🧮 algebra

1. The problem is to evaluate the expression $-12^{-12}$. 2. Recall the order of operations: exponents are evaluated before negation. So, $-12^{-12}$ means the negative of $12^{-12

1. **State the problem:** Simplify the expression $-12x^{-12}$. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and integer $n$, $a^{-n} = \frac{1}{a^n}$.

1. **State the problem:** Calculate the value of the expression $[-22,4] + [\sqrt{50}] - \left[\frac{7}{3}\right] + \{1,4\}$. 2. **Interpret the notation:** Assuming $[-22,4]$ mean

1. **State the problem:** We are given a hierarchical tree of mathematical expressions and asked to evaluate the root node labeled "5" based on the expressions and their relationsh

1. **Problem:** Simplify the product $$\left(\frac{5y^3}{32x}\right) \times \left(\frac{-4}{15x^2 y^3}\right)$$ 2. **Step 1: Factor all numerators and denominators completely.**

1. Problem: Multiply the rational expressions \(\frac{5y^3}{32x} \times \frac{-4}{15x^2 y^3}\). 2. Formula: To multiply rational expressions, multiply the numerators and denominato

1. **State the problem:** Decompose the rational expression $$\frac{3x^2 + 4}{(x-3)(x^2 + 2)}$$ into partial fractions. 2. **Formula and rules:** For a rational expression where th

1. **Problem statement:** Factorise each expression completely. 2. **Formula used:** Difference of squares: $$a^2 - b^2 = (a-b)(a+b)$$

1. **Stating the problem:** We have two men and parrots with combined heights given. The first man plus his parrot equals 200 units. The second man plus his parrot equals 170 units

1. **Problem Statement:** We have a rectangular cardboard of dimensions 60 cm by 40 cm. We cut out equal squares of side length $x$ cm from each corner and fold up the sides to for

1. **State the problem:** We have a function $f(x) = (x - 5)(x + a) - bx$ where $a > 0$ and constants $a, b$. When $f(x)$ is divided by $x - 5$, the remainder is 80.

1. Let's start by stating the problem: You want to understand the prime factorization method. 2. Prime factorization is the process of expressing a number as a product of its prime

1. Let's start by stating the problem: We want to find the Least Common Multiple (LCM) of two or more numbers. 2. The LCM of numbers is the smallest positive integer that is divisi

1. **Problem statement:** Given the polynomial $p(x) = 6x^3 + ax^2 + bx + c$ (assuming the polynomial form since the problem states $p(x)=6+a$ is incomplete, we interpret it as a c

1. Problem: Multiply \( \frac{5y^3}{32x} \) and \( \frac{-4}{15x^2y^3} \). Step 1: Multiply numerators and denominators:

1. Masalani bayon qilamiz: $y = x^2 - 4x + 6$ kvadrat funksiya grafigini chizish. 2. Kvadrat funksiyaning umumiy ko'rinishi: $$y = ax^2 + bx + c$$ bu yerda $a=1$, $b=-4$, $c=6$.

1. **State the problem:** Solve the equation $$4^x + 6^x = 9^x$$ for $x$. 2. **Rewrite the equation:** Notice that $4 = 2^2$, $6 = 2 \cdot 3$, and $9 = 3^2$. However, it is simpler

1. **State the problem:** Evaluate the expression $9 - 3 \div \left(\frac{1}{3}\right) + 1$. 2. **Recall the order of operations:** Division and multiplication are performed before

1. **Problem:** Determine the equation of the parabola after applying the transformation $(x,y) \to (x+4, \frac{1}{4}y)$ to the graph of $y = x^2$. 2. **Original equation:** $y = x

1. **Stating the problem:** We have a series with terms $y$ corresponding to $x$ values. The 5th term is given as 12.5. We need to find the 1st and 10th terms of the series. 2. **G

1. The problem is to simplify the expression $a+b$. 2. This is a simple algebraic expression representing the sum of two variables $a$ and $b$.