🧮 algebra

1. We are given the equation $1252^x = 1$ and asked to solve for $x$. 2. Recall that any nonzero number raised to the power $0$ is equal to $1$, so $a^0 = 1$ for $a \neq 0$.

**Problem 1:** Given matrices $$A=\begin{bmatrix}3 & 2 \\ -1 & 5\end{bmatrix}, \quad B=\begin{bmatrix}2 & -4 \\ 3 & 1\end{bmatrix}$$

1. The problem asks to find the real solutions of the inequality $x - 3 \leq 2$ where $x$ is the real part of the complex number $z = x + ij$. 2. To solve the inequality, isolate $

1. Stating the problem: Solve the quadratic equation $x^2 + 4x + 4 = 0$.\n\n2. Recognize this is a quadratic equation in standard form $ax^2 + bx + c = 0$ where $a=1$, $b=4$, and $

1. The problem is to solve the quadratic equation $x^2 + 4x + 4 = 0$. 2. First, recognize that the quadratic can be factored as a perfect square trinomial.

1. The problem involves plotting multiple quadratic equations to form a butterfly shape. 2. Each equation represents a part of the butterfly: right wing, left wing, upper and lower

1. Stating the problem: We analyze the function $$y=3x+1-4(3x+1)^{\frac{1}{2}}.$$\n\n2. Simplify and understand each term: The function is composed of a linear term $$3x+1$$ and a

1. សូមបញ្ជាក់បញ្ហា៖ យើងត្រូវគណនា $z = -2i^3 + i^{2024}$ និងប្រៀបធៀបជាមួយជម្រើសដែលបានផ្តល់ដូចជា ក. $1 + 2i$, ខ. $1 - 2i$, គ. $i$, ឃ. $2 - i$

1. The problem involves the expression $k_1 = \frac{x}{4}$ and the equation $\frac{x}{4} u1.5h + x = \frac{x}{\frac{x}{2}} u1.5, 8x$. 2. We first clarify each part: $k_1 = \frac{x}

1. **Problem:** Engr. Lota buys two square lots with unequal sides. The total area is 4,703 m², and enclosing them together requires 282 m fencing forming a hexagon. Find the lengt

1. Stating the problem: Simplify and factor the expressions $(x+6)^2$ and $x^2 - 36$. 2. Expand and simplify $(x+6)^2$:

1. **State the problem:** Simplify the expression $$\frac{x^2 - 9}{x + 3}$$. 2. **Factor the numerator:** Notice that $$x^2 - 9$$ is a difference of squares, so we can write it as

1. Let's begin with the expression you want to simplify. Please provide the specific expression so that I can assist you accurately. 2. Simplification typically involves combining

1. The problem is to simplify the expression $$\frac{x^2 - 9}{x + 3}$$. 2. Recognize that the numerator is a difference of squares: $$x^2 - 9 = (x - 3)(x + 3)$$.

1. **State the problem:** Find values of $m$ for which the line $y=mx-6$ is tangent to the curve $y=x^2-4x+3$, and find the points of tangency. 2. **Set the line equal to the curve

**Problem Set 3.2: Addition and Subtraction of Polynomials** 1. Add $(3m - 5k - h) + (-6m + 4k - 5h)$

1. Let's state the problem: Solve the inequality $$\frac{2 - x}{2} > -1$$. 2. Multiply both sides by 2 (which is positive, so inequality direction remains the same):

1. **Problem Statement:** We are given a sequence defined by the general term $$x_n = \frac{5n + 6}{5n}$$ and asked to analyze it. 2. **Simplify the expression:**

1. Simplify the expression $$\frac{2^{10} \cdot 3^{15}}{9 \cdot 3^{10} \cdot 12}$$ - Rewrite the bases: $$9 = 3^2, \quad 12 = 2^2 \cdot 3$$

1. Simplify $2^4 \cdot 2^{-1}$. Using the exponent rule $a^m \cdot a^n = a^{m+n}$:

1. **State the problem:** Kialani sells orchids and lilies at different prices. We know: