🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{2x^3 - 13x + 15x}{n + 3}$$. 2. **Combine like terms in the numerator:** Notice that $$-13x + 15x = 2x$$, so the numerator

1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$x + 4y = -56$$. 2. **Recall the intercept definitions:**

1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$5x + 3y = 15$$. 2. **Recall the definitions:**

1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$-3x + 2y = 6$$. 2. **Recall the intercept definitions:**

1. **State the problem:** We need to find two numbers where the difference between them is 12, and the larger number is twice the smaller number. 2. **Define variables:** Let the s

1. **State the problem:** Evaluate the expression $$\frac{5i}{3 - i}$$ where $i$ is the imaginary unit with the property $i^2 = -1$. 2. **Formula and rules:** To simplify a complex

1. **State the problem:** Solve the inequalities $4 - x \geq 6$ and $\frac{1}{2}x - \frac{1}{3} \geq 5$. 2. **Solve the first inequality:**

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: