🧮 algebra

1. The problem asks for the slope of the line passing through the points (1,0) and (2,4). 2. The formula for slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

1. **State the problem:** Find the highest common factor (HCF) of 156 and 260. 2. **Formula and method:** The HCF of two numbers is the largest number that divides both without lea

1. **Énoncé du problème :** Développer et simplifier l'expression $$A = (\sqrt{2} + 1)(\sqrt{2} - 1) - 1$$.

1. **Énoncé du problème :** Développer et simplifier l'expression $$A = (x^2 + 1)(x^2 - 1) - 1$$.

1. **State the problem:** Simplify the algebraic expression $3x - 9 - 6x + 12 + 4x$. 2. **Combine like terms:** Group the terms with $x$ and the constant terms separately.

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Divide the polynomial $x^4 - 2x^3 - 4x + 5$ by $3x^3 + 2$. 2. **Set up the division:** We want to find the quotient $Q(x)$ and remainder $R(x)$ such that:

1. **Stating the problem:** We are given a diamond-shaped grid with numbers in squares and triangles, and a central square subdivided into four triangles with numbers 12, 13, 3, an

1. The problem asks to express the decimal number $3.81$ as a mixed number. 2. A mixed number consists of a whole number and a proper fraction.

1. **Problem 1: Check if ordered pairs satisfy the equation $3x - y = 5$.** The equation is $3x - y = 5$.

1. Énoncé du problème : Soit $(a_n)$ une suite arithmétique de raison $r$ telle que $a_4 + a_5 = 11$ et $a_5 + a_6 = 17$. 2. Rappel de la formule d'une suite arithmétique :

1. **Problem:** Calculate the astronaut's mass after a five-week mission given weekly weight changes. 2. **Formula and rules:** To find the final mass, add or subtract the weekly c

1. The problem is to simplify the expression: $\frac{\text{nompor}}{2}$. 2. Since "nompor" is not a recognized mathematical term or number, we cannot simplify this expression furth

1. Stating the problem: Simplify the expression $9\sqrt{x}2 + 6\sqrt{x}2$. 2. Understand the terms: Here, $\sqrt{x}2$ means $2\sqrt{x}$ (the constant 2 multiplied by the square roo

1. **State the problem:** Calculate the sales tax on an item costing $3$ with a sales tax rate of $4.4\%$. 2. **Formula:** Sales tax is calculated as

1. The problem is to simplify the expression "szar". 2. Since "szar" is not a mathematical expression or equation, there is no algebraic or arithmetic operation to perform.

1. **State the problem:** Solve the system of equations using Cramer's rule: $$\begin{cases} 2x - 3y + z = 17 \\ x + 3y - 2z = -13 \\ x - y - z = 0 \end{cases}$$

1. **State the problem:** We are given two zeroes $\alpha$ and $\beta$ of a quadratic polynomial such that $\alpha + \beta = 24$ and $\alpha - \beta = 8$. We need to find the quadr

1. Stating the problem: We are given a polynomial with zeroes \(\alpha\) and \(\beta\). We need to find the relationship or values involving these zeroes. 2. Important formulas: Fo

1. The problem is to complete the table for linear equations in two variables by converting from standard form to slope-intercept form, finding the slope, x-intercept, and y-interc

1. **Problem statement:** Hitanshi invests money at an annual compound interest rate of $x\%$. After 11 years, the investment doubles in value. We need to find $x$. 2. **Formula us