🧮 algebra

1. Problemet är att förenkla två algebraiska uttryck så långt som möjligt. 2. Vi använder regeln för division av potenser med samma bas: $$\frac{x^a}{x^b} = x^{a-b}$$ och faktorise

1. **Stel het probleem vast:** We hebben de formule voor de veilige snelheid in een bocht: $$v = 3,5 \sqrt{5r}$$ waarbij $v$ de snelheid in km/u is en $r$ de straal van de bocht in

1. The problem appears to involve solving an equation related to the expression $4 + 12 \cdot 4 + = 5c$ and some steps involving $x$ and $c$. 2. From the notes, it seems you are tr

1. **State the problem:** We have a 3 3/4-inch candle that burns down in 3 hours. We want to find how long a 6 1/4-inch candle of the same type will take to burn down. 2. **Formula

1. **State the problem:** Ricky mixes white and blue paint in a ratio of 4 pints white to 12 pints blue. The total paint combined is 56 pints. We need to find how many pints are bl

1. **State the problem:** We are given the inequality $$29 > 2x + 7$$ and need to answer questions about its graph and solutions.

1. The problem gives the inequality $$29 > 2x + 7x + 7$$ and asks to analyze the graph and test some values. 2. First, simplify the inequality:

1. **State the problem:** Determine if the two algebraic expressions evaluated with given values are equivalent. 2. **Expressions given:**

1. Problemet handlar om att bestämma värdet på derivatan $f'(2)$ för funktionen $f$ baserat på grafen. 2. Derivatan $f'(x)$ vid en punkt $x$ är lutningen på tangenten till grafen v

1. Problemet: Vi har en funktion $f$ med grafen given som en nedåtvänd parabel. 2. Vi ska bestämma det bästa värdet för $f'(2)$, dvs. lutningen på tangenten till grafen vid $x=2$.

1. The problem asks us to evaluate the permutation expression $4P4$. 2. The formula for permutations is:

1. **Stel het probleem vast:** We hebben een lineaire grafiek en een kwadratische vergelijking gegeven. We moeten:

1. Problemet handlar om att bestämma den genomsnittliga förändringshastigheten för antalet gråsälare i Östersjön mellan den 1 augusti 2015 och den 1 augusti 2018. 2. Formeln för ge

1. El problema es resolver la ecuación $x^4 - 6x^2 + 8 = 0$. 2. Para resolver ecuaciones de cuarto grado que solo tienen potencias pares, podemos hacer un cambio de variable: sea $

1. **State the problem:** Solve the equation $10^{-3x+1} = \frac{1}{10}$. 2. **Recall the properties of exponents:** We know that $\frac{1}{10} = 10^{-1}$ because $10^{-1} = \frac{

1. **State the problem:** Simplify the expression $$\frac{\log^3}{5b} \quad 21a \quad 10b^2$$ as given in the first problem set. 2. **Analyze the expression:** The problem appears

1. **State the problem:** Simplify the complex fraction $$\frac{\frac{6a^3}{56}}{\frac{21a}{10b^2}}$$. 2. **Recall the formula:** Dividing by a fraction is the same as multiplying

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. **Stating the problem:** Solve the equation $$x^2 = -9$$ for real numbers $x$. 2. **Formula and rules:** The equation is a quadratic equation of the form $$x^2 = c$$.

1. **State the problem:** Lucy deposited 4000 into an account with 2.1% annual interest compounded monthly. We want to find the amount after 7 years. 2. **Formula used:** The compo

1. **State the problem:** Solve the equation $$x - \frac{x+2}{3} + 3(x-3) = 2 + \frac{2x+1}{3}$$ for $x$. 2. **Write down the equation and identify the goal:** We want to isolate $