🧮 algebra

1. **State the problem:** Calculate $\frac{16}{31} \div 8$. 2. **Recall the division of fractions rule:** Dividing by a number is the same as multiplying by its reciprocal.

1. Tehtävä: Sievennä lauseke. 2. Koska käyttäjä ei antanut tarkkaa lauseketta, oletetaan yleinen esimerkki: $$\frac{2x^2 + 4x}{2x}$$.

1. **State the problem:** Simplify the expression $$(2x+3)^2 + 3x^2$$. 2. **Recall the formula:** The square of a binomial is given by $$(a+b)^2 = a^2 + 2ab + b^2$$.

1. **State the problem:** Solve the quadratic equation $$\sqrt{2} x^2 + (\sqrt{2} - 2)x - 2 = 0$$ for $x$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$,

1. **State the problem:** Find the solutions to the simultaneous equations: $$x^2 + y^2 = 16$$

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor numerator and denominator

1. Il problema è risolvere un esercizio sui polinomi, ad esempio semplificare o fattorizzare un polinomio. 2. La regola principale è che un polinomio è una somma di termini di form

1. Given the problem: Solve for $x$ in the equation $2x + 3 = 7$. 2. Use the formula for solving linear equations: isolate $x$ by performing inverse operations.

1. **State the problem:** Simplify and solve the expression $$(2x^2 - x)^2 - (2x - x^2)^2$$. 2. **Use the difference of squares formula:** Recall that $$a^2 - b^2 = (a - b)(a + b)$

1. **State the problem:** Simplify the expression $5x \times \left(\frac{2}{5}x + 5\right)$.\n\n2. **Use the distributive property:** Multiply $5x$ by each term inside the parenthe

1. Il problema chiede di risolvere tutte le operazioni fornite, ma non sono state specificate operazioni nel messaggio. 2. Per risolvere un'operazione, è necessario conoscere l'esp

1. **State the problem:** Simplify the expression $$\left( \frac{\left( \frac{5}{3} \right)^{-2} \cdot \left( \frac{5}{3} \right)^{-3}}{\left( \frac{5}{3} \right)^{-1}} \right)^{-4

1. The problem asks to evaluate $0.6 \times 10^{-11}$. 2. Recall that $10^{-11}$ means $\frac{1}{10^{11}}$, which is a very small number.

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: