🧮 algebra

1. نبدأ بحل التعبير المعطى: $\left(\frac{1}{6} + 1\right) \left(\frac{1}{5} + 1\right) \left(\frac{1}{3} + 1\right) \left(\frac{1}{1} + 1\right)$. 2. نجمع الكسور مع الواحد في كل قو

1. **State the problem:** We are given a function $$f(x) = \frac{1}{50} \left[ c(x-1) + \frac{1}{2} \right]$$ for $$x=1,2,...,10$$ and the condition $$\sum_{x=1}^{10} f(x) = 1$$. W

1. **State the problem:** We need to graph the system of inequalities: $$x + y > -3$$

1. **State the problem:** Find the equation of the line passing through points $(0,3)$ and $(5,0)$ and write it in standard form. 2. **Find the slope $m$ using the formula:**

1. The problem is to analyze the quadratic function given by the equation $y = kx^2 + 2x + 3$. 2. This is a quadratic function of the form $y = ax^2 + bx + c$, where $a = k$, $b =

1. **State the problem:** Solve the equation $$\sqrt{x^{2} - 8x + 16} + \sqrt{x^{2} - 4x + 4} = 2.$$\n\n2. **Recognize perfect squares:** Notice that \(x^{2} - 8x + 16 = (x-4)^2\)

1. **State the problem:** Solve the equation $\frac{32}{a} = a - 4$ for $a$. 2. **Rewrite the equation:** Multiply both sides by $a$ (assuming $a \neq 0$) to eliminate the denomina

1. **State the problem:** Decompose the rational function $$\frac{x^2+x+1}{(x-1)(x+2)}$$ into partial fractions. 2. **Formula and rules:** For distinct linear factors in the denomi

1. **State the problem:** Solve the equation $$3(x - 5) - 7 = -2(-2x + 4) - 9x$$ for $x$. 2. **Apply the distributive property:**

1. **State the problem:** We are given the function $$f = 5x^2 + \sqrt{9x - x - 3} - x - 3$$ and asked to understand and graph it. 2. **Simplify inside the square root:** Simplify

1. Solve the inequality $1 < \frac{x}{2} < 3$. 2. Multiply all parts of the inequality by 2 (positive number, so inequality signs remain the same):

1. The problem is to find the remainder when one number is divided by another. 2. The remainder is the amount left over after division when one number cannot be divided evenly by a

1. The problem is to find the value of $i^{45}$, where $i$ is the imaginary unit with the property $i^2 = -1$. 2. Important rule: Powers of $i$ cycle every 4 steps because:

1. **Problem Statement:** Aghar lost 35 by selling a body for 430. We need to find the loss percentage. 2. **Given:**

1. დავწეროთ მოცემული პირობა: $a-b$ არის $a+b$ რიცხვის 20%, რაც ნიშნავს: $$a-b=0.2(a+b)$$

1. The problem is to understand cubes and cube roots. 2. The cube of a number $x$ is given by the formula $$x^3 = x \times x \times x$$ which means multiplying the number by itself

1. **State the problem:** We want to find the real root of the equation $x \log_{10} x = 1.2$ using Newton's iterative method, accurate to five decimal places. 2. **Rewrite the equ

1. **State the problem:** Solve the inequality $$\frac{1}{6} - \frac{1}{4}x \geq 2 + \frac{2x}{3}$$. 2. **Rewrite the inequality:** To solve for $x$, first get all terms involving

1. Problem: Find the area of the region bounded by the graph of the function $f(x) = |x - 2|$ and the coordinate axes. 2. Understanding the function: The function $f(x) = |x - 2|$

1. Problem: Doğrusal bir fonksiyonun işaret tablosu verilmiştir. Buna göre, fonksiyonun hangi ifade olabileceğini bulmamız gerekiyor. 2. İşaret tablosuna göre:

1. Problem: Given the piecewise function $$f(x) = \begin{cases} 3 - x & x \leq 1 \\ 2x & x > 1 \end{cases}$$