🧮 algebra

1. **State the problem:** Find the root(s) of the polynomial equation $$x(x-2)(x+3) = 18$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Find the roots of the polynomial equation $$x^4 + x^2 = 4x^3 - 12x + 12$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equ

1. **Problem statement for Aufgabe 2a:** Berechne $$\sqrt[4]{6^3} \cdot \frac{1}{\sqrt[4]{6^7}}$$. 2. **Formula and rules:** Wurzeln mit gleicher Wurzelzahl können als Potenzen mit

1. The problem asks for the average rate of change of the function $g(t) = \frac{1}{t}$ between $t=1$ and $t=3$. 2. The formula for the average rate of change of a function $g(t)$

1. **State the problem:** We need to find the average rate of change of the water depth $W$ between $x=100$ days and $x=300$ days. 2. **Formula:** The average rate of change of a f

1. Let's start by understanding the concept of Domain and Range in relations and functions. 2. The domain of a relation or function is the set of all possible input values (usually

1. The problem is to graph the piecewise functions \(f(x)\) and \(g(x)\) defined as follows: \[ f(x) = \begin{cases} -2^x, & x < -4 \\ -|x|, & -4 \leq x \leq 0 \\ 4 - x^2, & x > 0

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **Problem:** Do a factoring example. 2. **Formula used:** A common factoring pattern is the greatest common factor rule:

1. El problema nos pide llenar la tabla para la función $$y = 4x - 1$$ usando la regla dada. 2. La fórmula es $$y = 4x - 1$$, donde para cada valor de $$x$$ calculamos $$y$$ multip

1. El problema nos pide llenar la tabla para la función $$y = -2x + 5$$ usando la regla dada. 2. La fórmula es $$y = -2x + 5$$, donde para cada valor de $$x$$ calculamos $$y$$ sust

1. **State the problem:** Simplify the expression $$6 \div 2(1+2)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. **Problem:** Make a Venn diagram using numbers. 2. A Venn diagram uses overlapping circles to show how numbers can belong to different groups.

1. Vamos resolver a equação \((x - 2)^2 = 8 - 4x\).\n\n2. Primeiro, expandimos o lado esquerdo usando a fórmula do quadrado da diferença: \((a - b)^2 = a^2 - 2ab + b^2\).\n\n3. Ass

1. The problem is to solve a linear equation or expression (please provide the exact problem next time for precise help). 2. The general formula for solving linear equations is to

1. **State the problem:** Jessa's standard hourly pay is 110 pesos. We need to find her overtime pay for 11 hours at a 1.5 multiplier. 2. **Formula used:** Overtime pay per hour =

1. Nyatakan masalah: Kos, $C$, menghasilkan sebuah buku berubah secara langsung dengan bilangan halaman, $h$, dan secara songsang dengan bilangan naskhah, $n$. Diberi kos menghasil

1. The problem states that the cost $C$ varies directly with the number of pages $h$ and inversely with the number of copies $n$. This means we can write the formula as: $$C = k \f

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations. Important rules include doi

1. **Problem Statement:** Jonas has an annual salary of 312000, works 22 days per month, 8 hours per day. He worked 2 hours overtime on Monday and 3 hours night shift on Saturday (

1. We start with the equation given: $$\frac{1}{4 \sqrt{a^3}} = \frac{1}{32}$$ 2. To solve for $a$, first recognize that the denominators must be equal since the fractions are equa