🧮 algebra

1. **State the problem:** Simplify the expression $ (3x + 2x)(5x + 1x) $. 2. **Combine like terms inside each parenthesis:**

1. **State the problem:** Divide the polynomial $$9x^3 + 24x^2 + 18x + 14$$ by the binomial $$3x + 5$$ and find the quotient and remainder. 2. **Formula and method:** We use polyno

1. **State the problem:** Divide the polynomial $5x^4 - 2x^2 - 13x + 8$ by $x^2 + 1$ to find the quotient and remainder. 2. **Recall the division formula:** For polynomials $f(x)$

1. **State the problem:** We need to find the quotient and remainder when dividing the polynomial $5x^4 - 2x^2 - 13x + 8$ by a divisor. However, the divisor is not specified in the

1. **Problem Statement:** Find the formula for yearly compound amount (CA) for principal Rs. 'P', time 'T' years, and rate of interest R% per annum. 2. **Formula:** The compound am

1. The problem is to evaluate the expression $3 \times \frac{2}{3} - 1 \times \frac{3}{4}$.\n\n2. We use the rule that multiplication of a whole number by a fraction is done by mul

1. مسئله: حل معادله درجه دوم $2x^2 - x - 1 = 0$ برای یافتن جواب‌های $x$. 2. فرمول استفاده شده: معادله درجه دوم به صورت کلی $ax^2 + bx + c = 0$ است و جواب‌ها با فرمول

1. **State the problem:** We are given the algebraic equation $$100 = 5x + 40$$ and need to identify which verbal situations correspond to this equation. 2. **Understand the equati

1. مسئله را بیان می‌کنیم: تابع داده شده به صورت $$f(x) = \frac{1}{x^r - x} + \frac{1}{x^r - 1}$$ است و هدف ما ساده‌سازی یا حل این عبارت است. 2. ابتدا صورت مسئله را بررسی می‌کنیم و

1. **State the problem:** Simplify the expression $-3y + 4 - 7y$. 2. **Identify like terms:** The terms $-3y$ and $-7y$ are like terms because they both contain the variable $y$.

1. Masalah: Memahami konsep perpangkatan eksponen dan cara menyelesaikan soal-soal terkait. 2. Rumus dasar perpangkatan eksponen adalah $$a^m \times a^n = a^{m+n}$$ dan $$\left(a^m

1. The problem asks which graphs do not illustrate a function. 2. Recall the definition of a function: each input (x-value) must correspond to exactly one output (y-value).

1. مسئله: تابع $f(x) = \sqrt[3]{x + 1}$ داده شده است. مقدار تابع $f\big((f(x)-1)^3\big)$ را بیابید. 2. فرمول و قوانین مهم: تابع مکعبی معکوس تابع مکعبی است، یعنی اگر $y = \sqrt[3]{z

1. **State the problem:** Solve the inequality $2x - 3 \leq 11$. 2. **Write the inequality:**

1. **State the problem:** Solve the inequality $6a + 9 \geq 8a - 7$. 2. **Write down the inequality:**

1. **State the problem:** We need to find the commission earned by an employee based on total revenue, sales, and cancellations. 2. **Given data:**

1. The problem asks to insert two arithmetic means between 8 and 20. 2. An arithmetic mean between two numbers is a number that forms an arithmetic progression (AP) with the given

1. **State the problem:** Find the sum of the first 20 terms of an arithmetic progression (AP) where the first term $a_1=7$ and the common difference $d=3$. 2. **Formula used:** Th

1. Problem: Calculate the value of the expression $3 \times \frac{2}{5} + \frac{2}{3}$. 2. Formula and rules: To add fractions, they must have a common denominator. Multiplication

1. Stating the problem: Simplify the expression $$\left(\frac{2}{5}\right)^{-3} \times \left(\frac{2}{5}\right)^3 + \left(\frac{3}{5}\right)^5 \times \left(\frac{3}{5}\right)^{-5}.

1. **State the problem:** We need to find the amount owed after 10 years on a loan of 2000 at an 18% annual interest rate, compounded quarterly. 2. **Formula used:** The compound i