🧮 algebra

1. **State the problem:** We need to find the value of $f(-2 - g(3))$ given the functions $f(x) = \frac{3}{4}x + 10$ and $g(x) = x^2 - 3$. 2. **Calculate $g(3)$:** Substitute $x=3$

1. **Énoncé du problème :** Soit la suite arithmétique $(U_n)_{n\geq 1}$ telle que $U_5 = -12$ et $U_{11} = -30$. On doit :

1. **State the problem:** Solve the equation $$\frac{n \times n + n}{n} = 10$$ for $n$. 2. **Rewrite the equation:** The numerator is $n \times n + n = n^2 + n$, so the equation be

1. مسئله: حل معادله $2x + 3 = 7$ را داریم. 2. فرمول و قوانین: برای حل معادله‌های خطی، هدف این است که $x$ را تنها کنیم. برای این کار ابتدا باید عدد ثابت را از طرف معادله جدا کنیم.

1. **State the problem:** We need to identify which graph correctly represents the system of linear equations: $$y = -x + 2$$

1. **Problem statement:** Expand the logarithmic expressions using the properties of logarithms. 2. **Recall the properties:**

1. **Problem:** Solve the equation $$\sqrt{2x + 1} - \sqrt{2x - 3} = x - 1$$. 2. **Formula and rules:** To solve equations involving square roots, isolate one root and then square

1. نبدأ بحساب العبارة $$F = (2x + 3)(3x - 1) - (2x + 3)^2$$. 2. نوزع الحدود في كل جزء:

1. **State the problem:** Given the system of equations: $$x^2 = 2025y + x$$

1. **State the problem:** Given the system of equations: $$x^2 = 2025x + y$$

1. The problem asks whether $\sqrt{9}$ is an irrational number. 2. Recall that an irrational number is a number that cannot be expressed as a fraction $\frac{a}{b}$ where $a$ and $

1. **State the problem:** We need to find which expression is equivalent to $\sqrt{63}$.\n\n2. **Recall the property of square roots:** For any positive numbers $a$ and $b$, $\sqrt

1. The problem asks to explain the meaning of variables in an exponential function, their correlation with geometric sequences, and the meaning of "constant". 2. An exponential fun

1. The problem is to find the sum of the series: 1 + 3 + 5 + 7 + ... + 69. 2. This is an arithmetic series where the first term $a_1 = 1$, the common difference $d = 2$, and the la

1. Planteamos el problema: Encontrar el conjunto de verdad $Ap(x)$ para el predicado $$p(x) : -2\sin^2\left(\frac{x}{2}\right) + 2\cos^2\left(\frac{x}{2}\right) - 1 = 0$$ en el int

1. The problem is to convert the decimal number 5.67 into a fraction. 2. To convert a decimal to a fraction, we use the fact that the decimal part represents a fraction with a powe

1. **State the problem:** Simplify the expression $7x + 3 - 4(2x - 5)$. 2. **Use the distributive property:** Multiply $-4$ by each term inside the parentheses:

1. **State the problem:** Find the distance between the points $(2, -4)$ and $(2, 3)$. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is giv

1. **State the problem:** Simplify the expression $$-4 - \left(- \left(\frac{2}{9} - \frac{2}{3}\right)\right) - 1 - \frac{5}{6} + \frac{1}{2}$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $19 + X = 29$ for $X$. 2. **Formula and rules:** To solve for $X$, isolate $X$ on one side of the equation by performing inverse operat

1. Planteamos el problema: Dada la ecuación $$6x = 10\sqrt{3}$$ y la expresión $$ (x^n) \log_x 3 = 3 \log_{\sqrt{3}} x + 2^1 + 4 \log_x x $$, debemos calcular el valor de $$n$$. 2.