🧮 algebra

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

1. The problem is to arrange the digits 1, 2, 3, 5, 6, 7 in the equation $\square . \square \square \times 2 = \square \square . \square$ so that the multiplication is correct. 2.

1. The problem is to arrange the digits 1, 2, 3, 5, 6, 7 in the gaps of the equation $$\square . \square \square \times 2 = \square \square . \square$$

1. The problem is to solve the expression involving mixed numbers: $1 \frac{3}{10} + 2 \frac{7}{5} + 3 \frac{2}{3}$.\n\n2. Convert each mixed number to an improper fraction:\n- $1

1. **State the problem:** Vivian buys two tomatoes for 500 shillings each and sells them with a 7% profit. We need to find the profit amount. 2. **Calculate the total cost price:**

1. פתרון אי שוויונים: 1. פתרון \(\sqrt{x+3} - 2 < \sqrt{x+1}\):

1. State the problem: Solve the equation $$2(3x - 5) + 4x + 7 = 37$$ for $x$. 2. Expand the parentheses: $$2 \times 3x = 6x$$ and $$2 \times (-5) = -10$$, so the equation becomes $

1. Énoncé du problème : Deux cyclistes partent du même endroit avec un intervalle de 15 minutes. Le premier parcourt 9 km en 30 minutes. Le deuxième cycliste a pour équation de dis

1. The problem asks for the percentage of English books sold by A and B together compared to Hindi books sold by A. English books sold by A = 28

1. The problem states that for elements $i, j, k \in N$, the operation $\times$ satisfies the equation: $$i \times (j - k) = (i \times j) - (i \times k)$$