🧮 algebra

1. The problem is to find the function $f(x) = \ln x^2$ and understand its properties. 2. Recall that $\ln x^2 = \ln \left(x^2\right)$.

1. Énoncé du problème : On doit déterminer la véracité des affirmations pour l'exercice 1 et choisir la bonne réponse pour chaque question de l'exercice 2 concernant des polynômes

1. **Stating the problem:** Solve the equation $$273x^8 - 17x^{12} = 256$$ for $x$. 2. **Rearrange the equation:** Move all terms to one side:

1. The problem is to understand and interpret the expression $273x^8$. 2. The expression $273x^8$ means that the variable $x$ is raised to the eighth power and then multiplied by 2

1. The problem states that the function $u(x_1, x_2) = 2 x_2$. 2. This means that the value of $u$ depends only on the variable $x_2$ and is twice its value.

1. The problem is to find and explain the x and y values for a function or equation. 2. The x-values typically represent the inputs or independent variable values.

1. The problem is to find the domain and range of the function $$F(x) = x^3 - 1$$. 2. The domain of a function is the set of all possible input values $x$ for which the function is

1. Calcule le discriminant du polynôme $3x^2 - x + 2$. Rappel: le discriminant est donné par $$\Delta = b^2 - 4ac$$ avec $a=3$, $b=-1$, $c=2$.

1. Stating the problem: Simplify the expression $14-18+16$. 2. First, perform the subtraction $14-18$, which equals $-4$.

1. Stated problem: Solve the equation $$\sqrt[4]{x-6} + \sqrt{x^2+36} = 0$$. 2. Analyze the terms: The fourth root $$\sqrt[4]{x-6}$$ is defined only if $$x-6 \geq 0$$, so $$x \geq

1. **State the problem:** Simplify the expression $$\sqrt[4]{x-6} + \sqrt{x^2+36}$$ and analyze its domain. 2. **Analyze each term:**

1. Given $\log_{10} 2 = m$ and $\log_{10} 3 = n$, evaluate $\log_{10} 24$. We use the property that $\log(ab) = \log a + \log b$.

1. Planteamos el problema: Calcular $$\sqrt[3]{\frac{8}{27}} \times \sqrt[3]{\frac{30}{50}} + \sqrt[3]{\frac{1}{81}} \times \sqrt[4]{\frac{3}{4}} \times \sqrt[5]{\frac{16}{5}}$$.

1. **State the problem:** We want to find how many nurdles are equivalent to 28 ferrules, given the conversion rates: - 1 aglet = 5 ferrules

1. The problem states Ella has R$3390 and wants to convert this amount into Mexican pesos using the conversion rate R$1 = Mex$5.61. 2. To find the amount in Mexican pesos, multiply

1. Stating the problem: Solve the equation $$4x^2y + 9y^2x = 36$$ for variables $x$ and $y$. 2. Factor the left side to find a common factor:

1. Let's start by defining the total profit as $12000$. 2. The businessman said he used $\frac{1}{3}$ of the profit. Calculate this part:

1. Stating the problem: Calculate the determinant of the matrix $$\begin{bmatrix}4 & 4 \\ 4 & -4\end{bmatrix}.$$\n\n2. Recall the formula for the determinant of a 2x2 matrix $$\beg

1. Izračunaj izraze u zadatku 21: 1) $ (ab^{2})^{3} \cdot (a^{2}b)^{3} = a^{3}b^{6} \cdot a^{6}b^{3} = a^{3+6} b^{6+3} = a^{9} b^{9}$

1. Problematika: Farmer ima tri različita prosta broja kao brojeve krava, konja i svinja. Označimo broj krava s $k$, broj konja s $h$, i broj svinja s $s$. 2. Prema zadatku, brojev

1. State the problem: A businessman made a profit of $12000$. He saved $\frac{1}{3}$ of this profit, used $\frac{3}{5}$ of the remainder for food, and used the rest to improve his