🧮 algebra

1. **State the problem:** We know that 10% of a number is 22. We need to find 5%, 20%, 25%, 55%, and 75% of the same number. 2. **Formula and explanation:** Percentage means "per h

1. Masalani tushuntirish: Sizda boshlang'ich qiymat $24000$ va yangi qiymat $19200$ berilgan. Siz kamayish foizini topmoqchisiz. 2. Formulani eslatib o'tamiz: Kamayish foizi quyida

1. **State the problem:** Solve for $m$ in the equation $m - n \log_3 2 = 10 \log_9 6$. 2. **Recall logarithm properties:**

1. Muammo: 42 foiz 672 ga teng bo'lgan sonni toping. 2. Formulani eslatib o'tamiz: foizni son sifatida ifodalash uchun foizni 100 ga bo'lamiz. Ya'ni, $42\% = \frac{42}{100} = 0.42$

1. The problem is to simplify or understand the expression with the entire quantity $2t-5$ under the square root, which is written as $\sqrt{2t-5}$. 2. The square root function $\s

1. **State the problem:** We need to find the total number of spectators at a soccer match given that 60% are men, the rest are women and children, the number of children is \(\fra

1. Let's start by understanding what a variation table is. It shows how a function's value changes as the input changes, often indicating increasing or decreasing behavior. 2. Supp

1. **Stating the problem:** You want to solve a variation table where you have 3 given values but one value is missing. 2. **Understanding variation tables:** Variation tables show

1. **State the problem:** Determine the nature of the roots of the quadratic equation $x^2 + x - 1 = 0$. 2. **Recall the formula:** The discriminant $\Delta$ of a quadratic equatio

1. **State the problem:** Three housewives A, B, and C jointly purchased a basket of oranges costing 80. We need to find how much each paid.

1. **State the problem:** Three housewives A, B, and C jointly purchased a basket of oranges costing 80. We need to find how much each paid.

1. The problem is to understand polynomials in vector spaces. 2. A polynomial in a vector space is an expression of the form $$p(x) = a_0 + a_1 x + a_2 x^2 + \cdots + a_n x^n$$ whe

1. **Problem Statement:** We are given a table describing iterations of a fractal-like process with columns: Iteration number $n$, Number of Segments $4^n$, Length of Each Segment

1. The problem is to simplify the expression $M = -2 \times (3,2 - 5,7) + 4 \times (1,6 - 3,1)$. 2. First, perform the subtraction inside each vector:

1. **State the problem:** Divide 0.72 by 0.000144. 2. **Formula used:** Division of decimals can be done by converting to fractions or by moving the decimal point.

1. **Problem 48:** Solve the equation $$\left(\frac{1}{7}\right)^{-2x+3} + 49^{x-1} + 7^{2x-1} = 399$$. 2. **Step 1:** Express all terms with base 7.

1. The problem involves solving multiple exponential and logarithmic equations, and finding domains. 2. For each equation, we use properties of exponents and logarithms:

1. Problem 28: Solve the equation $$9^{x^{2}+1} + 3^{2x^{2} - 1} = \frac{28}{81}$$. 2. Use the fact that $$9 = 3^{2}$$ to rewrite the first term:

1. **Problem 15:** Solve the equation $((0.1(6))^{3x} - 5 = 1296)$. 2. **Problem 16:** Find how much the root of the equation $3^{x+1} \cdot 27^{x-1} = 9^7$ is less than 10.

1. **State the problem:** Solve the inequality $$2\left(\frac{1+\ln(x)}{x}\right) > 0$$ for $x$. 2. **Rewrite the inequality:** Since 2 is positive, the inequality depends on $$\fr

1. **State the problem:** Solve the inequality $$\frac{(x-2)(x+1)}{(x-1)} \leq 0$$ and find the sum of all positive integers satisfying it. 2. **Identify critical points:** The num