🧮 algebra

1. Let's clarify the problem: You want to understand how the equation for a variable $a$ is derived. 2. Typically, equations for variables like $a$ come from applying known formula

1. **Stating the problem:** We are given that a supervisor and 7 workers earn 1560 per month, and 2 supervisors and 17 workers earn 3660 per month. We need to find the monthly wage

1. The problem is to find the range of values of $k$ such that the graphs of $y = |(x+1)(x-3)|$ and $y = x + k$ have exactly two common points. 2. The absolute value function $y =

1. **State the problem:** We need to find the area of the region bounded by the curve $y = x^2 - 4x + 3$ and the x-axis. 2. **Find the points where the curve intersects the x-axis:

1. Planteamos el problema: Se nos da la función de costo total $$C(x) = 0,8x^2 - 288x + 43.781$$ que representa el costo de fabricar $x$ vestidos. 2. Queremos encontrar el costo un

1. The problem asks to identify the points where a straight line cuts both axes. 2. From the graph description, the line passes through (0, 3) on the y-axis and (3, 0) on the x-axi

1. The problem is to solve the equation $-x = -$. However, the equation appears incomplete or incorrectly formatted. 2. To solve an equation like $-x = -a$, where $a$ is a number o

1. **Stating the problem:** Simplify the expression $(x^2)^3 \times x^2$. 2. **Formula used:** When raising a power to another power, multiply the exponents: $\left(a^m\right)^n =

1. **State the problem:** Solve the equation $3x2^x=1$ for $x$. 2. **Rewrite the equation:** The equation is $3x2^x=1$.

1. The user states "answer graph is not like that," which suggests a concern about a graph or function representation. 2. Since no specific function or problem is given, I cannot p

1. The problem asks to find the fourth proportional of the numbers 15, 18, and 25. 2. The fourth proportional $x$ to three numbers $a$, $b$, and $c$ is defined by the proportion $$

1. **State the problem:** Simplify the expression $2\omega + 2\omega^2$ where $\omega$ is a complex cube root of unity. 2. **Recall the properties of cube roots of unity:** The cub

1. **State the problem:** Solve the equation $3x2^{-x} = 2x3^x$ for $x$. 2. **Rewrite the equation:** The equation is $3x2^{-x} = 2x3^x$.

1. **State the problem:** Solve the equation $-10x + 8y = 0$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we use basic algebraic operations: addition, subtrac

1. Masalah yang diberikan adalah menghitung hasil dari $ (2^3)^{-3} $. 2. Gunakan aturan pangkat: $ (a^m)^n = a^{m \times n} $.

1. **Problem:** Calculate $\log(1000 \times 1000)$. **Step 1:** Use the logarithm product rule: $\log(ab) = \log a + \log b$.

1. **State the problem:** Solve the quadratic equation $$x^2 + 8x + 15 = 0$$. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by

1. **State the problem:** Solve the equation $$\frac{9}{6x} + 2 - 3 = 25$$ for $x$. 2. **Simplify the equation:** Combine like terms on the left side:

1. **State the problem:** Solve the equation $6x - 3 = 20$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable on one side by performing inverse ope

1. **State the problem:** Calculate $6.022 \times 10^{23} \times 480 \div 24$. 2. **Write the expression:** $$\frac{6.022 \times 10^{23} \times 480}{24}$$

1. **State the problem:** We are given the quadratic function $$y = 2x^2 - 8x + 3$$ and want to analyze its properties, including vertex and points on the curve. 2. **Formula and r