🧮 algebra

1. **State the problem:** Solve the quadratic equation $$2x^2 - 20x = x^2 - 19$$ by completing the square. 2. **Rewrite the equation:** Move all terms to one side:

1. **State the problem:** Evaluate $16^{-1.5}$ without using a calculator. 2. **Recall the formula and rules:** For any positive number $a$ and real number $m$, $a^{-m} = \frac{1}{

1. Das Problem lautet: Finde die Gleichung der Geraden, die senkrecht zur Geraden $3x - 4y = 5$ ist und durch den Punkt $(-2, 1)$ verläuft. 2. Die allgemeine Form der Geradengleich

1. **Problem:** Simplify $\sqrt{2}(\sqrt{3}-\sqrt{2})^2$. 2. **Formula and rules:** Use the binomial expansion $(a-b)^2 = a^2 - 2ab + b^2$ and simplify radicals.

1. **State the problem:** We are given a table of input-output pairs for a linear function and need to find the output when the input is $n$. 2. **Given table:**

1. **State the problem:** We are given a table of input-output pairs for a linear function and need to find the output when the input is $n$. 2. **Identify the pattern:** The input

1. **State the problem:** We have a table of ordered pairs for a linear function with inputs 1, 2, 3, 4 and corresponding outputs 9, 13, 17, 21. We need to find the output when the

1. **Stating the problem:** Simplify and solve the first equation: $3x + 3 - 2x + 7 = $ ? 2. **Combine like terms:** Group the $x$ terms and constants separately.

1. **State the problem:** Find the real root of the cube root of 559, i.e., find $\sqrt[3]{559}$ rounded to the nearest thousandth. 2. **Formula and explanation:** The cube root of

1. **State the problem:** Solve the equation $$24x^2 - 2x^4 = 0$$ for $x$. 2. **Rewrite the equation:** Factor out the common term.

1. **State the problem:** We are given the function $$y=\frac{-2x^3}{x^2-4}$$ and want to analyze it. 2. **Identify the domain:** The denominator cannot be zero, so solve $$x^2-4=0

1. Solve for $x$: $$2x + 5 = 17$$ 2. Factorize the quadratic expression: $$x^2 - 5x + 6$$

1. **Problem:** Löse die Klammern mithilfe des Distributivgesetzes auf. 2. **Formel:** Das Distributivgesetz lautet $$a(b+c) = ab + ac$$. Es besagt, dass man jeden Term innerhalb d

1. **Énoncé du problème :** Résoudre l'équation $x^2 = (3x-2)^2$ dans $\mathbb{R}$. 2. **Formule et règles importantes :** Pour résoudre une équation de la forme $A^2 = B^2$, on ut

1. **State the problem:** We need to write the equation of a circle in standard form given its center and radius. 2. **Recall the standard form of a circle's equation:**

1. **State the problem:** We have a piecewise function defined as $$f(x) = \begin{cases} 3x + 1 & \text{if } x < -2 \\ x - 3 & \text{if } x \geq -2 \end{cases}$$

1. **Problem Statement:** Hank’s Ice Cream Shop sells single-scoop cones for 2.00 each and double-scoop cones for 2.50 each. He sold 230 cones total and made 498 in sales. We want

1. **State the problem:** Solve the system of linear equations: $$5 \cdot 26 = 2x + 5y$$

1. Stating the problems: Solve the systems of linear equations: (1) \(10x - 5y = 20\) and \(-4x + 4y = -4\)

1. **State the problem:** Solve the system of linear equations: $$4x + 3y = 15$$

1. **State the problem:** Solve the system of linear equations: $$-3x + 5y = 7$$