🧮 algebra

1. **State the problem:** We are given two lines, l and k, and need to draw them on a coordinate diagram, find their intersection point R, and then find the area of triangle RST fo

1. **Problem statement:** (a)(i) Find the slope of the line $l$ passing through points $P(-3,6)$ and $Q(9,-2)$.

1. **Problema:** Calcolare il quadrato dei seguenti binomi algebrici: (2x^2 + 7y)^2, (x - 4y^2)^2, (3x^2 + 5xy)^2.

1. **Stating the problem:** Calculate the product of the binomials $$\left(\frac{3}{5} ab^{2} + 6\right)\left(\frac{3}{5} ab^{2} - 6\right)$$ using algebraic identities. 2. **Formu

1. **Problem statement:** Solve the equation $12x - 3 = 8x + 1$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable $x$ by performing the same ope

1. Il problema richiede di moltiplicare due prodotti notevoli: \(\left(\frac{3}{5} ab^{2} + 6\right)\left(\frac{3}{5} ab^{2} - 6\right)\) e \(\left(\frac{1}{4} x + \frac{3}{5} x^{2

1. **Stating the problem:** Simplify the expression $3a - 2b + a - 5b$. 2. **Formula and rules:** To simplify algebraic expressions, combine like terms. Like terms have the same va

1. **Problem statement:** Simplify each algebraic expression by combining like terms. 2. **Formula and rules:** Like terms have the same variable raised to the same power. To simpl

1. **State the problem:** We need to determine which number is larger: $$0.2^{2^{15}}$$ or $$0.05^{2^{10}}$$. 2. **Recall the properties of exponents:** For positive numbers less t

1. **Stating the problem:** Simplify the expression $$\left( \frac{a+b}{ab^2} - \frac{a-b}{a^2b} \right)^2 \cdot \frac{a^5b^6}{a^5b^2 - ab^6} - \frac{2ab}{a^2 - b^2}$$

1. **Stating the problem:** We are given the quadratic polynomial $$f(x) = 2x^2 - 4x - 5$$ and asked to check if $$x = 3$$ is a root (nulpunkt) of $$f(x)$$. 2. **Formula used:** To

1. **State the problem:** Simplify the expression $$\frac{5}{x^2 - 5x - 14} \div \frac{5x + 25}{x^2 - 2x - 35}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. **Problemstellung:** Wir sollen untersuchen, ob die Funktion $f$ einen direkt proportionalen Zusammenhang beschreibt anhand der Wertetabelle mit den Punkten $(4,9)$ und $(5,11)$

1. **Problemstellung:** Gegeben ist die Funktion $f$ mit den Werten $f(2)=4$ und $f(3)=6$. Es soll untersucht werden, ob $f$ einen direkt proportionalen Zusammenhang beschreibt. 2.

1. **State the problem:** Solve the equation $$\frac{2}{3}x - 2 - \frac{x}{6} + \frac{x}{2} = \frac{x+2}{3}$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to is

1. **State the problem:** Solve the equation $$\frac{2}{3}X - 2 - \frac{X}{6} + \frac{X}{2} = X + \frac{2}{3}$$ for $X$. 2. **Combine like terms on the left side:** The terms with

1. Problemet: Vi har en rektangulär gräsmatta med en sida som är 45 meter och en area på 2250 m^2. Vi ska hitta längden på staketet runt gräsmattan, alltså dess omkrets. 2. Formler

1. The problem asks us to evaluate the cube root of the expression $$64 \times 10^{12}$$. 2. The formula for the cube root of a product is $$\sqrt[3]{a \times b} = \sqrt[3]{a} \tim

1. **State the problem:** We are given the function $$f(x) = 2x + \frac{x}{x^{2} - 1}$$ and we want to understand its behavior or simplify it if possible. 2. **Recall the formula a

1. **State the problem:** Solve the system of equations using the substitution method: $$-x + 3y = -15$$

1. **State the problem:** We need to find the price of an adult's ticket and a child's ticket given two total fare amounts for different group sizes. 2. **Set variables:** Let $a$