🧮 algebra

1. **Stating the problem:** Calculate the value of the expression $$3,6 \cdot 0,1\overline{1} + 2,1\overline{1} : 0,83\overline{3} - 0,93\overline{3}$$ where the overline denotes r

1. **State the problem:** Simplify the expression $$-8 a^4 b (+2 a^3 b^3)$$. 2. **Recall the distributive property:** When multiplying a term by a sum, multiply the term by each ad

1. **State the problem:** Simplify the expression $$(a - b - 3c)(a + b - 3c) + (a - b)^2 + (2 - 3c)^2 + (6a + 2b)(a + c).$$ 2. **Use the distributive property and FOIL method:**

1. **Stating the problem:** We need to draw the parabola given by the equation $$y + 5 = x(6 - x)$$ after rewriting it in standard form.

1. **Stating the problem:** We are given the function $b(t) = 4.5e^{1.4t}$ which models a context or application, possibly related to growth or decay over time $t$. 2. **Formula an

1. **Problemstellung:** Wir betrachten den Absatz der E-Bikes in Deutschland von 2012 bis 2016 mit den Werten: 380000, 410000, 480000, 535000, 605000.

1. **State the problem:** Solve the equation $y = \ln(3x)$ for $x$. 2. **Recall the definition of the natural logarithm:** The natural logarithm function $\ln(a)$ is the inverse of

1. **State the problem:** We need to find the value of $t$ for a line passing through points $(0, -4)$ and $(t, -3)$ with a slope of 1. 2. **Recall the slope formula:** The slope $

1. The problem asks for the slope of the line passing through the points $(1, -2)$ and $(5, 6)$.\n\n2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)

1. **State the problem:** Find the slope of the line passing through the points $(-4, 5)$ and $(2, -1)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and

1. **Problem:** What is 75% of 600? 2. **Formula:** To find a percentage of a number, use the formula:

1. **Problem statement:** (a) Fully factorise $a^2 + 2ab + b^2 - 49$.

1. Problem 1.3: Find the total percentage of annual salary Lauras far pays in arbejdsmarkedsbidrag and A-skat. 2. Given:

1. **Problem statement:** Factorise the quadratic expression $$6x^2 + 11xy + 5y^2$$. 2. **Formula and approach:** To factorise a quadratic expression of the form $$ax^2 + bxy + cy^

1. **State the problem:** Find the equation of the line of intersection between the planes given by $$x + 5y - z = 20$$

1. **State the problem:** Simplify the expression $$5 \cdot (25)^{n+1} - 25 \cdot 5^{2n}$$. 2. **Recall the rules:**

1. Das Thema ist quadratische Funktionen. Eine quadratische Funktion hat die allgemeine Form $$f(x) = ax^2 + bx + c$$, wobei $$a \neq 0$$ ist. 2. Wichtige Eigenschaften sind:

1. **State the problem:** Solve the equation $4x^2 - 5(x - 2) = 10$ for $x$. 2. **Expand and simplify:** Distribute the $-5$ across $(x - 2)$:

1. **State the problem:** Solve the quadratic equation $$3x^2 + 5(2x + \frac{5}{3}) = 0$$. 2. **Expand the equation:** Use the distributive property to expand the term $$5(2x + \fr

1. **State the problem:** Solve the linear equation $2x - 7 = 0$ for $x$. 2. **Write the equation:**

1. We are asked to solve the equation $3^x = 27^x$ using logarithms. 2. First, recognize that $27$ can be written as a power of $3$: $27 = 3^3$.