🧮 algebra

1. The problem asks us to find the value of $r$ in the equation $$\frac{5^6 \times 5^{10}}{5^2} = 5^r.$$\n\n2. We use the laws of exponents: when multiplying powers with the same b

1. The problem asks to find the value of $u$ in the equation $$9^{12} = 3^u.$$\n\n2. We start by expressing 9 as a power of 3 because both sides should have the same base to compar

1. **State the problem:** Solve the equation $$2(2x - 8) = 3(4 - x)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **Problem statement:** We need to find how long the temperature held steady based on the graph of temperature over time. 2. **Understanding the graph:** The temperature rises, s

1. Diberikan pola bilangan: 2, 9, 20, 35, 54, ... 2. Kita diminta menentukan suku ke-6 dari pola tersebut.

1. **State the problem:** Solve for $y$ in the equation $$e^{y + 5} = 5$$ and round the answer to the nearest hundredth. 2. **Recall the formula and rules:** To solve for $y$ when

1. Problem: Identify the pattern of the sequence 2, 5, 10, 17, 26, ... and explain the reasoning. 2. The sequence is given as: 2, 5, 10, 17, 26, ...

1. **State the problem:** Solve the equation $4p + 5 = 29 - 2p$ for $p$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $19 - 4x = 2x + 1$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Simplify the expression $-5i(3 + 6i)$ and express the answer in terms of $i$. 2. **Recall the rule:** When multiplying complex numbers, distribute and use

1. The problem asks to perform the operation and simplify the expression $(5i)^2$ where $i$ is the imaginary unit. 2. Recall that $i$ is defined as $i^2 = -1$.

1. Stating the problem: We need to multiply the complex numbers $11i$ and $-3i$. 2. Recall the rule for multiplying complex numbers: When multiplying, multiply the coefficients and

1. The problem is to simplify the expression $\sqrt{-8} \cdot \sqrt{-200}$.\n\n2. Recall the property of square roots: $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$, which holds for

1. **State the problem:** Express $-3\sqrt{-100}$ as a complex number. 2. **Recall the rule for square roots of negative numbers:** For any positive number $a$, $\sqrt{-a} = \sqrt{

1. **State the problem:** Add and subtract the complex numbers:

1. **State the problem:** Add and subtract the complex numbers \((6 - \sqrt{-16}) + (-16 + \sqrt{-9})\) and \((6 - \sqrt{-16}) - (-16 + \sqrt{-9})\).

1. **State the problem:** Find 50% of a given number (assuming the number is 2300 as in the previous problem). 2. **Formula:** To find a percentage of a number, use the formula:

1. **State the problem:** Find 165% of 2300. 2. **Formula:** To find a percentage of a number, use the formula:

1. Problem: Determine the domain $D$ of the function $f(x,y) = \frac{x}{y}$ and represent it geometrically. 2. Formula and rules: The domain of a function is the set of all input v

1. **State the problem:** Find the domain $D$ of the function $f(x,y) = \frac{x}{y}$ and represent it geometrically. 2. **Recall the domain rule for fractions:** The denominator ca

1. The user asks for formulas related to chapter 4, but no specific problem is given. 2. Since no specific problem is stated, I cannot solve or explain any particular formula.