🧮 algebra

1. **State the problem:** Simplify the expression $a^2 + b^2 - (a - b^2)$. 2. **Recall the rule:** When subtracting a parenthesis, distribute the minus sign to each term inside: $-

1. **State the problem:** We are given two points A(7.83, 5541.37) and B(7.86, 6464.80) and need to find the equation of the line passing through these points in slope-intercept fo

1. مسئله را بیان می‌کنیم: سوال این است که عبارت $a^2 + b^2 - (a - b)^2$ را ساده کنیم.

1. **Énoncé du problème :** Résoudre le système linéaire suivant par la méthode de l'inverse de matrice : $$\begin{cases} 2x + y - z = 2 \\ x - y + z = 7 \\ x + 2y - z = -1 \end{ca

1. مسئله را بیان می‌کنیم: عبارت $a^2 + b^2 - (a - b)^2$ را ساده کنیم. 2. فرمول مورد استفاده: برای مربع تفاضل داریم:

1. **State the problem:** Find the equation of the blue line passing through points $(1,6)$ and $(3,10)$.\n\n2. **Formula used:** The equation of a line in slope-intercept form is

1. The problem is to graph the points A(7.83, 5541.37) and B(7.86, 6464.80) and verify the slope of the line given by the equation $y = 30781x - 246556.6$. 2. The slope formula bet

1. **State the problem:** Find the equation of the blue line passing through points (1,6) and (2,10). 2. **Formula used:** The equation of a line in slope-intercept form is $$y = m

1. **State the problem:** We need to find the equation of the blue line passing through points approximately (1, 2) and (2, 6). 2. **Formula used:** The equation of a line in slope

1. Énoncé du problème : Soient $x$ et $y$ deux réels tels que $|2 - 3x| < 2$ et $1 < \sqrt{2y + 1} < 3$.

1. Énoncé du problème : Soient $x$ et $y$ deux réels tels que $|2-3x|<2$ et $1<\sqrt{2}y+1<3$. Montrer que $0<x<\frac{4}{3}$ et $0<y<4$. Encadrer $x+y$, $xy$, $x-y$ et $y^2$.

1. **State the problem:** We are given two points: Point A $(7.83, 5541.37)$ and Point B $(7.86, 6464.80)$. We want to find the equation of the line passing through these points fi

1. **Stating the problem:** We need to find the equation of a line first using the point-slope form and then convert it to slope-intercept form. 2. **Point-slope form formula:** Th

1. **State the problem:** Find the equation of the line passing through points A(7.83, 5541.37) and B(7.86, 6464.80) using the slope-intercept form. 2. **Formula used:** The slope-

1. مسئله: استفاده از روش فیبونیوس و معادله مفسر برای حل یک مسئله ریاضی. 2. روش فیبونیوس: دنباله فیبونیوس به صورت زیر تعریف می‌شود:

1. The problem asks for the y-intercept of the polynomial function $$f(x)=(1-x)(x-2)(x+6)(x-10)$$. 2. The y-intercept of a function is the point where the graph crosses the y-axis.

1. The problem is to understand and calculate exponents of integers. 2. The general formula for exponents is $a^n$, where $a$ is the base (an integer) and $n$ is the exponent (a po

1. **Problem statement:** Given the polynomial function $f(x) = 2x^3 - 3x^2 - 16x + 24$, we want to find intervals where the function has at least one real zero. 2. **Key idea:** B

1. **Problem Statement:** We are given a graph described by the equation $$y = \frac{1}{2} \text{agar} + x^2$$ and asked to draw the straight line on this graph and determine its i

1. **State the problem:** Write the equation of the line in slope-intercept form $y = mt + b$ with slope $m = \frac{a-5}{4}$ passing through the point $(5,0)$.

1. **Stating the problem:** Given the equation $$x - \frac{1}{x} = \sqrt{x} + \frac{1}{\sqrt{x}}$$ and the expression $$x^2 + x^{-2}$$, we want to find the value of $$x^2 + x^{-2}$