🧮 algebra

1. **Problem Statement:** Calculate $\log 891$. 2. **Formula and Rules:** The logarithm $\log a$ (base 10) is the power to which 10 must be raised to get $a$. We can use factorizat

1. \textbf{Problem statement:} We add 9 yellow balls. We have drawn at least one more yellow ball than the total of blue and red balls combined.\n\n2. \textbf{Understanding the pro

1. **State the problem:** Simplify or analyze the rational expression $$\frac{3x^3 + 7x - 4}{(x^2 + 2)^2}$$. 2. **Understand the components:** The numerator is a cubic polynomial $

1. The problem is to simplify the expression $3x^3 + 7x - 4 (Fq + 2)^2$. 2. We start by understanding the expression: it contains a cubic term $3x^3$, a linear term $7x$, and a pro

1. **بيان المسألة:** لدينا العبارة الجبرية $$F = 100x^2 - 49$$.

1. **State the problem:** Given the variables and equations: $$B=\frac{A \times 3}{12}$$

1. **State the problem:** Simplify the expression $\frac{x^2}{7} \times \frac{x^4}{7}$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying terms wit

1. The problem asks for the number of digits in the number $8^{10} \times 5^{22}$. 2. To find the number of digits of a positive integer $N$, we use the formula: number of digits =

1. **State the problem:** Solve the equation $$\frac{x + 1}{5} = \frac{7 - x}{6x}$$ for $x$. 2. **Clear the denominators:** Multiply both sides by $30x$ (the least common multiple

1. لنبدأ بفهم المشكلة: لدينا دالة تحتوي على نقاط (2, -9), (-4, 1), و (7, -9). المطلوب هو إيجاد العلاقة العكسية لهذه الدالة. 2. العلاقة العكسية لدالة تعني تبديل الإحداثيات بحيث تصبح

1. The problem is to find $\log 11136$.\n\n2. The logarithm function $\log x$ typically means the base 10 logarithm unless otherwise specified.\n\n3. To find $\log 11136$, we can u

1. Stating the problem: We are given several variables and equations involving $A$, and we want to find the value of $A$ given that $H = A + B + C + D + E + F = 8999.16$. 2. Given:

1. **State the problem:** Solve the inequality $2\ln(|x-1|) - 2 > 0$. 2. **Rewrite the inequality:** Add 2 to both sides:

1. **State the problem:** Expand and simplify the expression $$(4x - y)^2$$. 2. **Formula used:** The square of a binomial $$(a - b)^2$$ is given by the formula $$a^2 - 2ab + b^2$$

1. **State the problem:** Solve the inequality $$x^2 + 10x + 21 < 0$$. 2. **Formula and rules:** To solve a quadratic inequality, first find the roots of the quadratic equation $$x

1. **State the problem:** Simplify the expression $6\sqrt{20} + 7\sqrt{5}$. 2. **Recall the rule:** $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ and simplify square roots by fact

1. **State the problem:** Find the number of digits in the number $5^{22} \times 8^{10}$. 2. **Recall the formula for the number of digits:** The number of digits of a positive int

1. **State the problem:** Simplify the expression $$\left( \frac{49}{p^2} \right)^{\frac{1}{2}}$$. 2. **Recall the rule:** The exponent $\frac{1}{2}$ means taking the square root.

1. **State the problem:** Simplify and solve the expression $$\frac{1}{2} \left[ 8x + 10 - 6 \left( 1 - 4x \right) \right]$$. 2. **Apply the distributive property inside the bracke

1. **State the problem:** Simplify the expression $$\frac{x^{4/5}}{x^{1/5}}$$. 2. **Recall the rule for division of exponents with the same base:** When dividing powers with the sa

1. **State the problem:** Solve the inequality $-2\ln(x-1) \geq 0$. 2. **Rewrite the inequality:** Divide both sides by $-2$. Since dividing by a negative number reverses the inequ