🧮 algebra

1. **State the problem:** Solve the system of linear equations using the Sarrus method (which applies to 3x3 determinants): $$\begin{cases} x - y + z = 1 \\ x + y = 4 \\ 2x + 2y +

1. **State the problem:** Find the slope of the line passing through the points $(-5, 0)$ and $(0, 2)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)

1. **State the problem:** Find the slope of the line passing through the points $(-3,-7)$ and $(3,7)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1,y_1)$

1. **Problemstellung:** Berechne den Wachstumsfaktor $q$ für verschiedene prozentuale Wachstumsraten $p\%$. Die Formel lautet: $$q = 1 + \frac{p}{100}$$

1. **State the problem:** Find the slope of the line passing through the points $(-4, -1)$ and $(4, 5)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1

1. **State the problem:** Find the slope of the line passing through the points $(3, 3)$ and $(4, 6)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$

1. **Stato il problema:** Risolvere il sistema lineare: $$\begin{cases} x - y + z = 1 \\ x + y = 4 \\ 2x + 2y + 2z = 9 \end{cases}$$

1. **State the problem:** Find the equation of the line passing through the points $(3, 3)$ and $(4, 6)$.\n\n2. **Formula used:** The slope $m$ of a line through points $(x_1, y_1)

1. **Problema:** Risolvere il sistema lineare: $$\begin{cases} x - y + z = 1 \\ x + y = 4 \\ 2x + 2y + 2z = 9 \end{cases}$$

1. **State the problem:** Find the slope of the line passing through the points $(-2, -2)$ and $(1, 4)$.\n\n2. **Formula for slope:** The slope $m$ of a line through points $(x_1,

1. **State the problem:** Find the slope of the line passing through points $(-3, -2)$ and $(5, 2)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)$ a

1. The problem asks for the slope of the line passing through the points $(-3,-8)$ and $(3,8)$. 2. The formula for the slope $m$ of a line through two points $(x_1,y_1)$ and $(x_2,

1. **State the problem:** Find the slope of the line passing through the points $(-5, -3)$ and $(5, 3)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1

1. The problem asks to write the decimal numbers as simplified common fractions. 2. For 11b) 0.135:

1. **State the problem:** Solve the equation $$16^x \times \left(\frac{1}{2}\right)^x = 4^{x+3}$$ for $x$. 2. **Rewrite the bases as powers of 2:**

1. **State the problem:** We are given the function $$y = \log_a (x + 3) + \log_a (2x - 1)$$ where $a, b, c, d$ are positive constants.

1. **State the problem:** (i) Given the function $$y = \log_a (x + 3) + \log_a (2x - 1)$$, explain why $$x > \frac{1}{2}$$.

1. **State the problem:** Multiply and simplify the expression $4 w^3 \cdot 3 x^4 w^3 \cdot 3 x$. 2. **Write the expression:**

1. **State the problem:** We are given the parametric form of a line $r$ and a system of two linear equations $s$. We want to analyze the relationship between the line and the syst

1. Das Problem: Du möchtest mehr Übungsaufgaben wie die vorherige erhalten. 2. Da keine konkrete Aufgabe angegeben wurde, hier ein Beispiel für eine typische Algebra-Übungsaufgabe:

1. **State the problem:** Factorise the expression $$16 - 25(b+3)^2$$. 2. **Identify the formula:** This expression is a difference of squares, which follows the formula $$a^2 - b^