🧮 algebra

1. **State the problem:** We need to find values of $a$ for which the system $$\begin{cases} x + 2y - 3z = 4 \\ 3x - y + 5z = 2 \\ 4x + y + (a^2 - 14)z = a + 2 \end{cases}$$

1. Énonçons le problème : résoudre l'inéquation $f(x) > g(x)$ avec $f(x) = x^2 - 6x - 27$ et

1. The problem asks to factorize the quadratic equation $$4x^2 - 12x + 9$$ and solve for $$x$$. 2. Recognize that the equation is of the form $$(a - b)^2 = a^2 - 2ab + b^2$$.

1. The problem is to define and graph a piecewise function \(f(x)\) with three parts: - \(f(x) = \log_2(x)\) for \(a < x < b\)

1. Let's clarify the context of step 3 where division by 4000 occurs. 2. Typically, dividing by 4000 in a problem might be related to converting units, normalizing a value, or calc

1. **Énoncé du problème :** Nous avons une fonction linéaire qui convertit une valeur $X$ en dollars en une autre valeur $Y$ selon la formule $$Y = 1.005 \times X.$$

1. **State the problem:** X, Y, and Z invested 12000, 8000, and 10000 respectively in a business. Z received 2500 as his share of the profit. We need to find X's and Y's shares of

1. **State the problem:** Solve for $x$ in the equation $$6x + 5 = -6x - 9$$. 2. **Combine like terms:** Add $6x$ to both sides to get all $x$ terms on one side:

1. The problem asks to calculate the value of $951$ raised to the power of $\frac{2}{3}$. 2. Recall that raising a number to the power of $\frac{2}{3}$ means taking the cube root o

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