🧮 algebra

1. **State the problem:** Find the equation of the line passing through points $(-7, 48)$ and $(4, -18)$ in the form $y = mx + b$. 2. **Find the slope $m$ using the formula:**

1. Das Problem lautet: Wir sollen eine einfache algebraische Gleichung lösen, geeignet für die 10. Klasse. 2. Wir verwenden die Grundregel der Algebra: Um eine Gleichung zu lösen,

1. **State the problem:** Find the equation of the line with slope $m = -\frac{5}{4}$ passing through the point $(-8, -6)$ in the form $y = mx + b$. 2. **Recall the slope-intercept

1. **State the problem:** Find the equation of the line passing through the point $(-1, -1)$ with slope $\frac{9}{2}$. 2. **Formula used:** The point-slope form of a line is given

1. **State the problem:** Solve for $t$ in the equation $$30 = 5 \times 1.2^t$$. 2. **Isolate the exponential term:** Divide both sides by 5 to get $$\frac{30}{5} = 1.2^t$$.

1. **State the problem:** We are given two equations:

1. The problem is to simplify the expression $4XaXa$. 2. We recognize that $X$ and $a$ are variables and the expression is a product of these variables with coefficients.

1. **State the problem:** Solve the linear equation $3x - 12 = -x + 44$ for $x$. 2. **Write down the equation:**

1. The problem is to simplify the expression $4xaxa$. 2. We recognize that $a$ and $x$ are variables and multiplication is associative and commutative.

1. **State the problem:** Reduce the fraction $\frac{4}{64}$ to its simplest form. 2. **Formula and rules:** To simplify a fraction, divide both numerator and denominator by their

1. **Énoncé du problème :** Simplifier les expressions algébriques données. 2. **Rappel des règles importantes :**

1. **State the problem:** We want to find an exponential function $w=f(t)$ that models the number of whooping cough cases $w$ over time $t$ years since 1980, given $w(1)=1248$ in 1

1. **State the problem:** Solve the system of linear equations: $$3x + y = -16$$

1. **State the problem:** Solve the equation $$3(x + 7) = -12$$ for $$x$$. 2. **Isolate the term inside the parentheses:** Divide both sides of the equation by 3 to get $$x + 7$$ a

1. **State the problem:** We need to divide the polynomial $$x^5 + 4x^3 - 11$$ by $$x - 1$$ using synthetic division and find the quotient and remainder. 2. **Recall synthetic divi

1. **State the problem:** Solve the equation $15x - 10 = 65$ for $x$. 2. **Add 10 to both sides:**

1. **State the problem:** We are asked to perform polynomial division for the first problem: divide $$x^3 - 3x + 11$$ by $$x + 4$$. 2. **Recall the formula:** Polynomial division i

1. **State the problem:** We are given a piecewise function $$T(x)$$ defined as: $$

1. **Problem statement:** We need to show that the surface area $O(a)$ of a box with a square base of side length $a$ and volume 300 ml (or 300 cm³) can be described by the functio

1. **State the problem:** Solve the system of linear equations using row operations and find the solutions. 2. **Initial matrix:**

1. The problem asks to translate the graph of $y = x^2$ to get the graph of $y = (x - 1)^2$. 2. The formula for horizontal translation of a function $y = f(x)$ is $y = f(x - h)$, w