🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{(2m^2)^{-1}}{m^2}$$. 2. **Recall the rules:**

1. Problemet er at løse ligningen $\frac{2x+4}{3} = 6$.\n\n2. Vi bruger reglen om at fjerne brøker ved at gange begge sider af ligningen med nævneren. Her ganger vi begge sider med

1. Let's solve a simple algebraic equation: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. The formula to isolate $x$ is to get $x$ alone on one side of the equation by performi

1. **State the problem:** We need to find the value of $x$ given the equation $\log_e 2 \cdot \log_x 625 = \log_{10} 16 \cdot \log_2 10$. 2. **Rewrite the logarithms in a common ba

1. **State the problem:** We need to write a function $V(t)$ that represents the amount of coffee in milliliters (mL) at time $t$ seconds, where coffee is dropping into a 10-cup ca

1. **State the problem:** Simplify the expression $$\frac{5 \times 10^{7}}{2 \times 10^{5}}$$. 2. **Recall the rule for division of powers of 10:** When dividing powers of 10 with

1. **State the problem:** Solve the exponential equation $$7^{x+1} + 2 \cdot 7^x = 11$$. 2. **Rewrite the equation:** Use the property of exponents $$7^{x+1} = 7^x \cdot 7$$ to fac

1. **Stating the problem:** Solve the quadratic equation $$x^2 = 2(\sqrt{11}x + x - 2\sqrt{11})$$. 2. **Expand the right side:** Use distributive property:

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: