🧮 algebra

1. The problem is to expand and simplify the expression $ (x + 3)(x - 1)^2 $.\n\n2. First, expand the square term: $ (x - 1)^2 = (x - 1)(x - 1) $.\n\n3. Multiply out $ (x - 1)(x -

1. **Problem 1:** Given the function $$h = \frac{3s + 1}{1 - 2s}$$ Find the vertical and horizontal asymptotes.

1. **State the problem:** We are given two lines on a Cartesian plane and need to find the slope of the original line and the slope of a line perpendicular to it. 2. **Find the slo

1. The problem is to solve or understand a concept related to 8th grade math. Since no specific question was provided, let's consider a common 8th grade math topic: solving a linea

1. Problem: Solve $2x + 3 = 7$. Step 1: Subtract 3 from both sides: $2x = 4$.

1. To solve equations easily on Desmos, start by entering the equation into the expression line. 2. Use the graph to visually identify where the function crosses the x-axis; these

1. The problem asks to find the slope of the given line and the slope of a line perpendicular to it. 2. The given line is vertical, passing through $x=6$. A vertical line has an un

1. **State the problem:** We are given a line passing through points approximately $(-5,-3)$ and $(3,7)$, and we need to find its slope and the slope of a parallel line passing thr

1. **State the problem:** We are given two lines and need to find the slope of the original line and the slope of a line parallel to it. 2. **Identify points on the original line:*

1. Given the quadratic equation $x^2 - 6x + 5 = 0$, let its roots be $\alpha$ and $\beta$. From the equation, the sum of roots $\alpha + \beta = 6$ and the product $\alpha \beta =

1. **State the problem:** We are given a function $f: \mathbb{Z} \to \mathbb{Z}$ defined by $f(x) = x^2$. We need to determine if $f$ is one-one (injective). 2. **Recall the defini

1. The problem asks whether the function $f: \mathbb{N} \to \mathbb{N}$ defined by $f(x) = x^2$ is one-one (injective). 2. A function is one-one if for every pair of distinct input

1. The problem states that $d^2 = x = m$. We need to understand the relationship between these variables. 2. Given $d^2 = x$, this means $x$ is the square of $d$.

1. **Problem:** The line passes through points P(2,1) and Q(k,11) with gradient $-\frac{5}{12}$. 2. **Find the equation of the line in terms of $x$ and $y$.**

1. **State the problem:** We are given a line passing through points (-7, 7) and (4, -4). We need to find the slope of this line and then graph a line parallel to it, determining t

1. **State the problem:** We are given a line passing through points (-8, -8) and (6, 6). We need to find the slope of this original line and then graph a line parallel to it, dete

1. The first problem asks to identify an irrational number between 5 and 6. 2. Let's analyze each option:

1. Calculer les expressions A, B, C, D données : A = \frac{1}{x - 2} + \frac{3}{x - 4}

1. The first problem asks to find the irrational number between 5 and 6 from the options given: a) 5.5, b) \(\sqrt{5}\), c) \(\sqrt{30}\), d) \(\sqrt{10}\). 2. Recall that an irrat

1. **State the problem:** We want to find the largest whole number $x$ such that $5 + x$ is larger than $2x$. 2. **Write the inequality:**

1. The problem involves analyzing the quadratic function $y = x^2 + 600x + 500$ and solving two quadratic equations: $x^2 - 6x - 3 = 0$ and $x^2 - 7x + 5 = 0$. 2. First, let's anal