🧮 algebra

1. **State the problem:** Calculate the percentage increase in the number of cars made from 2016 to 2017.

1. **State the problem:** Solve the system of linear equations: $$-7x - 6y = -7$$

1. We stellen het probleem vast: de bevolking van Rome groeide van 600000 naar 1000000 in 100 jaar. 2. We willen het procentuele groeipercentage per decennium (10 jaar) berekenen.

1. **State the problem:** We need to simplify the function $$f(x) = \frac{4x^4 - 16}{6x^2 + 7x - 3}$$. 2. **Recall the formulas and rules:**

1. Stating the problem: Simplify the expression $$\frac{7}{10} - \left( \frac{3}{5} - \frac{1}{2} \right)$$. 2. Use the rule for subtraction inside parentheses: $$a - (b - c) = a -

1. **State the problem:** Solve the equation $$-(3x + 2) \cdot \left(x - \frac{2}{3}\right) = 0$$ for $x$. 2. **Recall the zero product property:** If a product of two factors equa

1. **State the problem:** Solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. We can

1. **State the problem:** We need to verify and understand the equation $$n^3 + 2 = n(n + 1)(n - 1) + 2$$ where $n \in \mathbb{N}$.

1. **Énoncé du problème :** Des employés doivent transporter 135 paquets de bardeaux du 8ème étage au 12ème étage en utilisant un monte-charge qui peut transporter 8 paquets à la f

1. **State the problem:** Solve the cubic equation $$x^3 - 5x^2 - 12x + 60 = 0$$ given that $$x = \pm 2\sqrt{3}$$ are solutions. 2. **Use the factored form:** Since $$x = 2\sqrt{3}

1. **State the problem:** Find the difference between the two expressions: $$\left(\frac{3}{4}x^{2} + 5x - 2\right) - \left(\frac{1}{2} x^{2} - \frac{3}{4} x + \frac{7}{2}\right)$$

1. **State the problem:** Solve the system of linear equations: $$3x + 3y = -6$$

1. **State the problem:** Given the quadratic function $$y = 2x^2 - 0.4x + 2.5$$, we need to find how many roots it has using the discriminant and then find the roots using the qua

1. **State the problem:** Simplify the expression $$-\frac{40}{5} - \frac{7}{8}$$. 2. **Simplify each term:**

1. **Problem:** Rewrite the number 24 as an expression using addition, subtraction, multiplication, and division exactly once each. 2. **Step 1: Understand the operations**

1. **State the problem:** Find the sum of the polynomials $$\frac{1}{2}x^2 - 3$$ and $$2x^2 - \frac{1}{4}x + \frac{5}{2}$$. 2. **Write the expression:**

1. **Stating the problem:** Solve the equation or expression given by the user. Since no specific problem was provided, please provide the exact math question to solve. 2. **Formul

1. We are given the sequence defined by $$a_n = \frac{7n - 3}{4n + 1}$$ and asked to find its limit as $$n$$ approaches infinity. 2. The formula for the limit of a rational sequenc

1. **State the problem:** Simplify fully the expression $$\frac{(\sqrt{6})x^{2}}{\sqrt{\frac{96}{x^{10}}}}$$. 2. **Rewrite the denominator:** Recall that $$\sqrt{\frac{a}{b}} = \fr

1. **State the problem:** Simplify the expression $$\frac{2}{1} \div \frac{1}{2} \times \left(\frac{2}{5} + \frac{1}{3}\right)$$ using BEDMAS (Brackets, Exponents, Division and Mul

1. The problem is to identify which gym membership corresponds to the linear function $y=15x$, where $y$ is the total cost and $x$ is the number of months. 2. The formula $y=15x$ m