🧮 algebra

1. **State the problem:** Calculate the value of $\frac{4}{7} \div \frac{1}{2}$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by

1. **State the problem:** Solve the quadratic equation by factoring: $$6x^2 - 5x + 6 = 6x + 3$$

1. **State the problem:** Solve the quadratic equation by factoring: $$2x^2 + 9x - 1 = 2x - 7$$ 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** We need to determine which of the given equations are true when $x=8$. 2. **List the equations:**

1. The problem asks to identify which variable is independent and which is dependent between time spent driving $t$ and distance driven $d$. 2. In general, the independent variable

1. **Stel het probleem vast:** We willen weten hoe vaak het wiel van de spuitkar moet ronddraaien om de buitenlijnen van het voetbalveld te kalken.

1. **State the problem:** We are given a rectangle with width $5a^{2}b^{4}$ and height $3ab^{2}$. We need to find the perimeter $P$ and area $A$ of this rectangle. 2. **Formulas:**

1. **Problem:** Factor the quadratic expression $4k^2 + 28k + 48$. 2. **Formula and rules:** To factor a quadratic expression of the form $ax^2 + bx + c$, we look for two numbers t

1. **State the problem:** Solve the equation $2x + x + 4 + x - 4 = 180$ for $x$. 2. **Combine like terms:** Group the terms with $x$ and the constant terms separately.

1. **State the problem:** Simplify the product using the distributive property: $$(3w + 9)(7w - 8)$$ 2. **Recall the distributive property:** To multiply two binomials, multiply ea

1. **State the problem:** Find the points of intersection A and B between the line $y=2$ and the parabola $y=\frac{1}{2}x^2$.

1. **State the problem:** Simplify the product using the Distributive Property: $$(a - 3)(a - 4)$$ 2. **Recall the formula:** The distributive property for two binomials is:

1. **Stel het probleem vast:** We willen weten hoeveel centimeter het uiteinde van de grote wijzer van een klok aflegt als deze 1 keer rondgaat. 2. **Formule:** De afstand die het

1. **Stel het probleem vast:** Berend wil 3 dezelfde kasten kopen, elk kost €230 exclusief 21% btw. 2. **Formule voor totaalprijs inclusief btw:**

1. **State the problem:** Simplify the expression $$(4x^2 + 3x - 5) + (2x^2 - x + 7)$$. 2. **Formula and rules:** When adding polynomials, combine like terms. Like terms have the s

1. **Stel het probleem vast:** Anne wil 3 lampen kopen, elke lamp kost 25 euro inclusief 21% btw.

1. **Stel het probleem vast:** Joeke wil drie lampen kopen. Normaal kost een lamp inclusief 20% heffing 30 euro.

1. The problem asks whether to "rise" or "run" first when graphing a line using slope. 2. The slope of a line is defined as $\text{slope} = \frac{\text{rise}}{\text{run}}$ where "r

1. **State the problem:** Find the slope of the line segment between two points. 2. **Formula for slope:** The slope $m$ between points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

1. **State the problem:** Simplify the expression $\left(3a^{4}b^{6}\right)^{3}$ by applying the exponent to each factor inside the parentheses. 2. **Formula used:** When raising a

1. **State the problem:** Simplify the expression \(\left(\frac{75p^{3}m^{-5}}{15p^{5}m^{-4}r^{-8}}\right)^0\). 2. **Recall the rule:** Any nonzero expression raised to the power o