🧮 algebra

1. **State the problem:** We need to find values of $x$ and $y$ such that the matrices $$\begin{pmatrix}-1 & -5x \\ 2y & 3\end{pmatrix} = \begin{pmatrix}-1 & 1 - 6y \\ 2 - 6x & 3\e

1. **Problem:** Find the next number in the sequence: -4, -1, 4, 11, 20, ... 2. **Step 1:** Identify the pattern by finding the differences between consecutive terms:

1. Problem: Find the next number in the sequence -4, -1, 4, 11, 20, .... 2. To find the next number, observe the pattern of differences between consecutive terms:

1. مسئله: مقدار عبارت $$\left(2x - 9\right)^2$$ را بیابید. 2. فرمول مورد استفاده: مربع یک عبارت به صورت $$\left(a - b\right)^2 = a^2 - 2ab + b^2$$ است.

1. مسئله را بیان می‌کنیم: می‌خواهیم مقدار عبارت $\sqrt{x}(2x - 9x^2)$ را ساده کنیم. 2. ابتدا توجه کنیم که $\sqrt{x}$ همان $x^{\frac{1}{2}}$ است.

1. **Problem Statement:** Find the Highest Common Factor (HCF) of 16, 20, and 70 using the long division method. 2. **Formula and Rules:** The HCF of two or more numbers is the lar

1. **State the problem:** Solve the system of complex equations:

1. **State the problem:** Solve the system of complex linear equations: $$2z + w = 4 + i$$

1. **State the problem:** We want to find the set $A = \{x \in \mathbb{R} \mid -1 \leq \frac{x-1}{2} < 3\}$. 2. **Understand the inequality:** The set $A$ contains all real numbers

1. Bài toán yêu cầu giải lại câu b theo kiến thức lớp 9 học kỳ 1. 2. Thông thường, kiến thức lớp 9 hk1 liên quan đến phương trình bậc nhất, bậc hai, hoặc hệ phương trình đơn giản.

1. The problem is to determine if the value of $a$ can be 58 based on given conditions or equations. 2. To decide if $a=58$ is possible, we need the specific equation or context wh

1. **State the problem:** Miss Lee had $12.50 more than Miss Mak initially. After Miss Lee spent $18, Miss Mak had 3 times as much money as Miss Lee had left. We need to find how m

1. Теңдемени чыгаргыла: а) $2\cdot 3^{x-6} + 6\cdot 9^{0.5x-2} = 56$ 2. Бул теңдемени чечүү үчүн, алдымен $9^{0.5x-2}$-ни $3$ негизинде жазалы. Себеби $9 = 3^2$, ошондуктан:

1. **State the problem:** We are given the function $$y = \left(\frac{6}{x}\right)^2$$ and need to understand its behavior. 2. **Rewrite the function:** Using the property of expon

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations to both sides of the equation.

1. The first problem is to express the function given by $y = \left(\frac{6}{x}\right)^2$. 2. This means $y = \frac{36}{x^2}$ because squaring the fraction squares both numerator a

1. **Problem Statement:** Given two functions $f(x) = x^3$ and $g(x) = x + 1$, find the nature of the composite function $(g \circ f)(x) = g(f(x))$. 2. **Formula and Explanation:**

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **Stating the problem:** Solve the equation $$2x^r - ax^r - v = 0$$ for $x^r$ and find $x$. 2. **Rewrite the equation:** Let $$t = x^r$$, then the equation becomes $$2t - a t -

1. The problem appears to involve solving the equation $$(x - 9)^2 = 81$$. 2. This is a quadratic equation in the form $$(x - a)^2 = b^2$$, which can be solved by taking the square

1. The problem is to understand and express the function $\cosh^n(x)$, which means the hyperbolic cosine of $x$ raised to the power $n$. 2. Recall the definition of hyperbolic cosi