🧮 algebra

1. **Problem:** Der Preis eines T-Shirts wird im Ausverkauf um $\frac{1}{4}$ des ursprünglichen Preises herabgesetzt. Das T-Shirt kostet nach der Ermäßigung 24 €. Wie hoch war der

1. **State the problem:** We are given two summations involving terms $y_i$: $$\sum_{i=1}^{4p^2-p} y_i = 4p - 1 - x$$

1. **State the problem:** We are given the function $$h(x) = \frac{6x^2 - 23x + 20}{2x - 5}$$ and need to express it in the form $$ax + b$$ where $$a, b \in \mathbb{Z}$$.

1. The problem is to find the dimensions of a rectangle given that its perimeter is 56. 2. The formula for the perimeter $P$ of a rectangle with length $l$ and width $w$ is:

1. **State the problem:** We need to find the missing number $x$ in the equation: $$75 + 1000 + 275 = x(3 + 40 + 11)$$

1. The problem asks for the quotient of $\frac{1}{2}$ divided by $\frac{2}{5}$. We need to find $\frac{1}{2} \div \frac{2}{5}$.\n\n2. Recall the rule for dividing fractions: \n$$\f

1. O problema pede para resolver o exercício 6, mas como não foi fornecido o enunciado, vou assumir que você quer ajuda com um problema comum de álgebra. 2. Suponha que o exercício

1. **Énoncé du problème :** Calculer le pourcentage d'augmentation lorsque la surface des nénuphars passe de 200 m² à 240 m² (augmentation de 40 m²).

1. **State the problem:** Solve the equation $$\frac{5x + 2}{4} - \frac{x - 2}{3} = \frac{x - 5}{16}$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fract

1. The problem is to solve part b of the second question, but since the exact problem statement is missing, I will assume it involves solving or simplifying an algebraic expression

1. Het probleem is om de vergelijking $2 = \frac{12}{5} + b$ op te lossen voor $b$. 2. We willen $b$ isoleren aan één kant van de vergelijking. Dit doen we door $\frac{12}{5}$ van

1. **State the problem:** Solve the equation $2 = 12$. 2. **Analyze the equation:** The equation $2 = 12$ is a statement that claims two numbers are equal.

1. **State the problem:** We have a line given by the equation $y = ax + b$ where $a = 0.6$ and we need to find the value of $b$. 2. **Recall the formula:** The equation of a line

1. **Stating the problem:** We need to find the cost of 20 litres of a paint mixture where white and blue paints are mixed in the ratio 3:2. 2. **Understanding the ratio:** The rat

1. **State the problem:** We are given a rational function with a vertical asymptote at $x = -2$ and a horizontal asymptote at $y = 0$. We need to write the equations of the asympt

1. **State the problem:** Solve the system of equations by substitution and graphing: $$y = 3x - 1$$

1. **State the problem:** We need to perform the operations: From the sum of $3a^2 - ab - 2b^2$ and $2a^2 + 5ab - 3b^2$, subtract $a^2 - 3ab - 4b^2$.

1. **State the problem:** Simplify the expression $$\frac{x + 6}{x^2 + 3x - 18} + \frac{1}{x - 3} + \frac{5}{2x + 12}$$. 2. **Factor denominators where possible:**

1. **State the problem:** Simplify the expression $$\frac{x^2 + 10x + 21}{2x^2 + 10x + 8} \div \frac{5x^2 - 20x - 105}{3x^2 + 15x + 12}$$

1. **Problem statement:** We are given two true statements about visitor numbers at a swimming pool and asked to verify them mathematically.

1. **State the problem:** Simplify the expression $8:2(2+2)$. 2. **Apply the order of operations (PEMDAS/BODMAS):** Parentheses first. Calculate inside the parentheses: