🧮 algebra

1. **State the problem:** Evaluate the expression without using a calculator or tables: $$\frac{3}{4} + \frac{12}{7} \div \frac{4}{7} \times \frac{7}{3} \times \frac{2}{3} \div \le

1. **Степенуване на рационални числа** Дадени са изрази за степенуване на рационални числа. При степенуване на отрицателни числа с цели степени, ако степента е четна, резултатът е

1. The problem is to factor the quadratic expression $x^2 - x - 6$. 2. The general form of a quadratic expression is $ax^2 + bx + c$. Here, $a=1$, $b=-1$, and $c=-6$.

1. مسئله: نمودار تابع $y=-|x|+4$ داده شده است و باید نمودار تابع $y=\lfloor x \rfloor$ را رسم کنیم. 2. تابع $y=-|x|+4$ یک تابع قدر مطلق است که ابتدا مقدار مطلق $x$ را می‌گیرد، سپس

1. **State the problem:** Solve the linear equation $2x + 45 = 12$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 45 fr

1. **Problem:** Given the equation and options, find the correct value. 2. **Formula and rules:** To solve such problems, substitute given values into the equation and simplify ste

1. **State the problem:** Find the function and analyze the expression for $$y = \left( \frac{x^3 - 1}{2x + 1} \right)^4$$

1. **Stating the problem:** Simplify or analyze the rational function $$f(x) = \frac{x^2 + 2x + 4}{3x + 2}$$. 2. **Formula and rules:** A rational function is a ratio of two polyno

1. Bài toán yêu cầu giải bất phương trình: $$x - 1 + x > 3 - 2$$ 2. Ta nhóm các biến về một phía và hằng số về phía kia:

1. The problem is to evaluate the expression \(\left[\;\right]\left[\;\right]\), which represents the product of two empty brackets. 2. Empty brackets typically indicate an empty m

1. **Problem statement:** Joe sees the time 9:25 in a mirror reflection of a clock. We need to find the actual time on the clock. 2. **Understanding the mirror clock problem:** Whe

1. Diberikan fungsi $f(x) = x + \frac{1}{x}$ dengan $x > 0$. Tentukan fungsi inversnya. 2. Untuk mencari fungsi invers, kita mulai dengan menuliskan $y = x + \frac{1}{x}$.

1. The problem states that the terms in the sequence increase by the same amount each time, meaning it is an arithmetic sequence. 2. The given terms are 12, ___, 26, ... and we nee

1. **State the problem:** Find the measure of the inner angle formed by the hour hand and the minute hand at exactly 8:20. 2. **Formula and rules:**

1. **Stating the problem:** We have two arithmetic sequences representing daily targets for two projects over 15 days.

1. **State the problem:** Find the value of $x$ in the equation $$\frac{6^{16} \times 6^{2}}{6^{9} \times 6^{4}} = 6^{x}$$.

1. **Stating the problem:** Simplify the expression $$\frac{12p^4 \times 3q^{-3}}{\frac{18p}{q^5}}$$. 2. **Write the expression clearly:**

1. The problem asks to find the result of the expression: $$\frac{5}{81} \times \frac{3}{8} \times \frac{5}{64} \times \frac{5}{94} \div \frac{1}{27} \times \frac{1}{1}$$

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Simplify and understand the function $f(x) = (x \cdot x^2 + 3x - 1)^3$. 2. **Rewrite the expression inside the parentheses:** Note that $x \cdot x^2 = x^{

1. **Énoncé du problème :** Calculer la valeur de $A = \frac{15}{7} \times \frac{2}{3} \times \frac{11}{5}$ et écrire le résultat sous forme de fraction irréductible. 2. **Formule