🧮 algebra

1. **Stating the problem:** Find the value of $x$ that satisfies the equation $$3^{2 - x} = 27.$$

1. The problem is to increase 2000 by 50%. 2. To increase a number by a percentage, use the formula: $$\text{New value} = \text{Original value} + \left(\frac{\text{Percentage}}{100

1. The problem is to simplify or understand the expression $a^2 + b^2 - ab$. 2. This expression is a quadratic form in terms of $a$ and $b$.

1. The problem asks to find the value of $b^3$ when $b = -3$. 2. The formula for raising a number to a power is $b^3 = b \times b \times b$.

1. **State the problem:** Find the highest common factor (HCF) of $y^6$ and $y^9$. 2. **Recall the formula:** The HCF of two powers with the same base is the base raised to the min

1. **State the problem:** Solve the equation $4 - 2x + 8 = -6$ for $x$. 2. **Combine like terms on the left side:** $4 + 8 = 12$, so the equation becomes:

1. **Stating the problem:** Given the operation $a * b = a + b - 1$, we want to understand how this operation works and possibly find some properties or results using it. 2. **Unde

1. **State the problem:** Given $m = -3$ and $n = 2$, find the product $mn$. 2. **Formula used:** The product of two numbers $m$ and $n$ is given by:

1. **State the problem:** Find the intersection point of the two lines given by the equations derived from the inequalities: $$3x - 5y = 2$$

1. The problem states: "three times a number plus eleven." We want to express this as an algebraic expression. 2. Let the number be represented by the variable $x$.

1. The problem is to express "decreased by 8 times Y plus three" as a mathematical expression. 2. "Decreased by" means subtraction.

1. The problem is to simplify the expression: $\frac{X - 20}{2} \times B$. 2. The formula used here is the order of operations (PEMDAS/BODMAS), which tells us to perform division a

1. **State the problem:** We need to express "seven less than the product of twelve and a number" as an algebraic expression. 2. **Identify the unknown:** Let the number be represe

1. **Problem:** Create a quiz question based on the topics: Ratio and Proportion, Algebra, Inequalities, Sequences, Functions. 2. **Step 1: Ratio and Proportion**

1. **State the problem:** We need to express "two times a number plus nine" as an algebraic expression. 2. **Define the variable:** Let the number be represented by $x$.

1. **State the problem:** Simplify and analyze the expression $$a^2 - 4ab + 4b^2 - x^2 + 6x + 9$$. 2. **Recognize patterns:** The first three terms $$a^2 - 4ab + 4b^2$$ form a perf

1. **Problem:** Find values of $x$ for which $\frac{x - 16}{x^2 - 3x}$ is undefined. 2. **Formula:** A rational expression is undefined where the denominator equals zero.

1. **State the problem:** Factorize the expression $$a^2 - 4ab + 4b^2 - x^2 + 6x + 9$$. 2. **Recognize patterns:** The first three terms $$a^2 - 4ab + 4b^2$$ form a perfect square

1. Pernyataan masalah: Hitung ketinggian anak tangga ke-n pada tangga dengan tinggi anak tangga 18 cm menggunakan rumus barisan aritmetika. 2. Rumus barisan aritmetika untuk suku k

1. Let's start by understanding what a function is: a function is a rule that assigns each input exactly one output. 2. The **domain** of a function is the set of all possible inpu

1. **Тэгшитгэлийг тодорхойлох:** Тэгшитгэл нь $$(x - 2)(x^2 + 3x - 1) = x^3 + \diamond + \square + 2$$ байна.