🧮 algebra

1. The problem asks to express a given improper fraction as a mixed fraction in its simplest form. 2. A mixed fraction consists of a whole number and a proper fraction.

1. The problem asks to express given improper fractions as mixed fractions in their simplest form. 2. A mixed fraction consists of a whole number and a proper fraction.

1. **State the problem:** Solve the quadratic equation $3y^2 - 6y = 0$ for $y$. 2. **Formula and rules:** To solve quadratic equations, we can factorize the expression and use the

1. **Problem:** Solve the system of linear equations by Gauss elimination method for (i): $$\begin{cases} 2x + 3y + 4z = 2 \\ 2x + y + z = 5 \\ 3x - 2y + z = -3 \end{cases}$$

1. The problem states that the turning point (titik pusingan) of a function is at the coordinates $(3, q)$. 2. A turning point of a function $y=f(x)$ occurs where the derivative $f

1. **Stating the problem:** Solve the system of linear equations for each set (a), (b), and (c).

1. **Problem 1: Evaluate the piecewise function** Given:

1. **Problem:** Sketch the function $$f(x) = 2 \cos^{-1}(-x + 1) + 1$$ and find its domain and range. 2. **Recall the inverse cosine function properties:**

1. **Problem 1:** Solve the inequality $3x + 5 \leq 3x - 3$. 2. **Step 1:** Write the inequality:

1. The problem is to analyze the curve given by the function $$y = x^4 - 4x^3$$. 2. We want to find key features such as intercepts and extrema.

1. **Problem Statement:** Find the distance of the point $P$ from the origin, where $P$ is the intersection of the common tangents to the parabola $x^2 = 4y$ and the circle $x^2 +

1. The problem is to solve the inequality $4x + 1 < -x + 6$ graphically. 2. We graph the functions $f(x) = 4x + 1$ and $g(x) = -x + 6$ on the same set of axes.

1. **Tujuan Pembelajaran** - Memahami konsep sistem persamaan linier tiga variabel.

1. The problem is to solve the equation $4x + 1 = -x + 6$ graphically. 2. To do this, we graph the functions $f(x) = 4x + 1$ and $g(x) = -x + 6$ on the same set of axes.

1. **Problem:** Show that $$\frac{x - a}{a} + \frac{1}{2} \left( \frac{a - x}{a} \right)^2 + \frac{1}{3} \left( \frac{a - x}{a} \right)^3 = \log a - \log x$$. 2. **Formula and Expl

1. **State the problem:** Solve the equation $5x + 1 = -x + 7$ for $x$. 2. **Write down the equation:**

1. The problem asks to solve the equation $5x + 1 = -x + 7$ graphically by plotting two functions and finding their intersection points. 2. We define the functions:

1. Stating the problem: Solve the equation $$\frac{1}{7}x = -8$$ for $x$. 2. Formula and rules: To solve for $x$ when it is multiplied by a fraction, multiply both sides of the equ

1. The problem is to express the perimeter $p$ of a rectangle in terms of the width $w$ and length $l$. 2. The formula for the perimeter of a rectangle is given by:

1. **Stating the problem:** Simplify the expression $x^{4}y^{2} - 3x^{3}y^{25}$. 2. **Formula and rules:** When simplifying expressions with variables and exponents, remember:

1. The problem is to analyze the quadratic function $h(t) = -5t^2 + 20t + 2$. 2. The general form of a quadratic function is $ax^2 + bx + c$ where $a$, $b$, and $c$ are constants.