🧮 algebra

1. **State the problem:** We are given that 5 grams of gold costs 2.963 rm. We need to find the cost of 1 gram of gold. 2. **Formula used:** To find the cost per gram, we use the u

1. The problem is to simplify the expression T5, which appears to be a variable or term labeled T5. 2. Since T5 is a single term without any operations or additional context, it is

1. مسئله: حل معادله $2x + 3 = 11$. 2. فرمول: برای حل معادله خطی، باید $x$ را تنها کنیم.

1. **State the problem:** We need to find the expression for the function $$F(t) = (t^3 - 2t + 1)(2t^2 + 3t)$$ by expanding and simplifying it. 2. **Formula used:** To multiply two

1. **State the problem:** Find the value of $x$ such that $$9^{3^x} = \sqrt{\frac{1}{27^x}}$$ without using a calculator.

1. **Problem (a): Solve the equation** $$\frac{3}{1-x} - \frac{2}{3x-1} = 0$$. 2. **Step 1: Find a common denominator and combine the fractions.**

1. **Problema:** Calcular los cuadrados y cubos de los números complejos dados. 2. **Fórmulas:**

1. **Problem statement:** Find the degree of the polynomial \( C = 8bc + 12ac + 21 - 6ax + 2ab + 12 - 7ac + 7ab \). 2. **Combine like terms:**

1. **State the problem:** Simplify the expression $2(ab+3)^2 - 7(5 - ab)$. 2. **Recall formulas and rules:** Use the expansion formula for a square:

1. Vous avez demandé de faire plus simple, mais sans contexte précis, je vais expliquer comment simplifier une expression algébrique basique. 2. Supposons que nous avons l'expressi

1. **State the problem:** Simplify the expression $\frac{\sqrt{3}}{\sqrt{3}}$. 2. **Formula and rules:** When dividing two identical non-zero numbers, the result is 1. Also, $\frac

1. **State the problem:** Simplify the expression $$10 \sqrt{20} \times \frac{1}{2 \sqrt{5}}$$. 2. **Recall the formula and rules:** When multiplying and dividing expressions with

1. **State the problem:** Solve the system of linear equations: $$\begin{cases}-4x + y = 6 \\ -5x - y = 21\end{cases}$$

1. **Problem statement:** Factorize the expressions by factoring out the greatest common factor (GCF). 2. **Formula and rules:** To factor out the GCF, find the largest factor comm

1. **State the problem:** Solve the system of equations: $$\frac{1}{2}x + 6y = 12$$

1. **State the problem:** Simplify the expression $x^2 (x^{-1} + y^{-1}) \cdot xy (x+y)^2$. 2. **Recall the rules:**

1. **Problema 11:** $v(r)=\frac{4}{3}\pi r^3$. Fórmula usada: $\frac{d}{dr}(r^n)=nr^{n-1}$.

1. Dada la función $$v(r) = \frac{4}{3} \pi r^3$$ 2. Dada la función $$G(y) = y^{10} + 7y^5 - y^3 + 1$$

1. **State the problem:** Solve the equation $4X - 3 = 2(X + 5)$. 2. **Use the distributive property:** Expand the right side:

1. **State the problem:** Solve the equation $4x - 3 = 2(x + 5)$. 2. **Write the formula and rules:** We use the distributive property and properties of equality to isolate $x$.

1. **Nêu vấn đề:** Chúng ta sẽ tìm hiểu về đơn thức, đa thức và các phép tính đại số cơ bản gồm cộng, trừ, nhân, chia. 2. **Đơn thức:** Là biểu thức đại số gồm một số và một hoặc n