🧮 algebra

1. **State the problem:** We have 50 stereo systems in total.

1. **Énoncé du problème :** Nous considérons la fonction $k$ définie sur $\mathbb{R}$ par $$k(x) = x^3 - 6x^2 + 3x + 4.$$

1. **State the problem:** Calculate the total cost when buying a computer at its regular price and a printer with a 40% discount.

1. **State the problem:** Solve the equation $$\frac{1}{2}(x+18) = 4(2x-6) - 9x$$. 2. **Distribute and simplify both sides:**

1. **Énoncé du problème :** On doit écrire sous forme de puissance les expressions suivantes, déterminer une valeur de $n$ pour que $123.4567 \times 10^n$ soit un entier naturel, c

1. The problem asks which expression correctly labels the like terms in the algebraic expression $-14m - 3n + 5 + 4n - 22 + 3n + 6m^2$. 2. Like terms are terms that have the same v

1. Let's start by stating the problem: We want to understand what a polynomial function is and how to work with it. 2. A polynomial function is a function of the form $$f(x) = a_n

1. **Énoncé du problème :** On doit écrire sous forme de puissance les expressions suivantes :

1. **State the problem:** Calculate the value of the expression $\frac{2}{-8} + \frac{4}{9}$.\n\n2. **Recall the formula:** To add fractions, they must have a common denominator. T

1. The problem states that $\ln(a) = \ln(b)$ and asks to find the relationship between $a$ and $b$. 2. Recall the property of logarithms: if $\ln(x) = \ln(y)$, then $x = y$ for $x,

1. **State the problem:** Solve the equation $5x - 3[7 - 4(3 - 2x)] = 5(3 - x) - 4$ for $x$. 2. **Apply the distributive property inside the brackets:**

1. The problem asks which ordered pair could be the missing point in the set \{(-4, 3), (5, -1), (0, 2), (x, y)\} so that the relation is a function. 2. A function assigns exactly

1. The problem asks to identify the domain and range of the given relation: $\{(3, -2), (0, 7), (2, -1), (4, 3)\}$.\n\n2. The domain of a relation is the set of all first elements

1. The problem involves identifying the missing numbers in sequences separated by double bars (||), which suggests a pattern or progression. 2. We are given the example sequence: 1

1. **State the problem:** We are given the function $f(x,y) = y^2 + xy \ln x$ and need to understand or analyze it. 2. **Recall the components:** The function involves variables $x

1. **State the problem:** Solve the equation $10 = -(x^3 + 3x^2 + 3x) + 3$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to isolate the polynomial.

1. The problem asks us to sketch the shifted exponential curves given by the functions $y=3^x+2$ and $y=3^{-x}+2$. 2. The general form of an exponential function is $y=a^x$, where

1. The problem is to find 20% of 90. 2. To find a percentage of a number, use the formula: $$\text{Percentage of a number} = \frac{\text{percentage}}{100} \times \text{number}$$

1. **State the problem:** We are given a function $f(x) = 4x^2 - 5x + 7$ and asked to find where $h \neq o$. 2. **Clarify the problem:** The notation $h \neq o$ is unclear in the c

1. **Statement of the problem:** Given the function $$f(x) = \frac{x^3 - 2x + 1}{(x+1)^2}$$ defined on $$\mathbb{R} \setminus \{-1\}$$, we are asked to calculate the limits of $$f$

1. **State the problem:** We need to determine the nature of the conic given by the equation $$x^2 - 2xy - 12y - 2y^2 + 6x = 20$$. 2. **Rewrite the equation:** Bring all terms to o