🧮 algebra

1. **State the problem:** Find the equation of the line in slope-intercept form that is parallel to the line $2x + 5y = 10$ and has the same $x$-intercept as the line $3x + 4y = 15

1. Állítsuk fel az első egyenletet: $$\log(x+1) + \log(x-1) - \log(x-2) = \log 8$$ 2. Használjuk a logaritmus azonosságokat: $$\log a + \log b = \log(ab)$$ és $$\log a - \log b = \

1. **State the problem:** We are given the expression $$S = \frac{(P - 1)}{(P - 2)} \times \frac{(P - 3)}{(P - \alpha)}$$ and asked to solve it by linear equations.

1. **State the problem:** Solve the equation $$\frac{|D^2 - 3|}{|D^2 - 1|} = \frac{|D^2 - 2|}{|D^2 - 1|}$$ for $D$.

1. **State the problem:** A wristwatch is sold at an 18% loss. If sold for 69 more, there would be a 5% gain. Find the cost price (CP) of the wristwatch. Also, find the total loss

1. Let's analyze the expression $\infty^0$ where $0$ is an absolute value, not a limit. 2. By definition, any nonzero number raised to the power of 0 is 1. However, $\infty$ is not

1. The problem is to evaluate the expression $$(2^2 + 5^2)$$. 2. Recall that squaring a number means multiplying the number by itself: $$a^2 = a \times a$$.

1. **State the problem:** Expand and simplify the expression $$(2t - 5)^2$$. 2. **Formula used:** The square of a binomial $$(a - b)^2 = a^2 - 2ab + b^2$$.

1. **بيان المشكلة:** لدينا الدالة $f(x) = \frac{x^2 + x + 1}{x + 1}$ معرفة على المجال $D = ]-\infty, -1[ \cup ]-1, +\infty[$. 2. **إثبات مجال تعريف الدالة:** الدالة غير معرفة عند $

1. The problem asks to solve for $y$ in the equation $$8x - 4y = -16$$ and express it in slope-intercept form, which is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-inter

1. **Problem:** Find the inverse of the function $f(x) = \frac{2x + 3}{2x - 3}$ where $x \neq \frac{3}{2}$. 2. **Formula and rules:** To find the inverse function $f^{-1}(x)$, we s

1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$-3x + 11y = 66$$. 2. **Recall the intercept definitions:**

1. The problem is to understand and analyze a polynomial function. 2. A polynomial function is a function of the form $$f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$$ where

1. **State the problem:** Given the system of equations: $$x + y = 6$$

1. The problem is to simplify the expression $81 - p^4$. 2. Recognize that $81$ is a perfect square since $81 = 9^2$.

1. The problem is to divide a fraction by a whole number. 2. The formula for dividing a fraction by a whole number is:

1. The problem asks to find the value of the function $$f(5\pi)$$ where $$f(x) = \sin\left(\frac{x}{2}\right)$$ defined on the interval $$[-\pi, \pi)$$ and extended as a $$2\pi$$-p

1. **State the problem:** We have a circle given by $$x^2 + y^2 - 4x - 2y - 69 = 0$$ and a line $$2y = mx + 15$$ that intersects the circle at point $$P(9,6)$$. We need to:

1. **Problem Statement:** Given an arithmetic progression (A.P.) with terms $a_1, a_2, a_3, \ldots$, and two distinct indices $m \neq n$, it is given that $m$ times the $m$th term

1. **Problem Statement:** Find two numbers given their sum and difference.

1. The problem asks to find the common number between several decompositions of numbers into products of two whole numbers, where one factor (the divisor) is between 3 and 4 digits