🧮 algebra

1. **State the problem:** Solve the linear equation $2x + y = 8$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by sub

1. **State the problem:** The ratio of the price of a dress to that of a shirt is 7:4. The dress costs 42 more than the shirt. We need to find the price of the dress. 2. **Set vari

1. **State the problem:** We have a motorist's journey represented on a distance-time graph from 07:30 to 11:00 am covering 70 km. The motorist stopped for breakfast between points

1. نبدأ بكتابة المسألة: $$R = \frac{3 + 2 \times 5(7 - \frac{6}{3} - 2 - 7)}{+ 3(-5 \times 1 - 10)}$$

1. Problem: Given functions $f(x) = 3x + 2$ and $g(x) = 2 - x$, find the composite function $(f \circ g)(x)$. 2. Formula: The composite function $(f \circ g)(x)$ means $f(g(x))$, w

1. Bài toán yêu cầu giải phương trình $x \cdot y - 5 \cdot y + 5 \cdot x - 24 = 12$. 2. Ta bắt đầu bằng cách viết lại phương trình:

1. The problem states that the variable $r$ is unknown, and we need to find its value. 2. To solve for $r$, we need an equation or context involving $r$. Since none is provided, le

1. **State the problem:** We want to prove a statement $P(n)$ is true for all natural numbers $n$ using mathematical induction. 2. **Induction principle:** To prove $P(n)$ for all

1. **Stating the problem:** We want to understand and verify the formula for the sum of squares of the first $n$ natural numbers, which is given as: $$P(n) = 1^2 + 2^2 + 3^2 + \cdo

1. **Problem Statement:** Sketch and analyze the curves for the following functions:

1. **State the problem:** Calculate $9 \times \frac{1}{12} \times 9$. 2. **Formula and rules:** Multiplication of fractions and whole numbers can be done by converting whole number

1. **Problem Statement:** Sketch and analyze the curves for the following polynomial functions:

1. The problem asks to solve question 1 parts 2, 3, and 4. Since only the first question is solved, we focus on part 2. 2. Without the exact question text, I will demonstrate a typ

1. مسئله را بیان می‌کنیم: حاصل عبارت $$6 - \sqrt{45} - 3\sqrt{(-\sqrt{5} - 3)^2}$$ را بیابید. 2. ابتدا هر قسمت را جداگانه ساده می‌کنیم.

1. Problem: Razmotrite kvadratnu funkciju $f(x) = ax^2 + bx + c$ i riješite nejednadžbe poput $f(x) > 0$, $f(x) < 0$, $f(x) \geq 0$, $f(x) \leq 0$. 2. Formula: Koristimo kvadratnu

1. **State the problem:** We are given two functions: $$g(x) = -2x^4 + 4$$

1. **State the problem:** Solve the quadratic equation $$x^2 = 9x$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem asks to sketch the graph of the function $$y = 4\ln(2x - 4)$$. 2. The natural logarithm function $$\ln(x)$$ is defined only for $$x > 0$$, so the domain of $$y = 4\l

1. The problem asks where the curve of the function $y = 3e^{x} + 1$ will go after sketching the graph. 2. The function is an exponential function with base $e$, scaled by 3 and sh

1. **State the problem:** Simplify the expression $\frac{2x - 5y}{6}$. 2. **Formula and rules:** When you have a fraction with a sum or difference in the numerator, you can write i

1. **State the problem:** Simplify the expression $\frac{-2x - 5y}{6}$. 2. **Formula and rules:** When you have a fraction with a sum or difference in the numerator, you can write