🧮 algebra

1. The problem presents a sequence: 2, 4, 8, 16, 23, 28, 38, ... and asks to analyze or continue it. 2. To understand the pattern, examine the differences between consecutive terms

1. **Тодорхойлолт:** Ганад 100 болон 500 төгрөгийн дэвсгэрт нийт 44 ширхэг байна. Нийт мөнгөн дүн 12000 төгрөг.

1. The problem is to find the values of $x$ for the quadratic equation $x^2 + 5x + 6 = 0$. 2. We use the factoring method for quadratic equations: if $ax^2 + bx + c = 0$, find two

1. The problem is to find the values of $x$ for the quadratic equation $x^2 + 5x + 6 = 0$. 2. The formula used to solve quadratic equations is the quadratic formula:

1. Problem: Find the next number in the series 50, 40, 31, 24, 18, ... 2. Observe the differences between consecutive terms:

1. The problem is to solve the equation $15$. 2. Since $15$ is a constant and there is no equation or variable to solve for, the solution is simply the value itself.

1. **Problem:** Find the angle between the hour and minute hands at 20:12. 2. **Formula:** The angle between the hour and minute hands is given by

1. **State the problem:** We are given the function $f(x) = \frac{1}{x^2 + 1}$ and want to understand its behavior. 2. **Formula and rules:** The function is a rational function wh

1. **State the problem:** We want to find the number $x$ that maximizes the difference between the number and its square, i.e., maximize the function $$f(x) = x - x^2.$$ 2. **Formu

1. **State the problem:** Calculate the value of the expression $(5 \times 4) + (3 \times 4) - (4 \times 3)$.\n\n2. **Recall the order of operations:** Multiplication and division

1. مسئله: حل معادله $$15 - 2(4 - x^3) - 3(4 - x^3)^2 = 0$$ است. 2. ابتدا متغیر کمکی تعریف می‌کنیم: $$y = 4 - x^3$$.

1. **Problem (b): Show that $A^2 = 5A$ for $A = \begin{bmatrix}-1 & -2 \\ 3 & 6\end{bmatrix}$.** 2. **Calculate $A^2$:**

1. The problem involves understanding the function $f: S \to S$ where $S = \{1, 2, 3, \ldots, 12\}$ and $f$ is onto (surjective). We are asked to analyze or solve something related

1. **State the problem:** Find the domain and range of the function $$f(x)=(x-2)^2+3$$ with the restriction $$x \leq 2$$, and also find the domain and range of its inverse function

1. **State the problem:** Solve the first system of linear equations:

Let's expand and simplify step by step! 🎉 **Step 1:** Imagine you have two groups:

1. **State the problem:** We need to find the value of the sum $$\sum_{n=2}^{43} 900(0.85)^{n-1}$$ and round it to the nearest integer. 2. **Identify the type of sum:** This is a g

1. **State the problem:** We need to find the value of the sum $$\sum_{n=2}^{25} 200(0.85)^{n-1}$$ and round it to the nearest integer. 2. **Identify the type of sum:** This is a g

1. **State the problem:** Simplify the expression $$\frac{1}{3\sqrt[3]{4} + \sqrt{2}}$$. 2. **Recall the formula and rules:** To simplify expressions with roots in the denominator,

1. **State the problem:** Simplify the expression $$\frac{1}{3\sqrt{9 + \sqrt{2}}}$$. 2. **Recall the formula and rules:** To simplify expressions with radicals in the denominator,

1. **State the problem:** Solve the inequality $x + 2 > 2$. 2. **Understand the inequality:** We want to find all values of $x$ such that when we add 2 to $x$, the result is greate