🧮 algebra

1. **State the problem:** Find the value of the limit $$\lim_{x \to +\infty} \frac{2^{-x}}{2^x}$$. 2. **Recall the properties of exponents:**

1. **State the problem:** We are given two functions:

1. **State the problem:** We want to find the number of days $t$ it takes for the video views $y$ to reach 2500, given the exponential growth function $$y = 80e^{0.2t}.$$ 2. **Writ

1. **Problem Statement:** Find the roots of the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula Used:** The roots of a quadratic equation $$ax^2 + bx + c = 0$$ are given by t

1. Masalah ini menanyakan berapa banyak titik potong grafik fungsi dengan sumbu x. 2. Titik potong pada sumbu x terjadi ketika nilai fungsi sama dengan nol, yaitu $y=0$.

1. The problem involves analyzing three quadratic functions: $$f(x) = -3x^{2} + 4x + 1$$

1. **State the problem:** We are given the number of boys in a school as 120 and the ratio of boys to girls as 5:7. We need to find the total number of students in the school. 2. *

1. **State the problem:** We are given the matrix equation $$\begin{pmatrix}4 & 5 \\ 4 & 3\end{pmatrix} \begin{pmatrix}-4 \\ -2\end{pmatrix} = k \begin{pmatrix}26 \\ 22\end{pmatrix

1. **State the problem:** Simplify the expression $$(X^2 + 4)^2 - (X^2 - 2)^2$$. 2. **Formula used:** This is a difference of squares, which follows the rule $$a^2 - b^2 = (a - b)(

1. The problem is to find the equation of the line passing through the points $(-1, 2)$ and $(3, 4)$. 2. The formula for the slope $m$ of a line through two points $(x_1, y_1)$ and

1. **State the problem:** Simplify the expression $$(X - 4)^2 - (X - 2)^2$$. 2. **Recall the formula:** This is a difference of squares, which can be factored using the identity $$

1. **Problem Statement:** Given the equation $$\log(\sec A - \tan A) + \log(\sec A + \tan A) - \log(\sin^2 A + \cos^2 A) = \log k,$$ find the value of $k$. 2. **Formula and Importa

1. **State the problem:** A woman bought 210 oranges for 65 and sold them at a rate of 3 oranges for 2. We need to find the profit she made. 2. **Calculate the cost price (CP) per

1. Let's start by understanding the problem: you want an explanation using an example. 2. Suppose we want to solve the equation $2x + 3 = 7$.

1. **State the problem:** A tank contains 250 liters of water. If 96 liters are used, we need to find what percentage of the original quantity is left. 2. **Formula used:** To find

1. **State the problem:** Kofi is 2 years older than Ama, and the sum of their ages is 16. We need to find Ama's age. 2. **Define variables:** Let Ama's age be $x$ years.

1. **Problem statement:** Find the value of each expression for given values of variables. 2. **Formula and rules:** Substitute the given values into the expressions and perform ar

1. **Problem:** P varies directly as the square of Q and inversely as the cube of Z. Given P=5, Q=3, Z=1, find: (i) The relationship between P, Q, and Z.

1. The problem is to solve a quadratic equation, which generally has the form $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are constants and $a \neq 0$. 2. The formula to find the

1. **Problem statement:** Two warehouses A and B have the same workload. Alone, A takes 10 hours to move goods in warehouse A, B takes 12 hours in warehouse B, and C takes 15 hours

1. **Problem statement:** Solve the inequality $$3x^2 + 2x - 8 \leq 0$$ given that $$3x^2 + 2x - 8 = (x + 2)(3x - 4)$$. 2. **Formula and rules:** To solve quadratic inequalities, f