🧮 algebra

1. The problem asks to calculate the arithmetic sequence term $u(n)$ given the term number $n-1$. 2. The general formula for the $n$-th term of an arithmetic sequence is:

1. **Problem:** You want to know how to do a quadratic equation. 2. A quadratic equation is usually written as $$ax^2+bx+c=0$$ where $a\neq 0$.

1. **State the problem:** Simplify the fraction $\frac{18}{24}$ to its lowest terms. 2. **Formula and rules:** To simplify a fraction, divide the numerator and denominator by their

1. **Problem:** Approximate $\sqrt{66}$ without a calculator and justify with inequalities. 2. **Problem:** Approximate $\sqrt{46}$ without a calculator and justify with inequaliti

1. **State the problem:** Simplify the expression $$(\sqrt{2} - 1)^2 - (\sqrt{2} + 3)(\sqrt{2} + 2).$$ 2. **Recall formulas and rules:**

1. **State the problem:** Simplify the expression $$\frac{5}{\sqrt{x}+3}$$ and relate it to the expression $2x^3$ given. 2. **Recall the formula and rules:** To simplify a fraction

1. **State the problem:** Factor the trinomial $$x^2 + 5x + 6$$. 2. **Recall the factoring formula:** For a trinomial of the form $$x^2 + bx + c$$, we look for two numbers that mul

1. **Problem:** Find the rate of change (slope) and y-intercept of the line given by the equation $5x - 15y = -10$. 2. **Rewrite the equation in slope-intercept form $y = mx + b$:*

1. **State the problem:** We are given the population of Africa in 2016 as 1.22 billion and in 2022 as 1,407,909,104. We need to:

1. Plantegem el problema: Resoldre el sistema d'equacions lineals $$\begin{cases} 2(x - 1) + y = 5 \\ 3x - (y + 2) = 4 \end{cases}$$

1. Plantegem el problema: Resolem els sistemes d'equacions lineals donats utilitzant el mètode d'aïllar una variable i substituir. 2. Sistema 5:

1. Problem: Schreibe mit einer Wurzel und berechne die folgenden Ausdrücke. 2. Wurzelgesetze:

1. **Plantejament del problema:** Resolem els sistemes d'equacions donats utilitzant el mètode d'igualació. 2. **Mètode d'igualació:** Consisteix a aïllar la mateixa variable en am

1. **Stating the problem:** Solve the systems of equations by isolating one variable without generating fractions. 2. **System 1:**

1. **Stating the problem:** Solve the system of equations: $$\begin{cases} x + y = 7 \\ x - y = 1 \end{cases}$$

1. Plantegem el problema: Tenim el sistema d'equacions $$\begin{cases} y = 2x + 1 \\ y = 3x - 1 \end{cases}$$

1. The problem is to find the value of $m$ given two graphs with lines and points. 2. From the description, the first graph shows a diagonal line passing through a point near the l

1. **State the problem:** Solve the system of inequalities by graphing: $$y < -2$$

1. Das Problem besteht darin, den Scheitelpunkt der quadratischen Funktion $f(x) = (x + 7)^2 + 3$ zu bestimmen. 2. Die allgemeine Form einer Parabel in Scheitelpunktform ist $$f(x)

1. **Problemstellung:** Wir sollen die Schnittpunkte der Funktion $f(x) = x^2 - 8x + 7$ mit der x-Achse berechnen. Diese Schnittpunkte nennt man auch Nullstellen. 2. **Formel:** Di

1. Gegeben ist eine Parabel mit Scheitelpunkt S(0|0) und einem Punkt P(10|2) auf der Parabel. 2. Die allgemeine Form einer Parabel mit Scheitelpunkt im Ursprung ist $$f(x) = a x^2$