🧮 algebra

1. Planteamos el problema: Dividir el polinomio $$1000x^6 + 90x^4 + 110x^3 + 10x^2 + 40x + 50$$ entre $$100x^3 - x + 1$$ y hallar el mayor coeficiente del resto. 2. Usamos la divis

1. **State the problem:** We are given the function $$y=\frac{1}{x-3}$$ and want to understand its behavior and key features. 2. **Formula and rules:** This is a rational function

1. **State the problem:** Solve the quadratic equation $$q_i^2 + 2q_i p_i - 2q_i = 0$$ for $q_i$, where $q_i$ and $p_i$ are allele frequencies. 2. **Rewrite the equation:** Factor

1. **State the problem:** We need to multiply the expression $9(c + 2d)$ using the area model and find the partial products. 2. **Recall the distributive property:** The distributi

1. **State the problem:** We want to multiply $7(20r + 10)$ using the area model. 2. **Formula used:** The distributive property states that $a(b + c) = ab + ac$.

1. **State the problem:** Given the functions \(f(x) = 3x - 7\), \(g(x) = 2x^2 - 3x + 1\), \(h(x) = 4x + 1\), and \(k(x) = -x^2 + 3\), find the value of \(f(x) - g(x)(-2)\). 2. **R

1. The problem is to solve the equation $9.0 = 9.6 + \log \frac{x}{0.1 - x}$ for $x$. 2. Start by isolating the logarithmic term:

1. **State the problem:** We are given four functions: $$f(x) = 3x - 7, \quad g(x) = 2x^2 - 3x + 1, \quad h(x) = 4x + 1, \quad k(x) = -x^2 + 3$$

1. The problem asks to find the value of the expression $5x^2 + 2x - 3$ when $x = -1$. 2. The formula is given: $5x^2 + 2x - 3$. We substitute $x = -1$ into the expression.

1. The problem asks to match each given value with its equivalent decimal, fraction, or percent. 2. We start by understanding equivalences:

1. **State the problem:** Solve the equation $2x - 5y = -7$ for $y$ in slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Isolate $

1. **State the problem:** Solve the equation $x - 8 = 20$ for $x$. 2. **Formula and rule:** To isolate $x$, add 8 to both sides of the equation. This uses the addition property of

1. **Énoncé du problème :** Soit la fonction $f$ définie sur $\mathbb{R} \setminus \{-1,1\}$ par :

1. Das Problem lautet: Bestimme die Nullstellen der Funktion $f(x) = x^4 - 24x^2$. 2. Wir verwenden die Regel, dass Nullstellen einer Funktion gefunden werden, indem man $f(x) = 0$

1. El problema es encontrar el dominio y rango de la función cuadrática $$y = 5x^2 - 15x - 50$$. 2. El dominio de una función cuadrática es siempre todos los números reales, es dec

1. Stating the problem: Solve the equation $x + 15 = 30$ for $x$. 2. Formula and rules: To isolate $x$, subtract 15 from both sides of the equation.

1. 문제: 지수 방정식 $$2^{2x+2} = 3^{3x+3}$$ 의 해를 구하시오. 2. 지수 방정식은 양변의 밑이 다를 때, 양변에 로그를 취하여 지수 부분을 식으로 변환하는 것이 일반적인 방법입니다.

1. **Problem:** Graph the equation $y = -3x + 2$, determine domain and range, and analyze function properties. 2. **Formula and rules:** This is a linear function of the form $y =

1. **State the problem:** We are given the equation $4t + 0 = 4t$ and need to identify the property it illustrates. 2. **Recall the relevant property:** The equation shows that add

1. The problem states that the length of one side of a square frame is $3x - 7$. 2. We need to find the perimeter of the square. The perimeter $P$ of a square with side length $s$

1. **State the problem:** List all the factors of the number 94. 2. **Recall the definition:** Factors of a number are integers that divide the number exactly without leaving a rem