🧮 algebra

1. **State the problem:** Calculate the value of $$C = \frac{4 \times 10^{-7} \times 45 \times (10^3)^2}{12 \times 10^{-3}}$$. 2. **Recall the rules:** When working with powers of

1. Let's analyze the pattern: 10, 6, 12, 8, 16, 12, 24, ... 2. Separate the terms into two subsequences based on their positions:

1. The problem is to calculate the total of a word by assigning numerical values to each letter and summing them. 2. A common method is to assign A=1, B=2, ..., Z=26.

1. **State the problem:** Given points $P=(-4,-3)$ and $Q=(2,1)$ as endpoints of the diameter of a circle, find the equation of the circle. 2. **Formula and rules:** The equation o

1. **State the problem:** Given points $P=(6,5)$ and $Q=(2,1)$ as endpoints of the diameter of a circle, find the equation of the circle. 2. **Formula and rules:** The equation of

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 $x=2$.