🧮 algebra

1. مسئله: نسبت مساحت دو بخش رنگی S_x و S_1 که توسط نمودار تابع $f(x) = kx^2$ و خطوط عمودی در نقاط $a$ و $b$ محدود شده‌اند را می‌خواهیم پیدا کنیم. 2. تابع داده شده یک سهمی است که از

1. The problem provides columns labeled $x$, $y$, $xy$, $x^2$, and $y^2$ with numerical data. 2. The columns $xy$, $x^2$, and $y^2$ represent derived values from $x$ and $y$:

1. The problem is to solve the equation or expression given by the user. However, no specific equation or expression was provided in the request. 2. To solve any algebraic problem,

1. The problem is to find the missing numbers in the multiplication expansion of $23 \times 102$ using the distributive property. 2. The distributive property states that $a \times

1. The problem is to simplify the expression $23 \times 102$ using the distributive property. 2. The distributive property states that $a \times (b + c) = a \times b + a \times c$.

1. **Problem:** Represent "6 more than four times the number n" as an algebraic expression. 2. **Formula and Explanation:** "Four times the number n" means multiplying n by 4, whic

1. **Problem:** Write an algebraic expression for "Seven more than a number divided by six". 2. **Understanding the problem:** We need to express the phrase "Seven more than a numb

1. **Stating the problem:** We are given two lists: Midterms scores ($x$) and Travel times ($y$). We need to create a table with columns $x$, $y$, $xy$, $x^2$, and $y^2$.

1. **State the problem:** We are given the price ratio of three types of cars: Suzuki Swift, Ford Fiesta, and Honda Jazz as $3 : x : 4$. The total price of all three cars is 300000

1. **State the problem:** Solve the system of equations using the Gauss Elimination Method: $$\begin{cases} 2y + z = -8 \\ x - 2y - 3z = 0 \\ -x + y + 2z = 3 \end{cases}$$

1. Problem: Calculate the value of $y$ for the equation $y = 32 - 4x + x^2$ when $x = 3$. 2. Formula: Substitute the value of $x$ into the equation and simplify.

1. **State the problem:** We have three types of cars: Suzuki Swift, Ford Fiesta, and Honda Jazz. Their prices are in the ratio $3:x:4$ respectively. 2. **Given:**

1. **Problem Statement:** We have two alloys A and B with Aluminum (Al) and Nickel (Ni) in ratios 4:3 and 3:5 respectively.

1. Stating the problem: Find the unknown percentage $x$ such that $$65\% \text{ of } 180 + x\% \text{ of } 210 = 80\% \text{ of } 225.$$\n\n2. Write the equation using decimals for

1. Let's start with the basics of Arithmetic Sequences (AS) and Geometric Sequences (GS). 2. An Arithmetic Sequence is a sequence where each term increases by a constant difference

1. Let's start by defining Arithmetic Sequence (AS) and Geometric Sequence (GS). An Arithmetic Sequence is a sequence of numbers where the difference between consecutive terms is c

1. **State the problem:** We are given the equation $$2(2x - 2) = 3x - 7$$ which relates the height of a door and the length of a garland. 2. **Write the equation and expand:** Use

1. **State the problem:** We are given the quadratic function $$y = -x^2 - 6x - 10$$ and want to analyze its properties such as shape, vertex, and intercepts. 2. **Formula and rule

1. **State the problem:** We need to analyze and solve the quadratic function $$y = -x^2 - 6x - 10$$. 2. **Formula and rules:** The quadratic function is in the form $$y = ax^2 + b

1. **State the problem:** Solve the quadratic equation $$2x^2 - 7x + 3 = 0$$ by factorisation. 2. **Recall the factorisation method:** For a quadratic equation $$ax^2 + bx + c = 0$

1. State the problem: Simplify each expression. 2. The three expressions to simplify are: a) $ (5x^2)^3 $.