🧮 algebra

1. **State the problem:** Resolve the expression $$\frac{3x^2 - x + 8}{(x+4)(x^2+4)}$$ into partial fractions. 2. **Set up the partial fractions:** Since the denominator has a line

1. نكتب العدد ٦/١٠ على صورة كسر عشري. القاعدة: لتحويل كسر إلى عدد عشري، نقسم البسط على المقام.

1. The problem asks if for part 3, the equation should be $b - a = c - d$ given that $a$ and $c$ are opposite points. 2. To analyze this, let's recall what it means for points to b

1. The problem is to prove the sequence converges and find its limit. 2. Suppose the sequence is defined by a recurrence relation or explicit formula (not provided in the question)

1. First, we need to identify question 2 and its steps 3 and 4. Since the user did not provide the original question 2, I will assume a generic algebraic problem for demonstration.

1. Énoncé du problème : Trouver l'ensemble des solutions réelles de l'inéquation $$(-7x - 4)(2x - 8) < -7x - 4$$. 2. Formule et règles importantes : Pour résoudre une inéquation pr

1. Énoncé du problème : Déterminer l'ensemble des solutions réelles de l'inéquation $$ (7x + 2)^2 \geq (6x + 8)^2 $$.

1. Állapítsuk meg az abszolútérték-függvények hozzárendelési szabályait a megadott grafikonok alapján. 2. Az abszolútérték-függvény általános alakja: $$y = a|x - h| + k$$, ahol $$h

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 $y = |2x + 1|$.