🧮 algebra

1. **State the problem:** We need to find the average length and average width per box from the given sums of lengths and widths. 2. **Identify the data:** Each entry in LENGTH and

1. **State the problem:** Simplify the expression $$\frac{\sqrt[3]{121}+20-8}{5\times10-\frac{5^2}{5}}$$. 2. **Recall the rules and formulas:**

1. **State the problem:** We want to simplify and analyze the function $$y = \ln\left(x^c (1-x)^{10} (x^3 + 1)^7\right)$$ where $c$ is a constant. 2. **Recall the logarithm propert

1. **State the problem:** Simplify and analyze the function $$y = \ln \left((x^3 + 1)^7\right) \cdot \left(x (1 - x)^{10}\right).$$ 2. **Recall logarithm properties:** The logarith

1. **Énoncé du problème :** Soit la suite $(U_n)_{n\in \mathbb{N}^*}$ définie par :

1. **State the problem:** Simplify the expression $(-13 - 2z)(-8 + 2z)$. 2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by each ter

1. **State the problem:** Calculate the value of the expression $8337.43 \times \left(\frac{14.189}{28.758}\right) \times 49.260\%$. 2. **Understand the components:**

1. **State the problem:** We want to analyze the sequence defined by $a_n = 3n \times \left(\frac{1}{3}\right)^n$. 2. **Formula and explanation:** The sequence is given by multiply

1. **Problem statement:** Find a polynomial $f(x)$ with roots 0, 1, and -1 having multiplicities 3, 2, and 1 respectively, and such that $f(2) = 24$. 2. **General form:** A polynom

1. Énonçons le problème : il s'agit de déterminer le tableau de signe de la fonction $$f(x) = \frac{3x+2}{-2xe^2 + x + 1}$$. 2. Rappelons que le signe d'un quotient dépend du signe

1. The problem is to simplify the expression $$(8 - \sqrt{11})(8 + \sqrt{11})$$. 2. This is a product of conjugates, which follows the formula $$(a - b)(a + b) = a^2 - b^2$$.

1. **State the problem:** Solve for $x$ in the equation $3x + 5 = 20$. 2. **Formula and rules:** To solve a linear equation, isolate the variable $x$ by performing inverse operatio

1. **State the problem:** Simplify the expression $2\sqrt{3} + 4\sqrt{12} - \sqrt{48}$. 2. **Recall the rule:** To simplify expressions with square roots, factor the radicand (numb

1. **State the problem:** Solve the cubic equation $$-x^3 + 6x^2 + 3x - 13 = 0$$ for $x$. 2. **Rewrite the equation:** Multiply both sides by $-1$ to simplify the leading coefficie

1. **State the problem:** We have a polynomial $$p(n) = n^3 + 2n^2 - 23n + k$$ and we know that when divided by $$n + 6$$, the remainder is $$-1$$. We need to find the remainder wh

1. **Énoncé du problème :** Nous avons deux fonctions $f$ et $g$ définies graphiquement et analytiquement :

1. **State the problem:** Simplify the expression $6\sqrt{3} - \sqrt{12} - \sqrt{48}$. 2. **Recall the rule:** $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, which helps simplify

1. **State the problem:** Simplify the expression $4\sqrt{10} - 2\sqrt{10}$. 2. **Recall the rule:** When subtracting terms with the same radical part, you can subtract the coeffic

1. Stating the problem: Simplify the expression $$5\sqrt{50} + \sqrt{98}$$. 2. Recall the rule: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$ and simplify square roots by factor

1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} 3x & \text{if } x \neq 0 \\ 1 & \text{if } x = 0 \end{cases}$$

1. **State the problem:** Solve for $x$ in the equation $$9x - 7 = 2(x - 7)$$. 2. **Use the distributive property:** Expand the right side: