🧮 algebra

1. The problem is to sketch the graph of the linear equation given as $y = -\frac{8}{3}x - 6$. 2. The general form of a linear equation is $y = mx + b$, where $m$ is the slope and

1. Diberikan fungsi $f(x) = 2x^2 - 3x - 5$. Kita diminta mencari nilai turunan pertama fungsi tersebut di titik $x=4$. 2. Rumus turunan fungsi polinomial $f(x) = ax^n$ adalah $f'(x

1. **State the problem:** Solve the quadratic equation $$3x^2 + 5x - 12 = 0$$. 2. **Formula used:** For a quadratic equation $$ax^2 + bx + c = 0$$, the solutions are given by the q

1. The problem is to find the range of the function $y = x^2$. 2. The function $y = x^2$ is a quadratic function where $x$ can be any real number.

1. **State the problem:** Solve the equation $n \times n \times n = n + n + n$. 2. **Rewrite the equation:** The left side is $n^3$ and the right side is $3n$, so the equation beco

1. **State the problem:** Simplify or factor the expression $x^5 - y^5$. 2. **Formula used:** The difference of fifth powers can be factored using the formula for the difference of

1. The problem is to factor the expression $a^4 - b^4$. 2. This is a difference of squares because $a^4 = (a^2)^2$ and $b^4 = (b^2)^2$.

1. **State the problem:** Factor the expression $x^3 - b^3$. 2. **Formula used:** The difference of cubes formula is

1. The problem is to simplify $-331$ modulo $5$. 2. The modulo operation finds the remainder when one number is divided by another.

1. The problem is to find the next number in the sequence: 10, 15, 5, 25, 20, ... 2. Let's analyze the pattern by looking at the differences between consecutive terms:

1. **State the problem:** We have the system of linear equations: $$4x + y + z = 6$$

1. The problem is to transpose the equation $$2x + 4y = 8$$ into slope-intercept form, which is $$y = mx + c$$ where $$m$$ is the slope and $$c$$ is the y-intercept. 2. Start with

1. **State the problem:** Find the equation of a line in slope-intercept form $y = mx + b$ where the gradient (slope) $m = -3$ and the line passes through the point $(4, 2)$. 2. **

1. The problem is to evaluate the expression $1 - 5x^2 + 5x + 5$ for $x = 1$. 2. Substitute $x = 1$ into the expression:

1. Problem 1: Given $f(x) = \frac{(1+2x)^2}{(1-x)^2}$ (i) Find the first 4 terms in the power series expansion.

1. **Problem:** Solve the equation $2x + 3 = 7$. 2. **Formula and Trick:** To solve linear equations like this, use the trick "undo operations in reverse order". Start by undoing a

1. **Problem Statement:** You want a quick introduction and tricks to solve problems on Geometric Progression (GP) for your exam. 2. **Introduction to GP:** A Geometric Progression

1. **State the problem:** Solve the equation $x^6 + x^6 = 2^{32}$ for $x$. 2. **Combine like terms:** Since both terms are $x^6$, we can add them:

1. The problem is about solving an equation and understanding the operations allowed on both sides. 2. When solving equations, the key rule is to perform the same operation on both

1. **State the problem:** Solve the linear equation $5a + 2 = -13$ for $a$. 2. **Recall the formula and rules:** A linear equation in one variable can be solved by isolating the va

1. Masalah yang diberikan adalah memahami rumus $f(n) + f(n+1) + f(n+2) + \ldots + f(2n)$ dan mengapa bentuk penjumlahan seperti itu muncul. 2. Rumus ini adalah penjumlahan dari fu