🧮 algebra

1. **State the problem:** Solve the equation $$-5 + 2 \ln(3x) = 5$$ for $x$, rounding to the nearest hundredth. 2. **Isolate the logarithmic term:** Add 5 to both sides:

1. مسئله: محاسبه مقدار عبارت $ (x - y + y)(x + y - y) $ است. 2. ابتدا عبارت را ساده می‌کنیم. توجه کنید که در هر پرانتز، $-y + y = 0$ و $+ y - y = 0$ است.

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. The problem asks to describe the end behavior of the polynomial function $$f(x) = 5x - 2$$. 2. The end behavior of a polynomial function depends on the leading term. Here, the l

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, multiply both sides by the

1. **State the problem:** Simplify the expression $2x + 4 + (3x - 2)$. 2. **Recall the rule:** When simplifying expressions, remove parentheses and combine like terms.

1. **State the problem:** Solve for $x$ in the equation $$\log_5(x + 22) - \log_5(x - 2) = 2.$$\n\n2. **Recall the logarithm subtraction rule:** \n$$\log_b A - \log_b B = \log_b \l

1. **State the problem:** Solve the formula $$Q_1 = P (Q_2 - Q_1)$$ for the variable $$Q_2$$. 2. **Write down the formula:** $$Q_1 = P (Q_2 - Q_1)$$

1. **State the problem:** We are given the formula for volume $V$ as $$V = \frac{1}{2} L (B + b)$$ where $B = 0.2$ m², $b = 0.5$ m², and $V = 0.21$ m³. We need to find the length $

1. Il problema chiede di scomporre l'espressione $ (3x + 6) - 5(x^2 + 4x + 4)^2 $.\n\n2. Iniziamo osservando che $3x + 6$ può essere fattorizzato come $3(x + 2)$.\n\n3. Notiamo che

1. **State the problem:** Solve the inequality $x^2 + 1 < 0$. 2. **Recall the properties of squares:** For any real number $x$, $x^2 \geq 0$. This means $x^2$ is always non-negativ

1. Il problema chiede di scomporre l'espressione $5x^4y^3 + \frac{625}{8}x$. 2. Per scomporre un'espressione algebrica, cerchiamo un fattore comune tra i termini.

1. Let's start by stating the problem: We need to determine if $x = -1$ is the correct solution for the given equation or problem (which is not explicitly provided). 2. Since the o

1. **State the problem:** Solve the equation $5x + 9 = 2(x + 3)$. 2. **Expand the right side:** Use the distributive property $a(b+c) = ab + ac$ to get $5x + 9 = 2x + 6$.

1. The problem appears to involve simplifying or evaluating expressions with exponents and variables, but the input is unclear. 2. Please provide the full expressions or clarify th

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

1. **State the problem:** Solve the inequality $x^2 + 1 > 0$. 2. **Recall the properties:** The expression $x^2$ is always non-negative for all real $x$, since squaring any real nu

1. Enunciat del problema: Estudiar la funció $y = -\frac{1}{x}$, analitzant domini, recorregut, aixíntotes, màxims/mínims relatius i absoluts, continuïtat i monotonia. 2. Fórmula i

1. Problema: Esegui le operazioni con radicali e semplifica, considerando le condizioni di esistenza. 2. Problema 20: Calcola $$\frac{\sqrt{3} - \frac{1}{3}}{\sqrt{1 - \frac{1}{9}}

1. **State the problem:** We need to divide the mixed number $5\frac{2}{3}$ by the mixed number $-1\frac{2}{15}$. 2. **Convert mixed numbers to improper fractions:**

1. The problem states that the graph of $y=\frac{1}{x}$ is transformed to the graph of $y=5(x-3)-4$ and asks for the scale factor of the vertical stretch about the x-axis. 2. First