🧮 algebra

1. **State the problem:** We need to eliminate the denominators in the equation $$\frac{2}{3} + 1 = \frac{3}{2}$$. 2. **Identify denominators:** The denominators are 3 and 2.

1. The problem asks to find equivalent fractions for each given fraction with specific denominators. 2. For each fraction $\frac{a}{b}$, find the factors to get the new denominator

1. The problem asks to find the inverse function of $f(x) = x + \frac{2}{3}$.\n\n2. To find the inverse function $f^{-1}(x)$, start by replacing $f(x)$ with $y$: $$y = x + \frac{2}

1. We are asked to multiply $3.4 \times 10^2$ by $4 \times 10^4$. 2. Multiply the decimal parts: $3.4 \times 4 = 13.6$.

1. The problem is to solve the equation $$3x = x - 9$$ for the variable $$x$$. 2. Start by subtracting $$x$$ from both sides to get all terms with $$x$$ on one side:

1. Calculate $6^5$. This means multiplying 6 by itself 5 times: $$6^5 = 6 \times 6 \times 6 \times 6 \times 6.$$\n2. Compute step-by-step: $$6 \times 6 = 36,$$ $$36 \times 6 = 216,

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