🧮 algebra

1. **State the problem:** Solve the equation $$30000x + 67500y + 30000xy = 39375$$ for one variable in terms of the other. 2. **Rewrite the equation:** Group terms involving $x$:

1. **State the problem:** Solve the equation $2m + 5 = 10$ for $m$. 2. **Formula and rules:** To solve for $m$, isolate the variable by performing inverse operations. Subtract 5 fr

1. The user asks for an answer in a style that helps them learn how to do it themselves. 2. Since no specific math problem is given, I will provide a general example of solving a s

1. **Problem Statement:** Solve the system of linear equations: $$\begin{cases} 3x_1 + x_2 + x_3 = 8 \\ x_1 + 4x_2 + 2x_3 = 15 \\ 2x_1 + x_2 + 5x_3 = 19 \end{cases}$$

1. **State the problem:** Solve the equation $8k - 1 = 15$ for $k$. 2. **Write the formula and rules:** To solve for $k$, isolate $k$ on one side of the equation by performing inve

1. **State the problem:** Find the inverse function of $f(x) = 7x^3 - \frac{2}{20}$ where $x \in \mathbb{R}$. 2. **Rewrite the function:** Simplify the constant term: $f(x) = 7x^3

1. The problem is to analyze the function $f(x) = \frac{10}{7x^3 - 2}$ where $x \in \mathbb{R}$. 2. This is a rational function where the numerator is a constant 10 and the denomin

1. The problem asks to find the inverse function of \( f(x) = \frac{10}{7x^3} - 2 \) where \( x \in \mathbb{R} \). 2. To find the inverse function \( f^{-1}(x) \), we start by sett

1. **State the problem:** We need to find the mean daily wage of all workers in the company. 2. **Given data:**

1. **State the problem:** Find the equation of the tangent line to the circle given by $$x^2 + y^2 + 14x + 18y - 39 = 0$$ at the point in the second quadrant where $$x = -2$$. 2. *

1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula or factorization to solve quadratic equations. The quadratic formula is:

1. **Énoncé du problème :** Résoudre l'équation $\frac{1}{15x} - 11 = 7x + 5$ pour $x$. 2. **Formule et règles importantes :** Pour résoudre une équation, on cherche à isoler $x$ e

1. **Problem:** Find the equation of the tangent line to the circle $$x^2 + y^2 + 14x + 18y - 39 = 0$$ at the point in the second quadrant where $$x = -2$$. 2. **Rewrite the circle

1. **Énoncé du problème :** Résoudre l'équation $15x - 11 = 7x + 5$ pour $x$. 2. **Formule et règles :** Pour résoudre une équation linéaire, on regroupe les termes en $x$ d'un côt

1. **State the problem:** Simplify the expression $(5 + \sqrt{12})(11 + \sqrt{3})$ and write it in the form $a + b\sqrt{3}$, where $a$ and $b$ are integers. 2. **Recall the formula

1. **Problem statement:** Majid pays a total of 51520 for his car insurance, which includes a basic charge plus 15% sales tax. We need to find the amount of sales tax Majid pays. 2

1. **Problem statement:** We have three players: Archie, Evelyn, and Jacob. Initially, their counters are in the ratio 7 : 5 : 6. At the end, the ratio changes to 4 : 3 : 5. We kno

1. The problem asks: "How many did he start with?" which implies we need to find the initial quantity of something. 2. To solve such problems, we often use the formula for initial

1. **State the problem:** Simplify the expression $7 - \{6 - 12 \div (5 + 9 \times 2 - 19)\}$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication

1. The problem involves comparing two ratios: $7:5:6$ and $4:3:5$, and a number $12$ is given, likely to be used in relation to these ratios. 2. To understand the relationship, we

1. The problem is to understand the number 25 and its properties. 2. 25 is a perfect square number because it can be expressed as $5^2$.