🧮 algebra

1. We hebben een koppel ratten dat gemiddeld 20 nakomelingen per jaar heeft. 2. Elke generatie leeft slechts één jaar, dus het aantal ratten per jaar is een exponentiële groei met

1. The problem asks to compare the steepness of the lines $g(x) = \frac{1}{3}x$ and $f(x) = x$. 2. The steepness of a line is determined by the absolute value of its slope.

1. The problem asks which lines have the same slope as the line given by the equation $y = 3x + 9$. 2. Recall that the slope-intercept form of a line is $y = mx + b$, where $m$ is

1. **Probleemstelling:** We weten dat $K$ evenredig is met $L$ en dat de rechte door het punt $B(7{,}5;85{,}05)$ gaat. We moeten $K$ berekenen als $L=42$. 2. **Formule:** Als $K$ e

1. We are given a line $k$ with equation $y = -1.4x + 5$ and a point $A(0, 3.4)$ through which line $N$ passes. 2. Since line $N$ is parallel to line $k$, it has the same slope. Th

1. **State the problem:** Simplify the expression $x^2 + 2x$ or factor it if possible. 2. **Recall the factoring formula:** For expressions like $ax^2 + bx$, you can factor out the

1. The problem is to understand the difference between using 108 and 1.08 in calculations. 2. When a number like 1.08 is used, it usually represents a value slightly greater than 1

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:**