🧮 algebra

1. Vi har en lineær funktion $f$ med værdier givet i tabellen: $$\begin{array}{c|c} x & f(x) \\ \hline 0 & -5 \\ 3 & 1 \\ 7 & 9 \end{array}$$

1. **State the problem:** We need to find the values of the function $g(x) = \sqrt{(y - 1)(y - 2)}$ at $x = 2$, $x = 0$, and $x = 4$. However, the function is given in terms of $y$

1. Das Problem lautet: Bitte erkläre die Lösung eines mathematischen Problems auf Deutsch. 2. Da keine spezifische Aufgabe gegeben ist, erkläre ich ein einfaches Beispiel: Lösen de

1. **Problem statement:** Factor the expression $$14 x^2 y^2 z^2 - 7 xyz + 21 x^3 y^3 z^3$$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in all terms.

1. The problem is to find when a quadratic expression becomes zero, which means solving for the roots of the quadratic equation. 2. A quadratic equation is generally written as $ax

1. **State the problem:** We are given a table of 8 ordered pairs $(x, y)$ and asked to find the average rate of change (AROC) between consecutive points and determine when it beco

1. We are given $x = 2\sqrt{3}$ and asked to find and rationalise the denominator for the expressions: a) $\frac{x+1}{x}$

1. **State the problem:** We need to find the value of the function $B(x) = 6x^2$ when $x = 1$. 2. **Formula used:** The function is given by

1. **State the problem:** Solve the simultaneous equations: $$x^2 + xy - 4y^2 = 2$$

1. Solve the equation $y(y - 2) = 18 + 5y$. 2. Start by expanding the left side:

1. **State the problem:** We have two rows of data representing ounces of Peanut Butter Ice Cream and Dark Chocolate Ice Cream. Some values are missing, and we need to find those m

1. **Problema 4a: Resolució del sistema lineal pel mètode de Gauss** Tenim el sistema:

1. **State the problem:** We are given that $y$ varies directly with $x$ and the constant of variation is $\frac{2}{3}$. We need to find the value of $x$ when $y=18$.

1. **State the problem:** Evaluate the expression $3 \times 10 + 8 - 4^2$. 2. **Recall the order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division fr

1. **State the problem:** Simplify the expression $3 \times 10 - 8 - 4^2$. 2. **Recall order of operations:** According to PEMDAS/BODMAS, calculate exponents first, then multiplica

1. **State the problem:** We have a rectangular pool where the length is three times the width. The perimeter of the pool is 32 metres. We need to find the length and width. 2. **D

1. **State the problem:** Simplify the expression $$\frac{10x - 5}{2x - 1} \times 10$$. 2. **Rewrite the expression:** The multiplication by 10 can be written as multiplication by

1. **State the problem:** Simplify the expression $(-5)^2 - 2 \times (-9) + 6$. 2. **Recall the rules:**

1. The problem is to determine the correct placement of the number 2 in an expression involving brackets. 2. When a number is outside the brackets, it usually means multiplication

1. **State the problem:** Simplify the expression $$\frac{6 - 18x}{2} \times \frac{5}{1 - 3x}$$. 2. **Rewrite the expression:**

1. **State the problem:** Solve the equation $6x - 2x = 32$ for $x$. 2. **Combine like terms:** Since both terms on the left side have $x$, subtract the coefficients: