🧮 algebra

1. **State the problem:** We want to divide the polynomial $$x^4+2x^3-4x^2-10x+5$$ by the polynomial $$x^2-5$$ using synthetic division. 2. **Important note:** Synthetic division i

1. **Menentukan $(f \circ g)(x)$** - Diketahui $f(x) = 3x - 2$ dan $g(x) = x^2 + 1$.

1. **Menjelaskan komposisi fungsi** Komposisi fungsi adalah penggabungan dua fungsi sehingga output dari fungsi pertama menjadi input fungsi kedua. Jika kita punya dua fungsi $f$ d

1. **Problem Statement:** We analyze and sketch various rational functions of the form $y = \frac{k}{x} + c$ and identify asymptotes, intercepts, and graph behavior.

1. Problem: If $20$ men take $30$ days to complete a job, in how many days can $25$ men complete the job? 2. Formula: Work done is inversely proportional to the number of men and d

1. **Problem:** If 20 men take 30 days to complete a job, in how many days can 25 men complete the job? 2. **Formula:** Work done is inversely proportional to the number of men whe

1. **State the problem:** We need to graph the system of quadratic inequalities:

1. **State the problem:** We need to solve the system of equations by graphing: $$2x - y = 2$$

1. **نص المشكلة:** حل المعادلة $$س \times ما \times ص = ص$$ حيث نريد إيجاد قيمة $$ما$$. 2. **صيغة المعادلة:** المعادلة المعطاة هي:

1. **State the problem:** The original pathway is represented by an equation of a line, which we assume to be $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept.

1. **State the problem:** We are given the parabola equation $$(x - 2)^2 = 12(y + 4)$$ and need to find its vertex, focus, directrix, axis of symmetry, and length of the latus rect

1. **State the problem:** Solve the equation $$\log(x+3) = 2 + \log^2$$ for $x$. 2. **Analyze the equation:** The equation as given is ambiguous because $\log^2$ is not a standard

1. **State the problem:** Solve the equation $$-3(t+5)=2(t-5)$$ for the variable $$t$$. 2. **Apply the distributive property:** Multiply $$-3$$ by each term inside the parentheses

1. **State the problem:** Solve the equation $$8w + 7 = -3w - 4$$ for the variable $$w$$. 2. **Write down the formula and rules:** To solve linear equations, we aim to isolate the

1. The problem is to find the square root of 49. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **Menentukan domain fungsi** Fungsi yang diberikan adalah $$h(x) = \sqrt{x + 9}$$.

1. **Stating the problem:** We need to find the domain of the function $$h(x) = \sqrt{x + 9}$$ and represent it on a number line. 2. **Formula and rules:** The square root function

1. Masalah yang diberikan adalah menentukan domain fungsi $$h(x) = \sqrt{x+9}$$. 2. Domain fungsi akar kuadrat adalah semua nilai $$x$$ yang membuat ekspresi di dalam akar tidak ne

1. **State the problem:** Factor the quadratic expression $x^2 + 6x + 9$. 2. **Recall the formula:** A quadratic expression $ax^2 + bx + c$ can be factored as $(x + m)(x + n)$ wher

1. **State the problem:** Solve the equation $$-\frac{3}{2}z = 22$$ for $z$ and simplify the answer. 2. **Formula and rules:** To isolate $z$, divide both sides of the equation by

1. **Problema:** Simplificar la expresión $3\log 4 - 4\log 3$. 2. **Fórmulas y reglas importantes:**