compo

1. **State the problem:** Simplify the expression $\frac{(3x+1)(x-4)}{3x^2 - 11x - 4}$. 2. **Write down the expression:**

1. نبدأ بكتابة المساواة التي نريد التحقق منها. 2. نستخدم القواعد الجبرية للتحقق من صحة المساواة، مثل التبسيط، التوزيع، أو جمع الحدود المتشابهة.

1. State the problem. Problem: Solve for $x$ in the equation $\frac{x^2 - 4}{x - 2} = 5$.

1. **State the problem:** We need to graph the parabola given by the equation $$y = x^2 - 2x + 3$$ and plot five points: the vertex, two points to the left of the vertex, and two p

1. **Stating the problem:** You asked for a question and its answer. 2. **Question:** Solve for $x$ in the equation $$2x + 3 = 7$$.

1. **Problem:** Find the points of intersection between the curve $$2x^2 - y + 19 = 0$$ and the line $$y + 11x = 4$$. 2. **Step 1: Express one variable from the line equation.**

1. **Problem:** Find the points of intersection of the curve $2x^2 - y + 19 = 0$ and the line $y + 11x = 4$. 2. **Step 1: Express $y$ from the line equation.**

1. **State the problem:** We have a crew where 12 men make up 60% of the total crew. We need to find the total number of people in the crew. 2. **Formula and explanation:** Let the

1. The problem is to solve the equation involving two special operators \(\oplus\) and \(\boxplus\) and an unknown \(\square\): $$5 \oplus 1 \boxplus \square = 3$$

1. **State the problem:** We need to sketch the graph of the function $$y=\frac{x^2}{x^2-4}$$. 2. **Identify the domain:** The denominator cannot be zero, so solve $$x^2-4=0$$ whic

1. **State the problem:** Simplify the expression $\frac{9}{4} - 1$. 2. **Recall the rule:** To subtract a whole number from a fraction, convert the whole number to a fraction with

1. **State the problem:** Simplify the expression $\frac{9}{4} - \frac{3}{4} \times \frac{10}{3} \div \frac{5}{2}$. 2. **Recall the order of operations:** Multiplication and divisi

1. **State the problem:** Solve the equation $|x - a| + |x + a| = 4$ for $a$ given a fixed $x$. 2. **Recall the definition of absolute value:**

1. **State the problem:** Solve the equation $|x - a| + |x + a| = 4$ for $x$. 2. **Recall the definition of absolute value:**

1. **Énoncé du problème :** Montrer que les vecteurs $a = (1, -2, 0)$, $b = (-1, 2, -3)$ et $e = (-2, 2, -1)$ forment une base de $\mathbb{R}^3$.

1. **Problem statement:** Factorise each of the following expressions completely. 2. **Recall the factoring rule:** To factorise an expression, find the greatest common factor (GCF