🧮 algebra

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: $$-3x + 5y = 7$$

1. **Solve the system:** $$\begin{cases} 2x - 3y = 2 \\ 3x + 2y = 16 \end{cases}$$

1. **State the problem:** We are given a quadratic function modeling the height of a slide: $$f(x) = a(x - 5)^2$$ with initial height 2.5 m at $x=0$. We need to find the height of

1. **State the problem:** Solve the equation $ (x - 3)(x - 5) = 35 $ for $ x $.\n\n2. **Use the distributive property (FOIL) to expand the left side:**\n$$ (x - 3)(x - 5) = x^2 - 5

1. **State the problem:** We need to find which value of $x$ satisfies the equation $$(x - 3)(x - 5) = 35.$$\n\n2. **Use the formula:** The equation is a product of two binomials e

1. **State the problem:** Simplify the expression $$\left(\frac{2n^4}{3m^3n^7}\right)^2$$ and write the answer using only positive exponents. 2. **Recall the formula:** When raisin

1. **State the problem:** Simplify the expression $$\left(\frac{a^7 b^6}{a^2 b}\right)^4$$ and write the answer using only positive exponents. 2. **Apply the quotient rule for expo

1. **Planteamiento del problema:** Queremos encontrar las raíces de la función cuadrática $$y = -1(x+4)(x+3)$$ y verificar su forma expandida $$y = -x^2 - 7x - 12$$.

1. **State the problem:** Simplify the expression $\log(n^3)$. 2. **Recall the logarithm power rule:** For any positive number $a$ and real number $b$, $\log(a^b) = b \log(a)$.

1. **State the problem:** Find all x-intercepts of the function $$f(x) = \frac{x^2 - 16x + 64}{3x^2 - 24x}$$ and write them as coordinate points. 2. **Recall the formula and rules:

1. **State the problem:** Find all x-intercepts of the function $$f(x) = \frac{9x^2 - 64}{6x^2 + 16x}$$.\n\n2. **Recall the rule for x-intercepts:** The x-intercepts occur where th

1. **State the problem:** Find all x-intercepts of the function $$f(x) = \frac{5x^2 + 3x}{x^2 - 2x - 63}$$. The x-intercepts occur where the function equals zero, i.e., where the n