🧮 algebra

1. **Stating the problem:** Vi har en parabel, der beskriver hvælvingen i vinkælderen med funktionen $$f(x) = -1,6x^2 + 3,4x$$ hvor $f(x)$ er højden over gulvet i meter, og $x$ er

1. The problem is to solve the inequality $$5x^2 + 5x > 10$$. 2. First, rewrite the inequality by moving all terms to one side:

1. **State the problem:** Solve the system of linear equations: $$2x + y = 7$$

1. **State the problem:** Solve the linear equation $2x + y = 7$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, subtract $2x$ from both sides of the equation.

1. **State the problem:** Harry converted 560 pounds to euros in February, then converted his remaining euros back to 120 pounds in April. We need to find how many euros he spent o

1. **State the problem:** We need to find the formula for cost based on the mass of coal, given by the linear equation: $$\text{cost} = m \times \text{mass of coal} + c$$

1. **State the problem:** Solve the equation $$\frac{1}{3}(x-3) - x + \frac{1}{3} + 3 + \frac{x}{3} = \frac{1}{3} - z - \frac{x}{3} + \frac{x}{3} + 1$$ for $x$ and $z$. 2. **Simpli

1. **State the problem:** Solve the equation $$\frac{1}{3}(x - 3) - \frac{x+1}{3} + \frac{3+x}{3} = \frac{1}{3} - \frac{2-x}{3} + \frac{y}{3} + 1$$ for $x$ and $y$. 2. **Rewrite th

1. We are asked to find the values of $g(0)$, $g(2)$, and $g(4)$ for the function $g(x) = -5x$. 2. To find $g(0)$, substitute $x=0$ into the function:

1. **State the problem:** Solve the equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the equation:**

1. **State the problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation.

1. The problem is to solve for the variable in the equation given as "User: 1" which is ambiguous and incomplete. 2. Since no specific equation or expression is provided, we cannot

1. **State the problem:** Simplify the expression $3.14 \times 3^3 \times 9$. 2. **Recall the order of operations:** Calculate exponents first, then multiplication.

1. **State the problem:** Calculate the value of the expression $\frac{4}{3} \times 3.14 \times 3^3$. 2. **Recall the formula:** This expression resembles the formula for the volum

1. The problem asks to write the populations of given countries in scientific notation. 2. Scientific notation expresses numbers as a product of a number between 1 and 10 and a pow

1. **State the problem:** Determine if the given numbers are correctly written in scientific notation and write numbers in scientific notation or standard form as requested. 2. **S

1. **State the problem:** Solve for $k$ given the equation $k^2 = 0.49$. 2. **Formula and rules:** To solve for $k$, take the square root of both sides. Remember, when taking the s

1. The problem is to simplify the fraction $\frac{19}{27}$ if possible. 2. To simplify a fraction, we find the greatest common divisor (GCD) of the numerator and denominator and di

1. **Problemstellung:** Bestimmen Sie die Größe (Fläche) des Grundstücks, das durch die Parabeln $f$ und $g$ begrenzt wird. 2. **Formeln und Regeln:** Die Fläche zwischen zwei Funk

1. **State the problem:** Solve for $p$ in the equation $p^3 = 125$. 2. **Formula and rules:** To solve for $p$ when $p$ is raised to a power, use the inverse operation, which is t

1. **State the problem:** Simplify the expression $\left(\sqrt{17.8}\right)^2$. 2. **Recall the formula:** The square of a square root simplifies as $\left(\sqrt{x}\right)^2 = x$ f