🧮 algebra

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.

1. **State the problem:** We are given the quadratic function $h(t) = -5t^2 + 20t + 2$ and need to analyze it. 2. **Formula and rules:** This is a quadratic function of the form $h

1. **Problem Statement:** Multiply and divide integers as per the given operation. 2. **Important Rules:**

1. **Problem Statement:** Solve the equation $x^2 - 5x + 6 = 0$. 2. **Formula and Rules:** This is a quadratic equation of the form $ax^2 + bx + c = 0$.

1. The problem asks us to evaluate the expression $$(3.4 \times 10^2) \times (2 \times 10^3)$$ and express the result in the form $a \times 10^b$. 2. Recall the rule for multiplyin

1. **State the problem:** Evaluate the expression $$(2.5 \times 10^3) \times (3 \times 10^2)$$ and express the result in the form $[?] \times 10$. 2. **Recall the multiplication ru

1. **State the problem:** We are given the quadratic function $h(t) = -5t^2 + 20t + 2$ and want to analyze it. 2. **Formula and rules:** This is a quadratic function of the form $h

1. **Stating the problem:** The problem statement is incomplete. Please provide the full problem or equation to solve. Since no specific problem or equation was given, I cannot pro

1. **State the problem:** Solve the equation $$2x^4 - x^3 - 6x^2 - x + 2 = 0$$ using the quadratic formula. 2. **Identify the approach:** This is a quartic equation, not a quadrati

1. **Problem Statement:** We have a function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = x + 1$. We need to check if $f$ is injective, surjective, or bijective. 2. **Definiti