🧮 algebra

1. **State the problem:** We want to find the number of tiles in the 100th pattern of a sequence where the number of tiles in each pattern is given by the formula: $$\text{number o

1. The problem is to evaluate the expression $67 + 67 \_ 67$. 2. First, we need to clarify the meaning of the underscore symbol "_" in the expression. In standard arithmetic, under

1. **State the problem:** We have a rectangular garden with a perimeter of 64 meters. The length is 8 meters longer than the width. We need to find the length and width. 2. **Formu

1. The problem asks for the first three terms of a sequence where each term is found by adding 6 to its position number. 2. The formula for the term at position $n$ is:

1. **State the problem:** Solve the equation $x + 8 = -4$ for $x$. 2. **Formula and rules:** To isolate $x$, subtract 8 from both sides of the equation. This uses the property of e

1. **Stating the problem:** Simplify the algebraic expression: $$2a \cdot (-3b) + (-3a^2) \cdot (-4b) - 4a^2b$$

1. **State the problem:** Simplify and express given algebraic expressions as repeated multiplications. 2. **Recall the rules:**

1. Nyatakan masalah: Hitung hasil darab ekspresi $(8x + 3y)$ dengan 3. 2. Gunakan formula distributif: $$a(b + c) = ab + ac$$

1. **State the problem:** Given functions $f(x) = 3x - 2$ and $g(x) = x - 3$, find the inverse functions $f^{-1}(x)$ and $g^{-1}(x)$. 2. **Find $f^{-1}(x)$:**

1. **Problem (a):** When the sum of $2a$ and 15 is divided by 7, the result is 11. Find the value of $a$. 2. **Formula and rules:** The problem states:

1. **Stel het probleem vast:** We hebben een parametrisch systeem van drie lineaire vergelijkingen in $x$, $y$, en $z$ met parameters $r$ en $s$: $$x=1+7r+2s$$

1. **State the problem:** Simplify the rational expression $$\frac{x^3 - 6x^2 + 11x - 6}{x^3 - 4x^2 + x + 6}$$ and verify it equals $$\frac{(x - 1)(x - 2)(x - 3)}{(x + 1)(x - 2)(x

1. **State the problem:** Simplify the expression $$\log_2 6 \cdot \log_3 6 - (\log_2 3 + \log_3 2)$$. 2. **Recall the change of base formula:** For any positive numbers $a,b,c$ wi

1. **Nyatakan masalah:** Lengkapkan Jadual 12 untuk persamaan $y = x^3 - 6x + 4$ dengan mencari nilai $y$ apabila $x = -3$ dan $x = 1$. 2. **Formula:** Gunakan persamaan yang diber

1. The problem is to solve the equation or expression given in the example. 2. Since the user asked for another example, let's consider solving a simple linear equation: $2x + 3 =

1. The problem asks: Why do we divide when calculating the gradient (slope) of a line? 2. The gradient formula is given by:

1. **Stating the problem:** Ayah berangkat kerja naik motor pukul 07.10 dengan jarak rumah ke kantor 24 km dan kecepatan motor 40 km/jam. Kita diminta mencari pukul berapa Ayah tib

1. **Тэнцэтгэл бишийг бодох:** Өгөгдсөн тэнцэтгэл биш: $$x^2 - 4x - 5 > 0$$

1. The problem asks to identify which of the given relations are functions. 2. A relation is a function if every input $x$ has exactly one output $y$.

1. The problem is to find the square roots of the given numbers: 3,721; 5,184; 6,400; 2,704; 7,225; and 8,416. 2. The formula for the square root of a number $x$ is $\sqrt{x}$, whi

1. **State the problem:** Solve the simultaneous equations: $$2^x \cdot 4^y = \frac{1}{8}$$