🧮 algebra

1. The problem is to find the total cost of making a product with the given ingredients and quantities. 2. The formula to find the total cost is to sum the costs of all individual

1. مسئله: محیط مستطیل با طول $y - 3x$ و عرض $y + x$ را پیدا کنید. 2. فرمول محیط مستطیل: $$\text{محیط} = 2 \times (\text{طول} + \text{عرض})$$

1. **بیان مسئله:** معادله داده شده را ساده کنیم: $$2(3x - 4y + 1) + 4(2y - 3x - \frac{1}{2})$$

1. The problem asks: In the equation of a straight line given by the gradient form $y = mx + c$, what does the constant $c$ represent? 2. The formula is $y = mx + c$, where:

1. Let's start by understanding the problem: why does $2i^2$ become $-4$? 2. Recall the definition of the imaginary unit $i$: by definition, $i^2 = -1$.

1. **Problem Statement:** Find a cubic equation with real coefficients given that two of its roots are $1$ and $3+2i$. Also, state the result being used. 2. **Key Result Used:** If

1. **Stating the problem:** Make $T$ the subject of the relation $$\frac{bg}{T} = \frac{w + m}{n}$$ 2. **Formula and rules:** To make $T$ the subject, we need to isolate $T$ on one

1. **Stating the problem:** Make $t$ the subject of the relation $$\frac{8}{t} = w + \frac{m}{n}$$ 2. **Formula and rules:** To make $t$ the subject, we need to isolate $t$ on one

1. **Problem:** Simplify the fraction $\frac{8}{24}$.\n - Factors of numerator: $8 = 2 \times 2 \times 2$.\n - Factors of denominator: $24 = 2 \times 2 \times 2 \times 3$.\n

1. **State the problem:** Simplify the fraction $\frac{8}{24}$ to its lowest terms. 2. **Formula and rules:** To simplify a fraction, find the Greatest Common Factor (GCF) of the n

1. المشكلة: لدينا عدد موظفي الشركة 42 موظفًا، ونريد معرفة كم عدد الموظفين السعوديين الذين يجب إضافتهم ليصبح عدد السعوديين نصف عدد موظفي الشركة. 2. المعطيات:

1. **State the problem:** We are given roots $\alpha$ and $\beta$ of the quadratic equation $x^2 + 3x - 5 = 0$ with conditions $\alpha^2 + \beta^2 = 19$, $\alpha - \beta = \sqrt{29

1. Let's start by understanding the problem you want to solve. Since you asked for the whole pattern of solving step by step, I will demonstrate a general approach to solving algeb

1. **Evaluate the expression:** $e^2 \div 5 \times 9 \times 4^2 + 3^2$ - First, calculate powers: $e^2$ is just $e^2$, $4^2 = 16$, and $3^2 = 9$.

1. **Problem statement:** Write the matrix $M = (a_{ij})$ of order $2 \times 3$ where: - For $i = j$, $a_{ij} = \frac{1}{2}(i^2 + j) - 3j$

1. State the problem. We are given the quadratic function $y=2x^2-5x-3$ and a table where $p$ is the value when $x=-\tfrac{1}{2}$ and $q$ is the value when $x=2$.

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 $a \times (b + c) = a \times b + a \times c$.