🧮 algebra

1. **Énoncé du problème :** Simplifier l'expression $\ln(3e)$.\n\n2. **Formule utilisée :** La propriété des logarithmes naturels est $\ln(ab) = \ln(a) + \ln(b)$.\n\n3. **Applicati

1. **Énoncé du problème :** Simplifier l'expression $\ln(3e)$. 2. **Formule utilisée :** Pour tout $a,b>0$, $\ln(ab) = \ln(a) + \ln(b)$.

1. **State the problem:** We want to find the population of Edinburgh after 4 years if the current population is 495000 and it increases at 1.8% per year. 2. **Formula used:** The

1. **State the problem:** We have a tree structure where expressions are added stepwise. On the right side, we want to find expressions $A$, $B$, and $C$ such that: - $A$ is added

1. Il problema è semplificare l'espressione data e verificare i passaggi algebrici. 2. La proprietà principale usata è la potenza di un prodotto: $$(xy)^n = x^n y^n$$ e la potenza

1. **State the problem:** Solve the inequality $$x(x+2) - 3(2x - 1) \leq 2^2$$. 2. **Rewrite the inequality:** Expand and simplify the left side.

1. **Problem statement:** We have points \(A, B, C\) with position vectors \(\overrightarrow{OA} = \begin{bmatrix} 2 \\ 2 \end{bmatrix}, \overrightarrow{OB} = \begin{bmatrix} 18 \\

1. **State the problem:** Check if the area calculated for $r=1.2$ inches is rounded to the hundredths place. 2. **Recall the value:** The area was calculated as $4.5216$.

1. **State the problem:** Simplify the rational expression $$\frac{x^2 - 7x - 18}{2x} \div (x - 9)$$. 2. **Rewrite the division as multiplication:** Dividing by a quantity is the s

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$ in a fraction equation, multiply both sides by the denominat

1. The problem is to find the range of a function, which means determining all possible output values (y-values) the function can produce. 2. To find the range, we often start by u

1. **State the problem:** We are given the linear function $f(x) = -\frac{4}{3}x - 1$ and asked to find its domain. 2. **Recall the domain of linear functions:** The domain of a li

1. **State the problem:** Solve the inequality $$x^2 - 3x > \frac{1}{2}x^2 - 4$$. 2. **Rewrite the inequality:** Move all terms to one side to compare with zero.

1. **State the problem:** We are given the function $f(x) = 5x + 6$ and asked to find the value of $x$ when $f(x) = 46$. 2. **Write the equation:** Set the function equal to 46:

1. Stating the problem: We need to find the value of $x$ such that $f(x) = 19$ for the function $f(x) = 2x + 3$. 2. Write the equation:

1. **State the problem:** Solve the equation $$\sqrt{5x - 1} + 4 = 11$$ for $x$. 2. **Isolate the square root term:** Subtract 4 from both sides to get $$\sqrt{5x - 1} = 11 - 4$$

1. **State the problem:** Solve the equation and check for extraneous solutions. 2. **General approach:** When solving equations, especially those involving radicals, fractions, or

1. Problema 605: Equazione $x^2 + 2kx - (1+k^2) = 0$. a. Radici antireciproche: il prodotto delle radici $p = -1$.

1. The problem is to solve the equation using a different method than previously used. 2. Let's assume the equation is $ax+b=0$ (since the user did not specify, we solve a general

1. **State the problem:** We are given the equation

1. The problem is to graph the line with slope 3 and y-intercept 2. 2. The formula for a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-inte