🧮 algebra

1. The problem asks to write the decimal numbers as simplified common fractions. 2. For 11b) 0.135:

1. **State the problem:** Solve the equation $$16^x \times \left(\frac{1}{2}\right)^x = 4^{x+3}$$ for $x$. 2. **Rewrite the bases as powers of 2:**

1. **State the problem:** We are given the function $$y = \log_a (x + 3) + \log_a (2x - 1)$$ where $a, b, c, d$ are positive constants.

1. **State the problem:** (i) Given the function $$y = \log_a (x + 3) + \log_a (2x - 1)$$, explain why $$x > \frac{1}{2}$$.

1. **State the problem:** Multiply and simplify the expression $4 w^3 \cdot 3 x^4 w^3 \cdot 3 x$. 2. **Write the expression:**

1. **State the problem:** We are given the parametric form of a line $r$ and a system of two linear equations $s$. We want to analyze the relationship between the line and the syst

1. Das Problem: Du möchtest mehr Übungsaufgaben wie die vorherige erhalten. 2. Da keine konkrete Aufgabe angegeben wurde, hier ein Beispiel für eine typische Algebra-Übungsaufgabe:

1. **State the problem:** Factorise the expression $$16 - 25(b+3)^2$$. 2. **Identify the formula:** This expression is a difference of squares, which follows the formula $$a^2 - b^

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.