🧮 algebra

1. Factor the expression $7xy - 3n - x + 21ny$ by grouping: Group terms: $(7xy + 21ny) - (x + 3n)$

1. The problem involves understanding the notation of \(\tau_{31}\) and \(\tau_{1}^{40}\).\n\n2. The symbol \(\tau\) often represents a variable or function, with subscripts and su

1. **State the problem:** We have three functions: $$f(x) = x + \frac{1}{2}, \quad g(x) = 2x - 1, \quad h(x) = x^2$$

1. **State the problem:** We are given three functions: - $f : \mathbb{R} \to \mathbb{R}$ defined by $f(x) = x + 1^2 = x + 1$

1. **State the problem:** Simplify and solve the expression $1 \times 3 - \frac{1}{4} = \frac{5}{12}$. 2. **Understand the expression:** The expression involves multiplication, sub

1. Tentukan nilai $x$ yang memenuhi pertidaksamaan $6 < 4x - 2 \geq 2$. Langkah-langkah:

1. **State the problem:** Florence bought 25 bags of dog treats with a 20% discount, paying 27.

1. **State the problem:** Solve the equation $$\frac{1}{\alpha} + \frac{3}{2}x = \frac{5}{2}$$ for $x$. 2. **Identify the goal:** We want to isolate $x$ on one side of the equation

1. **State the problem:** Divide the numbers written in scientific notation: $$\frac{4.6 \times 10^{4}}{2.5 \times 10^{-5}}$$. 2. **Recall the division rule for scientific notation

1. **State the problem:** We are given the function $f(x) = (x+2)(x-3)(x+3)$ and asked to solve it, which typically means finding the values of $x$ for which $f(x) = 0$. 2. **Formu

1. **State the problem:** Solve for $q$ in the equation $$q^3 = \frac{1}{8}.$$\n\n2. **Formula and rules:** To solve for $q$ when given $q^3 = a$, use the cube root: $$q = \sqrt[3]

1. **Problem Statement:** Find the missing value $B$ in each 3x3 matrix where $B$ appears as an unknown. 2. **Understanding the Samples:** The samples show 3x3 matrices with variab

1. **Problem Statement:** Solve the inequality $x^2 + 7x - 8 < 0$. 2. **Formula and Rules:** To solve quadratic inequalities, first find the roots of the quadratic equation $x^2 +

1. **State the problem:** Solve the equation $$x^5 + 4x = -40$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. **State the problem:** Simplify the expression $(2x) x^2$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying terms with the same base, add the e

1. **State the problem:** Simplify the expression $n^2 \cdot n^3$ without using exponents. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same bas

1. Let's clarify the problem: we want to find the exact solution to an equation or expression that equals 2. 2. Typically, to solve for an exact solution, we use algebraic manipula

1. Let's clarify the context where we add 1 in math problems. 2. Often, adding 1 appears in formulas involving counting or sequences, such as when calculating the number of terms b

1. The problem is to find the coefficient of the term with degree 3 in a polynomial or expression. 2. The degree of a term is the sum of the exponents of the variables in that term

1. Énoncé du problème : On considère la fonction $$g(x) = 1 - 3(x - a)^2$$ définie sur l'intervalle $$I = [0, \infty)$$.

1. **Stating the problem:** We are given the linear equation $x + y = 8$ and asked to understand its graph and properties. 2. **Formula and rules:** This is a linear equation in tw