🧮 algebra

1. **State the problem:** Simplify the expression $$-\cos^4 x + 4 \sin x - \frac{4}{3} \sin^3 x$$ and check if it equals $$\frac{1}{4} \cos^4 x$$. 2. **Recall identities:** Use the

1. **Stating the problem:** A notebook costs floui times the price of a pencil. The pencil costs 30p less than the notebook. We need to find the price of the notebook. 2. **Define

1. **State the problem:** Solve the equation $$-\frac{25}{16}a = -\frac{7}{4}$$ for $a$. 2. **Formula and rules:** To solve for $a$, we need to isolate $a$ by dividing both sides o

1. **State the problem:** Joe and Frank have the same amount of money initially. We want to find how much Joe must give Frank so that Frank has 10 cedis more than Joe. 2. **Define

1. **State the problem:** Solve the equation $$2 \arcsin(x^2 - 3x + 1) + \pi = 0$$ and find the sum of all values of $x$ that satisfy it. 2. **Isolate the arcsin term:**

1. Bài toán yêu cầu tính tổng tất cả các phần tử của ma trận nghịch đảo $A^{-1}$ với ma trận $A = \begin{bmatrix} 2 & 9 \\ 3 & 13 \end{bmatrix}$.\n\n2. Công thức tính ma trận nghịc

1. **State the problem:** Solve the equation $$-\frac{25}{16}a = -\frac{7}{4}$$ for $a$. 2. **Formula and rules:** To solve for $a$, we need to isolate $a$ by dividing both sides o

1. Bài toán yêu cầu tìm giá trị của $m$ để ma trận $$A = \begin{bmatrix} 1 & 0 & 3 \\ m & 5 & 3 \\ 2 & 0 & m \end{bmatrix}$$ không khả nghịch. 2. Một ma trận vuông không khả nghịch

1. The problem is to solve the equation given by the user. However, no specific equation was provided, so I will demonstrate solving a simple algebraic equation as an example: Solv

1. مسئله: عبارت $$\frac{(y001)^4 \cdot (0003)^\alpha}{12000}$$ را با استفاده از خواص توان‌ها تجزیه و ساده کنیم. 2. ابتدا باید بدانیم که اعداد داخل پرانتز را به صورت عددی ساده کنیم:

1. The problem is to explain why the equation $y = x + 9$ is a linear equation. 2. A linear equation in two variables $x$ and $y$ can be written in the form $$y = mx + b$$ where $m

1. Stating the problem: Evaluate the expression $\frac{\sqrt{(32)(165)(37)}}{\sqrt{25}\,(46)(53)} - 5\sqrt{(34)(37)}$. 2. Formula used: Use the product rule for square roots $\sqrt

1. The problem asks for the equation of a straight line passing through the point $(1, 5)$ and parallel to the line $y = -2x + 3$. 2. Recall that parallel lines have the same slope

1. We are asked to express each given rational function as partial fractions. 2. The general approach for partial fractions is to decompose a rational function \( \frac{P(x)}{Q(x)}

1. The problem asks for the equation of a straight line passing through the point $(1, 5)$ and parallel to the line $y = -2x + 3$. 2. Recall that parallel lines have the same slope

1. **Stating the problem:** Find the points of intersection between the two functions $$f_1(x) = x^2 - 4$$ and $$f_2(x) = x + 2$$. 2. **Formula and approach:** To find intersection

1. **State the problem:** Factorise the expression $5X^2 - 25XY$. 2. **Identify common factors:** Both terms have a common factor of $5X$.

1. The problem is to simplify the expression $a2$. 2. Assuming $a2$ means $a \times 2$, the expression can be rewritten as $2a$.

1. **State the problem:** Solve the equation $2x + 3x = 10$. 2. **Combine like terms:** Since both terms on the left side have $x$, add their coefficients: $2x + 3x = (2 + 3)x = 5x

1. **State the problem:** We know that $y$ varies directly as $x$ and inversely as the square of $z$. Given $y=8$ when $x=4$ and $z=1$, find $y$ when $x=9$ and $z=3$. 2. **Write th

1. Let's start by stating the problem: You want to understand how to combine like terms to solve equations. 2. Combining like terms means adding or subtracting terms that have the