🧮 algebra

1. **Problem:** Multiply the rational expressions $\frac{5y^3}{32x} \times \frac{-4}{15x^2 y^3}$ and simplify. 2. **Step 1: Factor all numerators and denominators completely.**

1. **State the problem:** Simplify the expression $5y^3 \cdot 32x - 4 \cdot 15x^3y^3$. 2. **Rewrite the expression clearly:**

1. **Problem:** Solve the equation $k(2k + 5) = 3$. 2. **Formula and rules:** This is a quadratic equation. Expand and rearrange to standard form $ax^2 + bx + c = 0$.

1. **State the problem:** We are given three points $(x, y)$ with $x$ values $-34$, $-17$, and $0$, and corresponding $y$ values $t$, $t + 29$, and $t + 58$, where $t$ is a constan

1. **State the problem:** We are given the system of equations: $$x - 3y = -9$$

1. The problem asks which numbers are greater than $$-\frac{185}{100}$$. 2. First, convert $$-\frac{185}{100}$$ to decimal: $$-\frac{185}{100} = -1.85$$.

1. **State the problem:** We are given the quadratic expression $p = n^2 + 21$ and need to find the value of $p$ for specific values of $n$. 2. **Formula:** The formula is $p = n^2

1. **State the problem:** Calculate the product of $\frac{7}{9}$ and $-\frac{9}{8}$. 2. **Formula used:** When multiplying fractions, multiply the numerators together and the denom

1. **Problem Statement:** Solve the determinant equation for part (a): $$\begin{vmatrix} 1 & 4 & 4 \\ 1 & -2 & 1 \\ 1 & 2x & x^2 \end{vmatrix} = 0$$

1. **State the problem:** Solve the system of linear equations: $$\begin{cases}-4r - 6s - 5t = 1 \\ -r + s - 2t = 2 \\ r - 3s + t = -5 \end{cases}$$

1. مسئله: بررسی درست یا نادرست بودن عبارت الف) معادله $x^4 - 5x^2 + 6 = 0$ دارای دو ریشه حقیقی متمایز است. 2. برای حل معادله $x^4 - 5x^2 + 6 = 0$، از جایگزینی $y = x^2$ استفاده می‌

1. مسئله: در محور اعداد نقطه A بین 2 و 3 قرار دارد. عددی که A نشان می‌دهد چیست؟ 2. برای تعیین مقدار A، باید موقعیت دقیق آن را روی محور اعداد بررسی کنیم. از نمودار مشخص است که A نزد

1. **Simplify using product law** (i) Simplify $\left(\frac{5}{4}\right)^2 \times \left(\frac{3}{7}\right)^4$

1. Let's start by stating the problem: Understanding ratio and proportion as explained in the 'The Leading' maths book for class eight. 2. A ratio is a comparison of two quantities

1. **Problem 1:** Factorize the cubic polynomial $x^3 - 13x^2 + 24x + 108$ given that one factor is $(x + 2)$. We want to find the other two factors. 2. Use polynomial division or

1. **State the problem:** Simplify the complex nested fraction expression given: $$\frac{\frac{1 + \frac{1}{3}}{1 + \left(2 - \frac{1}{3}\right)}}{\frac{1 - \left(2 - \frac{1}{2}\r

1. **State the problem:** We need to rewrite the given expression in a clean, readable format. 2. **Given expression:**

Let's look at the graph edges step by step! 🎉 **Step 1:** Imagine you have 6 vertices: $v_1, v_2, v_3, v_4, v_5, v_6$.

1. **State the problem:** Solve the equation $\frac{x}{2} + 1 = 3$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing invers

1. **Problem Statement:** A trader mixes 26 kg of rice costing 20 per kg with 30 kg of rice costing 36 per kg. He sells the mixture at 30 per kg. We need to find his profit percent

1. **Problem statement:** For the number 252, find the smallest whole number to multiply it by to get a perfect square, then find the square root of that perfect square. 2. **Step