🧮 algebra

1. **State the problem:** We are given the equation $\log x = 4$ and need to find the value of $x$. 2. **Recall the definition of logarithm:** The equation $\log x = 4$ means that

1. The problem is to add two fractions using Brahmagupta's method. 2. Brahmagupta's method for adding fractions $\frac{a}{b}$ and $\frac{c}{d}$ is given by:

1. The problem is to create a random equation that represents a certain concept or relationship. 2. A common type of equation in algebra is a linear equation, which has the form $$

1. **Problem statement:** We have two quadratic equations:

1. **State the problem:** Solve the quadratic equation $x^2 = 5x - 4$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem is to create two more math questions structured similarly to the original format. 2. Since the user did not specify the exact type of questions, I will create two al

1. **Problem Statement:** Find the LCM of two positive integers $p$ and $q$ where $p = ab^2$ and $q = a^3b$, with $a$ and $b$ being prime numbers.

1. **State the problem:** A theatre has a central block with $n$ seats per row. On each side of this block, there are blocks with 4 seats per row. The number of rows is 5 less than

1. **State the problem:** We are given the function $f(x) = \sqrt{3x - 2}$ and asked to find:

1. **State the problem:** Write the standard form equation of the circle given by the equation $137 + 6y = -y^2 - x^2 - 24x$. 2. **Rewrite the equation:** Move all terms to one sid

1. **Write the standard form equation of the circle from** $137 + 6y = -y^2 - x^2 - 24x$. 2. **Rewrite the equation by moving all terms to one side:**

1. **Problem:** Identify the center and radius of the circle given by the equation $$-9 = -y^2 - x^2$$. 2. **Rewrite the equation:** Multiply both sides by -1 to get $$9 = y^2 + x^

1. The problem is to identify and understand the function described by the graph, which starts at (1,1) and grows steeply to the right, resembling an exponential growth curve. 2. T

1. The problem states that \(\alpha = \{(x, y) : y = -2x + 3\} \subseteq \mathbb{R} \times \mathbb{R}\). This means \(\alpha\) is the set of all points \((x, y)\) in the plane wher

1. **Menentukan nilai dari penjumlahan** $$204 + 205 + 206 + 207 + 208 + 209 + 210 + 211 + 212 = ?$$

1. **State the problem:** We need to solve and write in standard form correct to 3 significant figures the expression $$\frac{5.34 \times 10^{5}}{3.26 \times 10^{-8}}$$. 2. **Recal

1. **State the problem:** Solve the equation $$n\sqrt{1 + y} + y\sqrt{1 + n} = 0$$ for $y$ in terms of $n$. 2. **Rewrite the equation:**

1. **State the problem:** Simplify the given masses: 0.5 kg, 1 kg, and 600 grams. 2. **Convert all masses to the same unit:** We will convert grams to kilograms since 1 kg = 1000 g

1. **State the problem:** Simplify the expression $$\frac{\sqrt{8}}{2} - \sqrt{6}$$. 2. **Recall the properties of square roots:**

1. **State the problem:** Simplify the expression $$\frac{\sqrt{8}}{2} - \sqrt{6}$$. 2. **Recall the properties of square roots:**

1. **State the problem:** Solve the equation $$x^2 - 4 = 15x (x - 1)$$ for $x$. 2. **Rewrite the equation:** Expand the right side: