🧮 algebra

1. **State the problem:** Solve the system of linear equations: $$x + 2y + 3z = 14$$

1. The problem is to find the solution for the variable $x$. 2. Since no specific equation or expression is given, we cannot solve for $x$ without additional information.

1. Problem: Find the product function $(fg)(x)$ where $f(x) = 4x - 2$ and $g(x) = 2x + 2$. Step 1: Recall that $(fg)(x) = f(x) \cdot g(x)$.

1. **State the problem:** We are given a relation $R$ defined by the inequalities $y \leq x - 2$ and $y \geq 2x - 4$. We need to sketch the graph of this relation. 2. **Understand

1. Énonçons le problème : Montrer que $$\frac{1}{1} + \frac{1}{a} > \frac{1}{a} + b$$. 2. Simplifions l'expression de gauche : $$\frac{1}{1} = 1$$ donc l'inégalité devient $$1 + \f

1. The problem is to find the value of $\frac{2}{5}$ divided by $\frac{3}{7}$.\n2. Dividing by a fraction is the same as multiplying by its reciprocal. So, we rewrite the division

1. **State the problem:** The maximum speed $S$ of a vehicle is partly constant and partly varies as the engine capacity $C$. Given two points: when $C=2000$, $S=240$ km/h and when

1. The problem is to solve the equation $$\log_3(x + 4) = 2$$ and analyze the function $$f(x) = -\log_3(x + 2)$$. 2. To solve $$\log_3(x + 4) = 2$$, recall that $$\log_b(a) = c$$ m

1. The first expression is $f(x) = \log_2(x)$. This is a logarithmic function because it defines $f(x)$ as the logarithm of $x$ with base 2. 2. The second expression is $\log_2(x)

1. Let's start by defining each term clearly. 2. A **logarithmic equation** is an equation that involves a logarithm with a variable inside it, for example, $\log_b(x) = y$ where $

1. The first expression is $2\log_{10}(x) = \log_{10}(50)$. This is an equation involving logarithms, so it is a **logarithmic equation**. 2. The second expression is $\log_3(x + 1

1. **State the problem:** We want to show that the recurring decimal $0.28\overline{13}$ equals the fraction $\frac{557}{1980}$. 2. **Express the decimal as a sum:** Let $x = 0.28\

1. **State the problems:** We have three problems involving logarithms:

1. Problem: Solve the equation $x + (x + 2) = 67$ to find $x$. 2. Combine like terms: $x + x + 2 = 67$ simplifies to $2x + 2 = 67$.

1. Problem 9: A farmer initially wants to build a square fence with side length 12 m. The perimeter of this square is $$P = 4 \times 12 = 48\text{ m}$$.

1. **Problem 3:** Given the function $h : x \to px - q$ with $h(-3) = -13$ and $h(2) = -3$, find: (a) The values of $p$ and $q$.

1. Masalah 18: Tentukan banyak produk per hari agar biaya operasional kedua mesin sama. Misalkan $x$ adalah banyak produk per hari.

1. Masalah 6: Berat 1 karung apel dan 1 karung mangga adalah 67 kg. Berat 1 karung apel 3 kg lebih berat dari 1 karung mangga. Tentukan berat masing-masing karung. 2. Misalkan bera

1. **State the problem:** XYZ Company bought a machine for 50000. Profits start at 7876 in March and increase by 2% each month. We want to find the month when total profits pay off

1. **Énoncé du problème :** Nous étudions la fonction $f(x) = \sqrt{x+1}$.

1. The problem states that Mya converted some amount in pounds (£) to Danish kroner (kr) at an exchange rate of £1 = 8.50 kr. 2. We know she received 867 kr after conversion.