🧮 algebra

1. **Stating the problem:** We are given the sum formula for a series:

1. The problem is to solve the equation $$0 = -\frac{5}{4}(x - \frac{6}{5})$$ for $x$. 2. The equation is in the form $$0 = a(b)$$ where $a = -\frac{5}{4}$ and $b = (x - \frac{6}{5

1. The user request is vague, so let's clarify by showing a simple example of calculations: solving a quadratic equation. 2. Problem: Solve the quadratic equation $$x^2 - 5x + 6 =

1. **State the problem:** We want to find the sum to infinity of the series $$1 - 2x^2 + 3x^3 - 4x^4 + \cdots$$ given that $$|x| < 1$$. 2. **Identify the series type:** This is an

1. **State the problem:** Solve the equation $$-\frac{1}{2} = \frac{3}{2}k + \frac{3}{2}$$ for $k$. 2. **Write down the equation:**

1. **State the problem:** Simplify the expression $3x \times 4 + 2x \times 3 - 4x \times 2 + x + 5$. 2. **Recall the distributive property:** Multiplying a variable by a number mea

1. The problem states the cubic equation $$4x^3 + 3x^2 + 2x = 12$$ and mentions finding its roots. 2. The solution approximates the only real root as $$x \approx 1.136$$ by testing

1. **Problem 1:** (a) Check if set A is a subset of set B.

1. **Problem Statement:** Solve the system of linear equations for each case (b to f) using the matrix method (Gaussian elimination). 2. **Formula and Rules:**

1. **State the problem:** Convert the quadratic function $y = 3x^2 - 12x + 1$ into vertex form and identify the vertex. 2. **Recall the vertex form:** The vertex form of a quadrati

1. **State the problem:** We are given the quadratic function $y = 3x^2 - 12x + 1$ and asked to rewrite it in vertex form and identify the vertex. 2. **Recall the vertex form:** Th

1. Problem b: Solve the system {

1. **State the problem:** We have a rectangle where the length is three times the width, and the perimeter is 96 cm. We need to find the length and width and label the rectangle ac

1. The problem is to solve the cubic equation $$4x^{3}+3x^{2}+2x=12$$ or equivalently $$4x^{3}+3x^{2}+2x-12=0$$. 2. The solution correctly identifies this as a cubic equation and a

1. **State the problem:** Solve the system of linear equations using matrix inverse or Cramer's rule. Given:

1. The problem is incomplete as only "A=" is given without any expression or value. 2. To solve or simplify an algebraic expression, we need the full expression or equation.

1. The problem is to understand or find the value of the variable $A$. 2. Since the user only provided "A=", it appears incomplete and lacks context or an equation.

1. **Problem Statement:** We have a rectangle with length $6x - 1$ and breadth $x - 2$. Both length and breadth are increased by 4 meters, and the new area is three times the origi

1. **State the problem:** Solve the cubic equation $$4x^{3} + 3x^{2} + 2x = 12.$$ 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem is to simplify the expression $2 \log_5 0.5 - \log_5 0.25$. 2. Recall the logarithm rules:

1. The problem involves verifying the algebraic identity and performing arithmetic and algebraic simplifications. 2. First, recall the difference of squares formula: $$(a+b)(a-b) =