🧮 algebra

1. **State the problem:** We are given the function $$g(x) = 1 - 2(x+2)^2 - \ln(x+2)$$ and we want to understand or analyze it. 2. **Rewrite the function clearly:**

1. **State the problem:** Solve the equation $$\frac{p}{x+r} + \frac{q}{x-r} = \frac{k}{2x}$$ for $x$. 2. **Formula and rules:** To solve rational equations, first find a common de

1. **Problem 4:** Find values of $k$ such that the equation $$p(x+1) + q(x-r) = \frac{k}{2}x$$ has two equal roots. 2. **Rewrite the equation:**

1. **Problem statement:** Find the value of $m$ such that the system of equations

1. **Problem:** Find the number of intersection points between the parabola $y=3x^2$ and the line $y=3x+5$. 2. **Set the equations equal to find intersection points:**

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle that to isolate $x$, we perform inverse operations to both sides of the equati

1. Vamos calcular o item a) do exercício: $\left(\frac{3}{7}\right)^2 \cdot \frac{16}{9}$. 2. Primeiro, elevamos $\frac{3}{7}$ ao quadrado:

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

1. **State the problem:** We need to find the sum $$\sum_{i=1}^{20} \left( x^2 \sqrt{\frac{9x^4}{x^8}} \sqrt[i]{4} + \sqrt{\frac{125}{5}}^{2 \log_5 5} + \log_3 243 \right)$$. 2. **

1. نبدأ ببيان المشكلة: لدينا معادلة تربيعية جذورها أحدها هو $2+i$. 2. بما أن المعاملات حقيقية، فإن الجذر الآخر هو المرافق المركب لـ $2+i$، أي $2 - i$.

1. **State the problem:** Solve the inequality $$x^2 + 7x + 12 \geq 0$$. 2. **Formula and rules:** To solve quadratic inequalities, first find the roots of the quadratic equation $

1. **Problem:** Solve the inequality $x^2 - 3x + 2 > 0$. 2. **Formula and rules:** For quadratic inequalities of the form $ax^2 + bx + c > 0$, first find the roots by solving $ax^2

1. **State the problem:** Simplify the expression $$3^{n+2} + \left(3^{n+3} - 3^{n+1}\right)$$ and determine which of the given options it equals. 2. **Recall the properties of exp

1. **State the problem:** Simplify the expression $$ (25^{-1}) + (25^{-2}) $$ and understand why the answer might be 26. 2. **Recall the rules for negative exponents:** For any non

1. **State the problem:** Solve the equation $\log_3(x-2) + 2\log_9(x+3) = \log_3 14$ for $x$. 2. **Recall the properties of logarithms:**

1. Diketahui FPB dari $6^{2} + m$ dan 28 adalah 14 dengan $m > 0$. Kita harus mencari nilai terkecil dari $m$. 2. Hitung nilai $6^{2}$:

1. The problem is to simplify the expression $2x$. 2. The expression $2x$ means $2$ times $x$, where $x$ is a variable.

1. Diketahui KPK dari tiga bilangan yaitu $10^2 - 88$, $16a + 20$, dan 45 adalah $m$. 2. Pertama, hitung nilai dari $10^2 - 88$:

1. **State the problem:** Simplify or analyze the expression $2x + 1$. 2. **Understand the expression:** This is a linear expression in terms of $x$, where $2$ is the coefficient o

1. **Problem Statement:** Find the domains and ranges of the functions $f(x) = 2$, $g(x) = x^2 + 1$, $\frac{f}{g}$, and $\frac{g}{f}$.\n\n2. **Recall definitions:**\n- The **domain

1. **Problem Statement:** Find the number of terms and the 12th term for the sequences in problems 4, 5, and 6.