🧮 algebra

1. **State the problem:** Solve the equation $$y^2 = 9y$$ for $y$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. Énoncé du problème : Résoudre l'équation $$y^2 = 9y$$. 2. Formule et règles importantes : Pour résoudre une équation quadratique, on peut la mettre sous forme factorisée. Ici, o

1. **State the problem:** Solve the equation $$c = \left( x \sqrt{3} \right)^{\frac{1}{3}} = \left(1 - \sqrt{2 - 5x} \right)^{\frac{1}{2}}$$ for $x$.

1. **State the problem:** Solve and verify the equality $$(x\sqrt{3})^2 = (-\sqrt{1.5} x)^2$$ and simplify both sides. 2. **Recall the formula:** The square of a product is the pro

1. **State the problem:** Find the inverse function $f^{-1}(x)$ for the function $f(x) = 2x^2 + 4$. 2. **Understand the function:** The function $f(x) = 2x^2 + 4$ is a parabola ope

1. The problem is to find the inverse function $f^{-1}(x)$ of the function $f(x) = e^{3x + 5}$. 2. To find the inverse, we start by setting $y = f(x)$, so:

1. **Énoncé du problème :** Associer chaque équation à ses solutions en $y$.

1. **State the problem:** Simplify the expression $\log_8 27 + \frac{\log_2 5}{\log_4 9} - \log_{\frac{1}{4}} 25$. 2. **Recall the change of base formula:**

1. Énoncé du problème : Associer chaque équation à sa solution correcte. 2. Première équation : $10x + 1 = 8x$

1. **Problema 283:** Da un rettangolo viene ritagliato un quadrato. Trova il valore di $a$ per cui il semiperimetro del rettangolo supera di 5 il perimetro del quadrato. 2. **Dati:

1. **State the problem:** Solve the quadratic equation $$-3x^2 + 8x - 7 = 0$$ using the quadratic formula. 2. **Quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solu

1. **Stating the problem:** We need to solve the equation or expression given by the user. Since no specific problem was provided, let's consider a simple example: solve for $x$ in

1. O problema pede para resolver as outras expressões ou equações, mas como não foi especificado, vou assumir que você quer que eu continue com um exemplo comum de álgebra. 2. Vamo

1. We are asked to solve the quadratic equation using the product-sum method: $$x^2 - x - 90 = 0$$

1. **Stel het probleem vast:** We moeten de vergelijking $x^2 + 3x - 10 = 0$ oplossen met de product-som methode. 2. **Formule en regels:** De product-som methode zoekt twee getall

1. Stating the problem: We need to simplify the expression $\sqrt{45} \times \sqrt{20}$.\n\n2. Use the property of square roots: $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$.\n\n

1. Das Problem: Löse die Gleichung $2x + 3 = 7$. 2. Formel: Um $x$ zu isolieren, subtrahiere 3 von beiden Seiten: $$2x + 3 - 3 = 7 - 3$$

1. Problemet är att lösa ekvationen $3x - 7 = 11$. 2. Vi använder formeln för att lösa linjära ekvationer: $ax + b = c \Rightarrow x = \frac{c - b}{a}$.

1. **Problem statement:** We are given the system of equations: $$y = 3x + 2$$

1. **State the problem:** Solve the equation $x^2 - 5x + 6 = 0$. 2. **Recall the formula:** For a quadratic equation $ax^2 + bx + c = 0$, the solutions are given by the quadratic f

1. **State the problem:** Find the coordinates of the points of intersection of the line $x - y = 1$ and the circle $x^2 + y^2 = 13$. 2. **Rewrite the line equation:** From $x - y