🧮 algebra

1. The problem asks which point lies on the line given by the equation $$y = -x + 4$$. 2. To check if a point $ (x, y) $ lies on the line, substitute the $x$ and $y$ values into th

1. **State the problem:** Factorise the expression $18a^2 - 98$. 2. **Identify common factors:** Both terms have a common factor of 2.

1. **State the problem:** Resolve the following into partial fractions: $$\frac{x}{x^2+x+4}$$ and $$\frac{x-2}{x^2+4x+4}$$

1. The problem asks us to find the form of any point on the line given by the equation $$y = 3x$$. 2. The equation $$y = 3x$$ means that for every value of $$x$$, the value of $$y$

1. **Problem (a): Sketch the graph of** $y = |2x - 3|$. 2. The absolute value function $y = |u|$ outputs the distance of $u$ from zero, so it is always non-negative.

1. We are given the first system of linear equations: $$\begin{cases} 2x_1 + 3x_2 + x_3 = 9 \\ x_1 + 2x_2 + 3x_3 = 6 \\ 3x_1 + x_2 + 2x_3 = 8 \end{cases}$$

1. **Problem statement:** Find a formula for the sum of the first $n$ even positive integers. 2. **Understanding the problem:** The first $n$ even positive integers are $2, 4, 6, \

1. **State the problem:** We are given two functions $f(x) = x^2 + kx$ and $g(x) = \sqrt{x} + 1$. We need to find all values of $k$ such that the compositions satisfy $$(f \circ g)

1. **Nyatakan masalah:** Faktorkan persamaan algebra berikut: i. $5p^2q - 10pq^2$

1. **Énoncé du problème :** Montrer que pour tout $x \in \mathbb{R}$, on a $$-1 \leq \frac{2x}{1+x^2} \leq 1.$$

1. **Problem Statement:** A machine costing 50000 depreciates at a constant rate of 8% per year. 2. **Formula for Depreciation at Constant Rate:**

1. مسئله را بیان می‌کنیم: رابطه‌ای بین c0 و c وجود دارد که باید بررسی شود. 2. ابتدا باید مشخص کنیم که c0 و c چه مقادیری دارند و چه رابطه‌ای بین آن‌ها برقرار است.

1. **Problem Statement:** (a) Sketch the graph of $y = |2x + 1|$.

1. The problem is to simplify the expression $2^4 \times 2^{n+2} - 2 \times 2^{n+2}$ and check if it can be written as $2^4 \times -2 + 2^{n+2} \times 2^{n+2}$. 2. Recall the laws

1. **State the problem:** Given the equation

1. **State the problem:** We have a function defined by the functional equation $$f(x+1) = x - f(x)$$ with the initial condition $$f(1) = 1$$. We need to find $$f(2025)$$. 2. **Und

1. **State the problem:** We have 15 students with exam scores. The mode and median are both 76, the mean score is 80, and the total score of the 7 lowest-scoring students is 515.

1. Let's clarify the concept of exponents. 2. When a number has no visible exponent, it actually means the exponent is 1, not 0.

1. **State the problem:** We are given two equations of lines: $$-7x - 6y = 4$$

1. **State the problem:** Solve the system of linear equations: $$-3y + 4x = 13$$

1. **Problem 1:** Find the quotient and remainder when $6x^4 + x^3 - x^2 + 5x - 6$ is divided by $2x^2 - x + 1$. 2. **Problem 2:** Find the quotient and remainder when $2x^4 + 1$ i