🧮 algebra

1. Nelygybės $x > -4$ sveikieji neigiami sprendiniai yra tie skaičiai, kurie yra maži už $-4$ arba mažesni, bet neigiami ir sveikieji. Sveikųjų neigiamų skaičių intervalas nuo $-3$

1. **State the problem:** Given positive real numbers $a$, $b$, and $c$ satisfying $$\frac{a}{a+b} = \frac{a+b}{a+b+c} = \frac{c}{b+c}$$

1. First, we state the problem: Given integers $m$ and $n$ with $1 < m \le n$, define $$f(m, n) = \left(1 - \frac{1}{m}\right) \times \left(1 - \frac{1}{m + 1}\right) \times \cdots

1. Masalah yang diberikan ialah ketaksamaan: $$-5x < 15$$. 2. Untuk menyelesaikan ketaksamaan ini, kita perlu membahagikan kedua-dua pihak dengan $$-5$$.

1. Stating the problem: Simplify the expression $\frac{7}{8} + \frac{4}{1} \div 4 + \frac{15}{16}$. 2. First, evaluate the division part: $\frac{4}{1} \div 4 = \frac{4}{1} \times \

1. The problem asks to solve the inequalities involving absolute values: (i) \(|x| < 2\)

1. **State the problem:** We have positive real numbers $a$, $b$, $c$ such that $$\frac{a}{a+b} = \frac{a+b}{a+b+c} = \frac{c}{b+c}$$

1. **State the problem:** We are given a sequence of values $a_1 = 16944930$, $a_2 = 36736961$, $a_3 = 42442472$, $a_4 = 418656672$, $a_5 = 435042998$. We want to find the common d

1. **State the problem:** We have two quadratic equations: - Equation 1: $2x^2 - mx + 8 = 0$ with roots $\alpha$ and $\beta$.

1. We are given the system of equations: $$xy=12$$

1. The problem is to solve the simultaneous equations. Since the specific equations are not provided, I will explain the general method. 2. Suppose the simultaneous equations are:

1. The problem requires the lumber quantity to be an integer value. 2. Let's assume the previous question involved calculating the amount of lumber needed as a number, possibly a d

1. **State the problem:** You have 3 lumber units to spend. Each lumber can buy 160000 HP directly.

1. The problem is to verify whether the correct fraction is $\frac{135}{574}$ or $\frac{135}{287}$.\n\n2. Check if $\frac{135}{287}$ can be simplified or if it matches any known so

1. **State the problem:** You have 50 lumber to allocate between hp and defense (def). Each lumber gives 160k hp or 640 def. Each point of defense increases hp by 2%. 2. **Define v

1. Let's understand your problem: You have 1000 units of lumber and want to allocate it somehow. 2. To help, I need more information about how you'd like to allocate it. For exampl

1. Masalah yang diberikan adalah mencari faktor bagi dari 32. 2. Faktor bagi adalah nombor yang boleh membahagi nombor tertentu tanpa meninggalkan baki.

1. Simplifica cada expresión aplicando las propiedades de potencias. ### a. $$\frac{(-4)^8}{(-4)^3}$$

1. Problema: Simplificar la expresión $\frac{(-4)^8}{(-4)^3}$ utilizando propiedades de la potenciación. Paso 1: Aplicar la propiedad $\frac{a^m}{a^n} = a^{m-n}$.

1. The problem involves understanding why the answer is $\frac{135}{574}$. 2. Without more context, we assume a fraction was simplified or derived from a probability or ratio calcu

1. **Problem Statement:** We see a polynomial curve $p(x)$ that crosses the x-axis before $x=1$, has a local maximum between $x=1$ and $x=2$, and then a local minimum near $x=2$. A