🧮 algebra

1. **Statement of the problem:** We have two sequences $(u_n)$ and $(v_n)$ defined on $\mathbb{N}$ with given conditions and formulas. We need to solve several questions about thes

1. **Stating the problem:** We are given polynomial functions and asked to perform operations such as multiplication and subtraction on them. 2. **Recall the distributive property:

1. The problem is to solve the equation $x^5 = 95$ and find the value of $x$. 2. To solve for $x$, we use the property of exponents that taking the fifth root of both sides will is

1. **Stating the problem:** We need to solve the algebraic expression or equation given by the user. Since no specific problem was provided, let's consider a general example: Solve

1. **State the problem:** Solve the system of equations: $$5x - 2y = 23$$

1. **State the problem:** Given the function $f(x) = \frac{3x - 5}{x + 2}$, we need to find the inverse function $f^{-1}(x)$ and then evaluate $f^{-1}(2)$. 2. **Formula and rules:*

1. **State the problem:** Simplify the expression $$5 \times 1 \times 2 \times \left(\frac{1}{4} + 2 \frac{1}{7}\right) \div 8 \frac{4}{7}$$. 2. **Convert mixed numbers to improper

1. Sederhanakan $\frac{2^8 \times 2^{-2}}{2^3}$. Gunakan aturan pangkat: $a^m \times a^n = a^{m+n}$ dan $\frac{a^m}{a^n} = a^{m-n}$.

1. **State the problem:** We are given the sequence terms: $2, 3; 2, 1; 1; 2, 0; 1; 2, 1;$ and asked to find the common difference and write down the next 3 terms of the sequence.

1. **State the problem:** Calculate the cost of buying carpet for each room and the cost of creating a fenced lawn area, then find the total cost. 2. **Given prices:**

1. **State the problem:** We need to find the expression for $\alpha^3 + \beta^3$ in terms of $\alpha$ and $\beta$. 2. **Recall the formula:** The sum of cubes can be factored usin

1. The problem is to find a formula for $\alpha^3 + \beta^3$. 2. Recall the sum of cubes formula: for any two numbers $a$ and $b$,

1. **State the problem:** We need to calculate the cost of buying carpet for each room and the cost of creating a fenced lawn area, then find the total cost. 2. **Identify given pr

1. **Stating the problem:** We have a right triangle on the coordinate plane with vertices at (0, 60), (90, 0), and (0, 0). The line forming the hypotenuse has the equation $$y = 6

1. **State the problem:** Solve the system of simultaneous equations: $$3v - w = 4$$

1. **State the problem:** Solve the equation $$z = px + qy + \sqrt{1 + p^2 + q^2}$$ for variables or interpret its meaning. 2. **Understanding the equation:** This equation express

1. Let's clarify the problem you want to solve differently. 2. Many algebraic or calculus problems can be solved using alternative methods such as substitution, factoring, completi

1. **Problem Statement:** Find the quadratic functions in vertex form for two downward opening parabolas given their vertices and points on the graph. 2. **Formula:** The vertex fo

1. **Graph the inequality $2x + y \geq 8$** - The problem asks to graph the region where $2x + y$ is greater than or equal to 8.

1. The problem is to simplify or understand the expression $\sqrt{x}299$. 2. The square root symbol $\sqrt{x}$ means the principal square root of $x$, which is the number that when

1. **State the problem:** Simplify and solve the equation $27^{\frac{2}{3}} \times 3^n = 9^5$ for $n$. 2. **Recall the rules:**