🧮 algebra

1. **Problem:** Solve the quadratic equation $x^2 + 3x + 9 = 0$. 2. **Formula:** Use the quadratic formula:

1. **State the problem:** Solve the quadratic equation $x^2 + 3x + 2 = 0$. 2. **Formula and rules:** The quadratic formula to solve $ax^2 + bx + c = 0$ is:

1. **Problem Statement:** Find $n$ such that $$\frac{x^{n-5}+y^{n-5}}{x^{n-6}+y^{n-6}}$$ is the Harmonic Mean (H.M.) between $x$ and $y$. 2. **Recall the Harmonic Mean formula:**

1. لنبدأ بكتابة المتباينة المعطاة: $$4 \geq x > 9$$. 2. هذه المتباينة تعني أن $x$ أصغر أو يساوي 4 وأكبر من 9 في نفس الوقت.

1. Énoncé du problème : Résoudre l'équation quadratique suivante $$2x^2 - 4x - 6 = 0$$. 2. Formule utilisée : Pour résoudre une équation quadratique de la forme $$ax^2 + bx + c = 0

1. **State the problem:** We want to find the partial fraction decomposition of the rational expression $$\frac{x^4 - 2x^3 + 8}{x^2(x - 2)}$$.

1. Masalah yang diberikan adalah menentukan jumlah solusi dari sistem persamaan simultan dengan dua variabel, di mana satu persamaan adalah linear dan yang lain adalah polinomial k

1. Masalah yang diberikan adalah mencari jumlah solusi dari sistem persamaan simultan dengan dua variabel, di mana satu persamaan adalah linear dan yang lain adalah polinomial kubi

1. **State the problem:** We are given the system of equations:

1. **State the problem:** Solve the equation $3^{x+y} = \sqrt[3]{27}$ for $x+y$. 2. **Recall the properties of exponents and roots:** The cube root of a number $a$ is $a^{1/3}$, so

1. **State the problem:** We need to find an unknown number $x$ such that the product of $x$ and 4 is less than 35, and $x$ is divisible by 4. 2. **Write the inequality:** The prod

1. **State the problem:** We have the sequence 1, 12, 23, 34, 45, ? and need to find the number that fits in place of the question mark. 2. **Analyze the pattern:** Look at the dif

1. Let's start by understanding what a vertical asymptote is. 2. A vertical asymptote occurs in a function when the function approaches infinity or negative infinity as $x$ approac

1. **State the problem:** Simplify the expression $$\frac{3x - 1}{1 - 3x}$$. 2. **Recall the rule:** When you have a fraction with a numerator and denominator that are negatives or

1. **Problem:** Find the asymptotes of the rational function $$y = \frac{x^2 + 12x + 35}{3x^2 + 19x + 20}$$. 2. **Vertical asymptotes:** These occur where the denominator is zero (

1. The problem states that the sequence $a_n = 3^n$ for $n \geq 2$ satisfies the recurrence relation: $$2a_{n-1} - a_{n-2} = a_n$$

1. **State the problem:** Max starts with $9.89236 \times 10^{923738393930237303939227837338388}$ candy bars and gives away $5.35 \times 10^{8227383738389272}$ candy bars. We need

1. The problem is to solve for the constants in an equation or expression, but the specific equation is missing from your message. 2. To solve for constants, we typically need an e

1. The problem is to solve the second question of q2, but since the exact question is not provided, I will assume a typical algebraic problem for demonstration. 2. Let's consider t

1. **Problem:** Find the value of $$(256)^{0.16} \times (256)^{0.09}$$. 2. **Formula:** When multiplying powers with the same base, add the exponents:

1. **State the problem:** Find the domains of the functions $$f(x) = \sqrt[4]{x - 9}$$ and $$g(x) = \sqrt[3]{3x - 9}$$ and express them in interval notation. 2. **Recall domain rul