🧮 algebra

1. **Solve** $3 \log_a - \log_a (x+2)$. - The problem involves simplifying logarithmic expressions.

1. **Problem Statement:** Evaluate the given addition and subtraction problems involving mixed numbers and fractions. 2. **Formula and Rules:**

1. **State the problem:** Helen finished a race in 516.06 seconds. Her brother finished 6.46 seconds after Helen. We need to find how long it took Helen's brother to finish the rac

1. **Stating the problem:** We are given the matrix equation

1. The problem is to find the values of $\alpha$, $b$, $c$, and $d$ such that the matrices $$\begin{bmatrix} \alpha & 3 \\ -1 & \alpha + b \end{bmatrix} = \begin{bmatrix} 4 & d - 2

1. **State the problem:** Convert the improper fraction $\frac{149}{11}$ to a mixed number. 2. **Formula and rules:** A mixed number consists of a whole number and a proper fractio

1. The problem is to express the mixed number 7 3/8 as an improper fraction. 2. A mixed number consists of a whole number and a fraction. To convert it to an improper fraction, use

1. The problem asks for the function that represents the image of the curve $y=f(x)$ after a vertical translation 5 units downward. 2. Recall that a vertical translation of a funct

1. The problem asks for the function $g(x)$ which is the image of $f(x)$ after a translation 4 units to the left. 2. Translation rules for functions:

1. The problem is to graph and analyze polynomial functions given by their formulas. 2. The leading coefficient test helps determine the end behavior of polynomial graphs: if the l

1. **Problem Statement:** Graph each polynomial function and understand their behavior. 2. **Leading Coefficient Test:** This test helps determine the end behavior of a polynomial

1. **State the problem:** A company produces three products daily with total production 90 kg.

1. **State the problem:** We are given the equation $$(3 + \sqrt{a})(4 + \sqrt{a}) = 17 + k\sqrt{a}$$ where $a$ and $k$ are positive integers. We need to find the values of $a$ and

1. **State the problem:** We are given the equation $(3 + \sqrt{a})(4 + \sqrt{a}) = 17 + k\sqrt{a}$ where $a$ and $k$ are positive integers. We need to find the values of $a$ and $

1. **State the problem:** Simplify the expression $$\frac{9^{x-1} \cdot 25^x}{5^{x-2} \cdot 15^{x+2} \cdot 3^x}$$. 2. **Rewrite bases as prime factors:**

1. المشكلة: حل المعادلة $5x = 5$. 2. القاعدة المستخدمة: لحل معادلة من الشكل $ax = b$ حيث $a \neq 0$، نقسم الطرفين على $a$ لنجد $x = \frac{b}{a}$.

1. **State the problem:** Factorize the quadratic expression $x^2 + 11x + 24$. 2. **Recall the factoring formula:** For a quadratic $x^2 + bx + c$, we look for two numbers that mul

1. The problem is to find the largest prime factor of 26. 2. Prime factors are prime numbers that divide a number exactly without leaving a remainder.

1. The problem asks to identify an irrational number from the given options: $\sqrt{11}$, $4.2$, $\frac{3}{4}$, and $\sqrt{81}$.\n\n2. An irrational number is a number that cannot

1. **State the problem:** Find the least common multiple (LCM) of 250 and 140. 2. **Recall the formula:** The LCM of two numbers $a$ and $b$ can be found using the formula:

1. لنبدأ بتعريف القيمة المطلقة: القيمة المطلقة لعدد حقيقي $x$ هي المسافة بين $x$ والصفر على خط الأعداد، وتُكتب $|x|$. 2. السؤال الأول: حل المعادلة $|x - 3| = 5$.