🧮 algebra

1. **State the problem:** We have a vehicle whose value $D$ in dollars depreciates over time $t$ in years according to a function (not explicitly given in the prompt). We want to f

1. **State the problem:** Anon runs a snowboard business charging 12 per snowboard with 36 rentals per day. For each 0.50 decrease in price, rentals increase by 2. We want to find

1. Write an equation to find the number of oranges in each basket if there are 25 oranges in total and 4 baskets plus 3 extra oranges: 4x + 3 = 25 2. Solve for x by undoing operati

1. **State the problem:** Given the linear function $y = 2x + 3$, find the value of $y$ when $x = 2$. 2. **Formula used:** The function is already given as $y = 2x + 3$.

1. Stwierdźmy problem: Rozwiążemy równanie $$(2 - \sqrt{2})(3\sqrt{3} - x) = 4 - 2\sqrt{2}$$. 2. Użyjemy własności mnożenia i rozkładu wyrażeń algebraicznych oraz uprościmy obie st

1. **State the problem:** We are given the function $f(x) = 5(x-8)(x+2)$ and asked to analyze or simplify it. 2. **Formula and rules:** This is a quadratic function in factored for

1. **Problem Statement:** Find the zeros of a quadratic function, which are the values of $x$ where the function equals zero. 2. **Formula:** The quadratic function is generally wr

1. **State the problem:** Simplify the expression $3x(-1)x^8$. 2. **Recall the rules:** When multiplying terms with the same base, add the exponents: $x^a \cdot x^b = x^{a+b}$.

1. The problem is to understand what matrices are and how they work. 2. A matrix is a rectangular array of numbers arranged in rows and columns.

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