🧮 algebra

1. **State the problem:** Evaluate the expression $\left(1 - d_1\right)\left(1 - d_2\right)\left(1 - d_3\right)$ given $d_1 = 0.18$, $d_2 = 0.42$, and $d_3 = 0.08$. 2. **Substitute

1. Problema: Rezolvă exercițiul $x * y = -xy + x + 2y + 3$ folosind legea de compoziție asociativă. 2. Definim operația $*$ astfel: pentru orice $x, y$, avem

1. **Problem statement:** Given the quadratic function $f(x) = a(x - h)(x - k)$ with $h < k$, and the parabola passes through points $(1,0)$, $(5,0)$, and $(0,15)$, find: (a) value

1. **Énoncé du problème** : Écrire chaque expression sous forme d'une seule puissance avec base unique. 2. **Calcul de A** :

1. **State the problem:** Kavita saved money over three months to buy a laptop. She saved \(\frac{1}{3}\) of the laptop's cost in the first month, \(125\) less than that in the sec

1. **State the problem:** Kavita saved money over three months to buy a laptop. She saved \(\frac{1}{3}\) of the laptop's cost in the first month, \(125\) less than that amount in

1. Calculer les expressions suivantes : 1.1. Calcul de $(-\sqrt{7})^0$ :

1. Calculer $(-\sqrt{3})^4$. On sait que $(-\sqrt{3})^4 = ((-\sqrt{3})^2)^2$.

1. **Problem 1:** Solve the system using Gaussian and Gauss-Jordan elimination. Given:

1. Let's start by understanding the problem. Kavita wants to buy a laptop and saves money over three months. 2. She saves \( \frac{1}{3} \) of the laptop's cost in the first month.

1. **State the problem:** Kavita wants to buy a laptop. She saves money over three months: in the first month, she saves one-third of the laptop's cost. In the second month, she sa

1. **State the problem:** Kavita saved money over three months to buy a laptop. She saved \(\frac{1}{3}\) of the laptop's cost in the first month, \(125\) less than that amount in

1. The degree of the expression $2x - 4xy^2 + 5x^2y^3$ is the highest sum of exponents in any term. - Term $2x$ has degree $1$.

1. The problem is to find the equation of a parabola given its vertex and x-intercepts. 2. The parabola opens downward with vertex at (0, 6) and x-intercepts at -2 and 1.

1. The degree of the expression $2x - 4xy^2 + 5x^2y^3$ is the highest sum of exponents in any term. - For $2x$, degree is $1$.

1. **Problem:** Find the degree of the expression $2x - 4xy^2 + 5x^2y^3$. The degree of a term is the sum of the exponents of the variables in that term.

1. The degree of the expression $2x - 4xy^2 + 5x^2y^3$ is the highest sum of exponents in any term. - Term $2x$ has degree $1$.

1. The problem involves finding the roots $x_2$, $x_3$, and $x_4$ of a polynomial or equation where you already have $x_2 = 1.348$. 2. To find $x_3$ and $x_4$, you typically use me

1. The problem asks to find the $x$-coordinate where the curve $y=x^3 - x$ crosses the horizontal line $y=1$. 2. Set the curve equal to 1: $$x^3 - x = 1$$

1. **Task 1: Representing and solving the toy cost problem** (i) Let the costs of the three toys be $x$, $y$, and $z$.

1. **State the problem:** We are given that 25% of a number is 80, and we need to find the number. 2. **Translate the problem into an equation:** 25% means 25 per 100, or \frac{25}