🧮 algebra

1. The problem asks to rationalise the denominators of given expressions and simplify the answers where possible. 2. Rationalising the denominator means eliminating any square root

1. **State the problem:** We have a straight line graph showing volume $V$ in litres over time $t$ in seconds. We need to find the gradient of the graph, explain what the gradient

1. **Problem Statement:** Rationalise the denominators of the given expressions and simplify where possible. 2. **Formula and Rule:** To rationalise a denominator containing a squa

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. O problema pede para encontrar a fração irredutível $\frac{a}{b}$ que gera a dízima periódica $3,012012\ldots$ e depois calcular o valor de $a-b$. 2. A dízima periódica é um núm

1. **Problem 2: Find the area and perimeter of the rectangle with sides $\sqrt{45}$ cm and $\sqrt{80}$ cm.** 2. **Formula for area and perimeter of a rectangle:**

1. **State the problem:** Solve the system of linear equations: $$4x + 5y = 14$$

1. **State the problem:** Solve the linear equation $5x + 2y = 17$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by m

1. **State the problem:** We need to evaluate the expression $$n = \frac{1.65^2 \times 0.5 \times 0.5 \times 70}{70 \times 0.1^2 + 2.72^2 \times 0.3 \times 0.7}$$

1. Vamos resolver a equação $5x^2 - 45x = 0$. 2. Primeiro, observe que podemos fatorar o termo comum $5x$.

1. **Problem statement:** Simplify each expression by combining like surds and leaving answers in simplified surd form. 2. **Formula and rules:**

1. **Stating the problem:** We are given a cuboid with dimensions $5 - \sqrt{3}$ cm, $2 + \sqrt{3}$ cm, and an unknown side $x$ cm. The volume is $2$ m³. We need to find $x$ in sim

1. **Problem:** Rationalise the denominators of the given fractions and simplify where possible. 2. **Formula and rule:** To rationalise a denominator with a square root, multiply

1. **State the problem:** Nathalie bought shoes at a sale price of 54 after a 10% reduction from the original price. 2. **Formula used:** Sale price = Original price \times (1 - Di

1. **State the problem:** We need to find the percentage reduction when the price of a car decreases from 12500 to 11625. 2. **Formula for percentage change:**

1. El problema es graficar la función $$y = e^{2x} - x^2 + 1$$ y hallar el valor del vértice. 2. Para encontrar el vértice de una función, primero calculamos la derivada para encon

1. **Problem Statement:** Rationalise the denominators of the following expressions and simplify where possible. 2. **Formula and Rule:** To rationalise a denominator containing a

1. **Problema:** Dada la función cuadrática $$f(x) = x^2 - 2x + 1$$, hallar las asíntotas (si existen) y el valor del vértice. 2. **Fórmula y reglas importantes:**

1. El problema es calcular el producto de las fracciones $$\frac{11}{4} \times \frac{3}{5} \times \left(-1 \frac{1}{3}\right)$$. 2. Primero, convertimos el número mixto $$-1 \frac{

1. **State the problem:** Simplify the expression $\sqrt{50} + \sqrt{78}$. 2. **Recall the formula and rules:** The square root of a product can be expressed as the product of squa

1. **Problem statement:** Find the remainder when $f(x) = 3x^3 - 14x^2 - 47x - 14$ is divided by $(x - 3)$.