🧮 algebra

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

1. **State the problem:** We need to simplify the expression $$M=\left[(1+\frac{6}{1})(1+\frac{7}{1})(1+\frac{8}{1})(1-\frac{6}{1})(1-\frac{7}{1})(1-\frac{8}{1})\right]^{-1}$$. 2.

1. **State the problem:** Convert the equation $2x + 4y = 8$ into slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Start with the

1. El problema es resolver la ecuación cuadrática $$Y = 5x^2 - 15x - 50$$ para encontrar los valores de $x$ cuando $Y=0$. 2. La fórmula general para resolver ecuaciones cuadráticas

1. El problema es resolver la ecuación cuadrática $$Y = 5x^2 - 15x - 50$$ para encontrar los valores de $x$ cuando $Y=0$. 2. La fórmula general para resolver ecuaciones cuadráticas

1. **State the problem:** We have a complex number $$z = (a - 1) + (a^2 + a - 2)i$$ where $$a$$ is a real number. We want to find the values of $$a$$ for which $$z$$ is purely imag

1. Problema: Risolvere l'equazione (i) del Esercizio 2: $$2 \cdot 3^{7+3x} - 5 = 49$$ 2. Formula e regole: Per risolvere equazioni esponenziali, isoliamo la potenza e applichiamo i