🧮 algebra

1. **Problem:** Identify the domain and range of the given graphs based on the descriptions. 2. **Understanding Domain and Range:**

1. **Stating the problem:** Simplify the expression $$\frac{a^2 - ab}{ab - b^2}$$ and solve the equation $$\frac{1}{r}x - \frac{1}{m} = \frac{\omega}{y}$$. 2. **Simplify the fracti

1. Problem: Decompose 642352 into whole numbers with divisors of 3 to 4 digits. 2. Formula: For a number $N$, find divisors $d$ such that $100 \leq d \leq 9999$ and $N = d \times k

1. **Problem Statement:** We want to understand the concept of inequalities and how they relate to graphs, especially in the context of a triangle defined by three inequalities. 2.

1. **Problem:** Write the domain and range for the function shown on the graph (Graph 1). 2. **Understanding domain and range:**

1. **Problem Statement:** Identify the domain and range of the given parabola graph. 2. **Graph Description:** The parabola opens upwards with vertex at the origin $(0,0)$.

1. مسئله: عددی را بیابید که پنج برابر آن به علاوه یک برابر آن عدد منهای هفت باشد. 2. فرمول و توضیح: فرض کنیم عدد مورد نظر $x$ باشد. طبق صورت مسئله داریم:

1. Let's create an algebra problem involving quadratic equations. 2. Problem: Solve the quadratic equation $$2x^2 - 4x - 6 = 0$$.

1. The problem is to understand and analyze a polynomial function. 2. A polynomial function is generally expressed as $$f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$$ where

1. Let's start by understanding what factorization means. Factorization is the process of breaking down an expression into simpler expressions (factors) that when multiplied give t

1. The problem asks to find the function $g(x)$ which is a translation 1 unit to the left of the function $f(x) = x^2$. 2. The general rule for horizontal translations is: if $f(x)

1. The problem asks to find the function $g(x)$ which is the translation 9 units up of the function $f(x) = x^2$. 2. The general form for a vertical translation of a function $f(x)

1. The problem asks for the actual simplified answer, but no specific expression or equation was provided. 2. To simplify an expression, you typically combine like terms, factor wh

1. **State the problem:** We need to simplify and solve the given complex fractional expressions involving polynomials in $s$ and $t$. 2. **Identify the expressions:** The problem

1. **State the problem:** We are given the quadratic expression $2x^2 - 5x + 2$ and want to analyze it.

1. The problem is to understand the concepts of domain and range of a function. 2. The domain of a function is the set of all possible input values (usually $x$) for which the func

1. **Problem Statement:** We need to find the growth percentage for product C in 2016 over 2015 such that the revenue from product C in 2016 is at least equal to the combined reven

1. The problem states that in question 2, part b2, only the $x$ in the numerator is squared. 2. This means the expression looks like $\frac{x^2}{\text{denominator}}$ where only the

1. Given a group of 90 students playing three sports: கிரிக்கட் (Cricket), கரப்பந்து (Football), and கார்ப்பந்து (Basketball). 2. The pie chart shows the angles for each sport sect

1. The problem is to compare the values of the expressions $6^9$, $2^{10}$, $8^9$, and $2^{11}$. 2. We use the property of exponents that allows expressing numbers as powers of pri

1. The problem is to find the simplified form of the product of the algebraic expressions $x^2 - 9$ and $3(x - 3)^2$. 2. Recall the difference of squares formula: $$a^2 - b^2 = (a