🧮 algebra

1. Das Problem lautet: Löse die quadratische Gleichung $$0 = v_2' \cdot (-6 + 2v_2')$$ nach $$v_2'$$ mit der Mitternachtsformel (quadratische Lösungsformel). 2. Die Gleichung kann

1. **State the problem:** We need to expand and simplify the expression $ (3x - 2\sqrt{7})(x + \sqrt{7}) $.

1. **Problem 6: Simplify $4 + \frac{3}{7}$** We need to add a whole number and a fraction.

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. Let's start by stating the problem: you want to solve for an unknown variable in an equation. 2. The general approach to solving for a variable is to isolate it on one side of t

1. **Stating the problem:** Simplify the expression $$\left(\frac{2b}{5c}\right)^2$$. 2. **Formula used:** When raising a fraction to a power, apply the exponent to both numerator

1. The problem is to solve the equation or expression exactly without rounding between steps. 2. To solve algebraic problems without rounding, we keep all numbers in fractional or

1. **Problem:** Factorise and solve the quadratic equation $2x^2 + 11x + 12 = 0$. 2. **Formula and rules:** To solve quadratic equations by factorisation, we look for two numbers t

1. **State the problem:** Simplify the expression $$2(6-2)2 \div 2 - 7$$. 2. **Apply the order of operations (PEMDAS/BODMAS):** Parentheses, Exponents, Multiplication and Division

1. The problem is to simplify the expression: $$4x^2 - 6mn - 18mn^2$$ and verify the factorization $$-6mn(2 + 6n)$$. 2. First, observe the terms: $$4x^2$$, $$-6mn$$, and $$-18mn^2$

1. **Stating the problem:** Expand and simplify the expression $2x(x + 4) + x(2x + 7)$. 2. **Using the distributive law:** Multiply each term inside the parentheses by the term out

1. Simplify each fraction: a) $\frac{x}{x} = 1$ (assuming $x \neq 0$)

1. **State the problem:** Simplify the expression $$-3 \times \frac{3}{5} \cdot \left( 2 \times \frac{5}{6} - 1 \times \frac{5}{12} \right)$$. 2. **Recall the rules:** Multiplicati

1. The problem is to verify if the given equations are correct by filling in the blanks and checking the arithmetic. 2. The general formula for subtraction is $a - b = c$, where $a

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} 2x + 9 & \text{for } x < -3 \\ 2x - 2 & \text{for } x > 4 \end{cases}$$

1. The problem asks to complete the table and graph the pairs of values given in the matrix: $$\begin{matrix}6 & 2 \\ 3 & 4 \\ 6 & 6\end{matrix}$$

1. **State the problem:** A student runs 2 minutes for every 10 minutes she walks. We need to complete the table of running and walking times and find how long she would walk if sh

1. The problem asks for the domain of the difference function $f - g$. 2. The domain of $f - g$ is the intersection of the domains of $f$ and $g$.

1. **State the problem:** Find the difference function $(f - g)(x)$ where $f(x) = 4x + \sqrt{7} - x$ and $g(x) = x^2 - x + 1$.

1. **State the problem:** We need to find the equation that models the proportional relationship between the number of pancakes ($x$) and the amount of flour in cups ($y$). 2. **Un

1. **State the problem:** We need to find which company, Talk-n-Text or Country Connect, charges a lower rate per minute and by how much. 2. **Identify the rates:** For Talk-n-Text