🧮 algebra

1. The problem is to find the sum of the numbers: 1, 2, 3, 4, 5. 2. The formula for the sum of the first $n$ natural numbers is:

1. The problem asks if the equation $\frac{x}{5} = 46$ is a linear equation. 2. A linear equation in one variable is an equation that can be written in the form $ax + b = 0$, where

1. **State the problem:** Find the vertical asymptotes of the function $$f(x) = \frac{x}{x^2 - 36}$$. 2. **Recall the rule for vertical asymptotes:** Vertical asymptotes occur wher

1. **Énoncé du problème :** Soit la suite $(u_n)$ définie par $u_0 = \frac{1}{2}$ et $u_{n+1} = f(u_n)$ où $f$ est définie sur $]2, +\infty[$ par $f(x) = \frac{a + bx}{ax + b}$ ave

1. **State the problem:** Convert the general form of the circle equation into center-radius form for the first equation: $$3x^2 + 3y^2 + 12x - 18y - 33 = 0$$ 2. **Divide entire eq

1. **State the problem:** Find the domain of the function $$f(x) = \frac{x}{x^2 - 36}$$ using interval notation. 2. **Recall the domain rule:** The domain of a function includes al

1. **State the problem:** We are given that $y$ varies directly as $x$, meaning $y = kx$ for some constant $k$. We need to find the unknown values in each case. 2. **Formula and ru

1. **State the problem:** Solve the equation $112 + (X - 1)^2 = X^2$ for $X$. 2. **Expand the squared term:** Recall that $(X - 1)^2 = X^2 - 2X + 1$.

1. **State the problem:** We need to find the sum of the first ten terms of the series \(\log x + \log x^2 + \log x^3 + \cdots + \log x^{10}\). 2. **Use logarithm properties:** Rec

1. **State the problem:** Solve the expression $2x 9$. It seems like the problem is to multiply $2x$ by $9$. 2. **Apply multiplication:** Multiply the coefficient $2$ by $9$ while

1. **State the problem:** Find the vertical asymptotes of the function $$f(x)=\frac{x^2 + 2x + 1}{x^2 - x - 2}$$. 2. **Recall the rule for vertical asymptotes:** Vertical asymptote

1. **State the problem:** Solve the quadratic equation $-66 = -17x + x^2$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

**TEST ONE: Algebra Homework Assignment** 1. Solve the equation $\sqrt{x-8} - \sqrt{2x-2} + 3 = 0$.

1. **State the problem:** Solve the equation $$\sqrt{x-2} = 8 - x$$ for $x$. 2. **Understand the domain:** The expression under the square root must be non-negative, so:

1. **State the problem:** Find the vertical asymptotes of the function $$f(x)=\frac{x^2 + 2x + 1}{x^2 - x - 2}$$. 2. **Recall the rule for vertical asymptotes:** Vertical asymptote

1. **Énoncé du problème :** On considère les nombres $a=1008$ et $b=16200$. Il faut déterminer le PGCD (Plus Grand Commun Diviseur) et le PPCM (Plus Petit Commun Multiple) de $a$ e

1. **Nyatakan masalah:** Diberi lengkung L₁ dengan fungsi $y = a^x$ dan L₂ adalah pantulan L₁ pada garis lurus $y = x$. Kita diminta mencari nilai sudut $\alpha$ dan fungsi bagi le

1. The problem asks to find the composition function $fg(x)$ given two functions: - $f(x) = 3x + \ln x$, where $x > 0$

# SHS Mathematics Assignment ## Test One

1. **Énoncé du problème :** Simplifier le radical $$\sqrt[3]{\frac{a^m + 3}{b^{3m-1}}}$$ où $a,b,c$ sont des variables et $m$ un exposant. 2. **Formule et règles importantes :** Po

1. **Stating the problem:** We need to understand what a rational number is and provide an example. 2. **Definition:** A rational number is any number that can be expressed as the