🧮 algebra

1. Problem: Given $f(x) = 2 - x$ and $g(x) = -2x + 3$, find:\ a. $f + 2g$ and evaluate $(f + 2g)(2)$\

1. **State the problem:** Find the domain of the function $$f(x) = \ln(x^2 - 12x)$$. 2. **Recall the domain condition for natural logarithm:** For $$f(x) = \ln(u)$$, the argument $

1. Stating the problem: Solve the equation $$(2x - 5)^2 = -9$$. 2. Analyze the equation: The left side is a square of a real expression, which is always non-negative. The right sid

1. Solve the equation $0 \cdot 6 - 5 \cdot 4 = 3 \cdot 2 - x - x$. Simplify both sides:

1. The problem is to simplify the expression $5x + 5$. 2. Identify the common factor in both terms. Here, the number 5 is common in $5x$ and $5$.

1. We are given the inequality involving a function $f(x)$: $$\sqrt{x} + 7 \leq f(x) \leq \frac{x - 1}{2}.$$\n\n2. This inequality states that the value of the function $f(x)$ is b

1. Let's state the problem: Simplify the expression $5x + 5$. 2. Look at the terms: Both terms contain a factor of 5.

1. **Stating the problem:** You have two given equations involving fractions and triangular operations represented by downward (▼) and upward (▲) triangles:

1. Mari kita mulai dengan menyatakan masalahnya: Temukan jumlah semua faktor prima dari bilangan $27000001$. 2. Untuk menemukan faktor prima, pertama kita harus melakukan faktorisa

1. **Stating the problem:** We need to construct and interpret a table of values for two linear relations and graph the relations.

1. **Problem Statement:** Develop a lesson plan for Basic 9 on the indicator B9.2.1.1.1: Constructing a table of values for two linear relations and graphing these relations. 2. **

1. **State the problem:** We need to find the points where the graphs of $$y = x^2 - 4x + 2$$

1. Solve the equation $\frac{1}{x} = 2x + 3$. Multiply both sides by $x$ (assuming $x \neq 0$) to get:

1. We are asked to subtract $\frac{3}{4}$ from $\frac{2}{3}$. 2. To subtract these fractions, we need a common denominator. The denominators are 3 and 4. The least common denominat

1. The problem asks to find the value of $\frac{1}{3} - \left(-\frac{2}{3}\right)$.\n2. Subtracting a negative number is the same as adding its positive counterpart, so this become

1. The problem is to simplify the expression: $\frac{1}{3} - \left(-\frac{2}{3}\right)$. 2. Start by recognizing that subtracting a negative number is the same as adding its positi

1. The problem is to subtract the fractions $\frac{2}{9}$ and $\frac{3}{9}$. 2. Since both fractions have the same denominator, you can subtract the numerators directly.

1. The problem asks to find the result of $\frac{1}{5} - \frac{3}{5}$.\n2. Since the denominators are the same (both 5), subtract the numerators: $1 - 3 = -2$.\n3. Keep the denomin

1. We start with the first set of fraction additions: 1/4 + 3/4 = 4/4 = 1

1. Let's state the problem: Simplify the expression $\frac{5}{7} + \left(-\frac{11}{14}\right)$.\n\n2. First, identify the common denominator for the fractions $\frac{5}{7}$ and $-

1. Stating the problem: We need to add the fractions $\frac{1}{8}$ and $-\frac{7}{12}$.\n2. Find a common denominator: The denominators are 8 and 12. The least common denominator (