🧮 algebra

1. **State the problem:** Calculate 15,000 multiplied by 2.5%. 2. **Formula and rules:** To find a percentage of a number, convert the percentage to a decimal by dividing by 100, t

1. **State the problem:** Calculate 15000 multiplied by 5%. 2. **Formula:** To find a percentage of a number, use the formula $$\text{Percentage value} = \text{Total} \times \frac{

1. The problem is to calculate the value of $\frac{297,973}{890,960} \times 100$. 2. The formula used here is to find the percentage of one number relative to another: $$\text{Perc

1. **State the problem:** Solve the equation $2x + 3x = 15$ by collecting like terms and isolating the variable. 2. **Formula and rules:** When adding terms with the same variable,

1. The problem asks to find 1% of 109,153. 2. The formula to find a percentage of a number is: $$\text{Percentage value} = \frac{\text{percentage}}{100} \times \text{total number}$

1. **State the problem:** We need to find a number based on place value clues: - 1 ten thousand

1. **Problem statement:** Solve the system of equations: $$x^2 - y^2 = \frac{15\sqrt{x} - 17\sqrt{y}}{4\sqrt{xy}}$$

1. Du hast mich gebeten, nur die Scheitelpunkte jeder Aufgabe anzugeben. 2. Der Scheitelpunkt einer Parabel in der Form $y = ax^2 + bx + c$ wird mit der Formel $\left(-\frac{b}{2a}

1. Das Problem verlangt nur die Scheitelpunkte einer Funktion. 2. Der Scheitelpunkt einer Parabel $y = ax^2 + bx + c$ wird mit der Formel $x = -\frac{b}{2a}$ berechnet.

1. Problem: Berechne die Schnittpunkte der Funktionen f(x) und g(x) für jede Aufgabe. 2. Allgemeine Methode: Schnittpunkte zweier Funktionen erhält man, indem man f(x) = g(x) setzt

1. **Problem statement:** Find the intersection points of the functions \(f(x) = -3x\) and \(g(x) = x^2\). 2. **Set the functions equal to find intersection points:**

1. The problem is to find the correct premium subscription price using the revenue function, which is linear. 2. The revenue function is given by $$R(p) = p \times q(p)$$ where $p$

1. **State the problem:** We are given a revenue function depending on the number of basic subscribers $c$ and premium subscribers $d$. We need to find the price of each subscripti

1. **Problema:** Factorice completamente $w^2 - 2w - 15$. 2. **Fórmula y reglas:** Para factorizar un trinomio cuadrado de la forma $ax^2 + bx + c$, buscamos dos números que multip

1. The problem asks which function represents the graph of $f(x) = e^x$ shifted 3 units horizontally to the right. 2. The rule for horizontal shifts is: shifting a function $f(x)$

1. The problem asks to identify the graph transformation of the function $g(x) = e^{x+1}$ from the graph of $f(x) = e^x$. 2. The general rule for horizontal shifts in functions is:

1. The problem is to sketch the graph of the function $h(x) = \log_2(x + 2)$ and state its domain, range, and asymptote. 2. The logarithmic function $\log_b(x)$ is defined only for

1. **State the problem:** Solve the equation $$\log_9(x - 5) + \log_9(x + 3) = 1$$ for $x$. 2. **Recall the logarithm property:** The sum of logarithms with the same base can be co

1. **State the problem:** Factorise the expression $$14y^2 + 14$$ completely. 2. **Identify the common factor:** Both terms have a common factor of 14.

1. **State the problem:** Factorise the expression $$11y^2 + 11$$ completely. 2. **Identify the common factor:** Both terms have a common factor of 11.

1. **State the problem:** Solve the linear equation $8x - 2y = 5$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we use basic algebraic operations: addition, su