🧮 algebra

1. ננתח את הנתונים: הסדרה היא חשבונית עם האיבר הראשון $a_1=52$ והפרש $d=56-52=4$. 2. סכום $n$ האיברים הראשונים בסדרה חשבונית הוא לפי הנוסחה:

1. The problem is to analyze the linear function $M=4x-20$. 2. This function is in slope-intercept form $M=mx+b$ where $m=4$ is the slope and $b=-20$ is the y-intercept.

1. The problem involves points A, B, D, and E with given coordinates and values such as AB = 9.6 and AB = 1.6, and some numeric values like 3884, 705.739425, 816.37422, 35.9871, 60

1. **فكك العدد x=154 إلى جداء عوامل أولية:** - 154 عدد زوجي، إذن يقبل القسمة على 2: $$154 \div 2 = 77$$

1. We are asked to simplify the expression: $$gx^2 - 3hx^2 - 6fy^2 - gy^2 + 6fx^2 + 3hy^2$$. 2. Group like terms by variables and coefficients:

1. **State the problem:** Simplify the expression $$\frac{\left(10^{3} \cdot 20^{2}\right)^{3}}{5^{5} \cdot 2} \cdot \frac{250^{4} \cdot 8^{3}}{75^{2}}$$

1. **State the problem:** Savio drives 50 miles to work, thinking his average speed is 40 miles per hour. We need to find the arrival time if this speed is correct. 2. **Use the fo

1. **State the problem:** Simplify the expression $$\frac{14x^8}{\sqrt{7x^5}}$$. 2. **Rewrite the square root in the denominator:** Recall that $$\sqrt{a} = a^{\frac{1}{2}}$$, so

1. **Problème 20 : Consommation d'essence et distance parcourue** Une voiture consomme 7 L pour 100 km. Le prix de l'essence est 129 ¢/L, soit 1,29 par litre. Avec 10 d'essence, co

1. **State the problem:** We need to order the given expressions from least to greatest. 2. **Evaluate each expression:**

1. The problem is to draw the graph of the function $f(x) = \lfloor 2x \rfloor$ where $\lfloor \cdot \rfloor$ denotes the floor function, which maps a real number to the greatest i

1. The problem is to understand and analyze the function $F(x) = \iint x + 1$ with the domain constraint $|x| \le 2$. 2. The notation $\iint$ typically represents a double integral

1. The problem defines a piecewise function: $$F(x) = \begin{cases} x+1, & |x| \leq 2 \\ 5 - x, & |x| > 2 \end{cases}$$

1. **State the problem:** We are given a piecewise function: $$F(x) = \begin{cases} x+1 & \text{if } |x| \leq 2 \\ 5 - x & \text{if } |x| > 2 \end{cases}$$

1. Stating the problem: Simplify the function $$F(x)=\frac{\sqrt{x^2+3-2}}{x-1}, \quad x\neq1$$. 2. Simplify inside the square root: $$x^2 + 3 - 2 = x^2 + 1$$.

1. The problem is to simplify the function $$F(x) = \frac{\sqrt{x^2 + 3 - 2}}{x - 1}, \quad x \neq 1.$$\n\n2. First, simplify the expression inside the square root: $$x^2 + 3 - 2 =

1. The problem is to analyze the function $$F(x) = \begin{cases} \frac{\sqrt{x^2 + 3 - 2}}{x - 1}, & x \neq 1 \\ 2, & x = 1 \end{cases}$$ 2. Simplify the expression inside the squa

1. We are given the function $$F(x) = \frac{\sqrt{x^2+3}}{x-1}$$ with the domain restriction $$x \neq 1$$ because the denominator cannot be zero. 2. To understand the behavior of t

1. The problem is to simplify the expression $$\frac{u_3 - u_2}{u_3 + u_2}$$. 2. This expression is a fraction where the numerator is the difference of two variables $u_3$ and $u_2

1. The problem asks to express the sum \(\frac{y+7}{1} + \frac{y+5}{1}\) as a single fraction in simplest form. 2. Since both fractions have denominator 1, we can add the numerator

1. The problem is to express the equation $$(2x + 1)(x - 3) = \frac{\square}{2x + 1} - \frac{\square}{x - 3}$$ by finding the numerators in the fractions on the right side. 2. Star