🧮 algebra

1. **State the problem:** A man and his apprentice paint a room. The man takes 1 hour less than the apprentice to paint alone. Together, they take 72 minutes to paint the room. Fin

1. **State the problem:** Solve the equation $5x - 15 = 15$ for $x$. 2. **Write down the equation:**

1. **State the problem:** We need to find the inequality that represents the total money raised from selling tickets before and during the event.

1. **State the problem:** Simplify the expression $$\frac{8r^4 s^9}{4r^3 s^3}$$. 2. **Recall the rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a

1. **State the problem:** Simplify the expression $$\frac{g^7 h^9}{5 g^2 h^7}$$ and express the answer using exponents. 2. **Recall the exponent rules:** When dividing like bases,

1. **State the problem:** Factorise completely the expression $ab^2 - bc$. 2. **Identify common factors:** Look for common factors in both terms. The terms are $ab^2$ and $bc$.

1. **State the problem:** Simplify the expression $$\frac{8 - 4\sqrt{18}}{50}$$. 2. **Simplify the square root:** Note that $$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{

1. **State the problem:** Simplify the expression $\frac{b^3}{b^0}$. 2. **Recall the exponent rules:** When dividing powers with the same base, subtract the exponents:

1. **State the problem:** Simplify the expression $\left(\frac{1}{4}\right)^{-3}$.\n\n2. **Recall the rule for negative exponents:** For any nonzero number $a$ and integer $n$, $a^

1. **State the problem:** Simplify the expression $$\frac{8 - 4 \sqrt{18}}{50}$$. 2. **Recall the rules:** Simplify the square root first, then simplify the fraction by factoring a

1. Problema: Aplicar la definición de logaritmos para encontrar $x$ en $\log_2 \left( \frac{4\sqrt{2}}{4} \right) = x$. 2. Recordemos que $\log_a b = c$ significa que $a^c = b$.

1. Let's clarify steps 6 and 7 from your problem. 2. Step 6 usually involves simplifying an expression or performing an operation like factoring or canceling terms.

1. The problem states: Simplify the expression $x^0 \times y^0$ and check if it equals $xy$. 2. Recall the rule: Any nonzero number raised to the power of zero equals 1. That is, f

1. **Planteamiento del problema:** Resolver la ecuación logarítmica $\log x + \log 4 = 0$. 2. **Fórmula y reglas importantes:**

1.1 Consider the pattern: 10; 7; 4; 1; ... 1.1.1 Determine the formula $T_n$, the general term of the sequence.

1. Consider the pattern: 10; 7; 4; 1; ... 1.1 Determine the formula $T_n$, the general term of the sequence.

1. **State the problem:** Multiply $x^{-2}$ by $x^{-3}$. 2. **Recall the rule for multiplying powers with the same base:**

1. **State the problem:** Simplify or evaluate the expression $2^N + 2$ for a given value of $N$. 2. **Formula and rules:** The expression consists of an exponential term $2^N$ plu

1. **State the problem:** Find the equation of the straight line passing through the points $(0,7)$ and $(2,0)$ in the form $y = mx + c$. 2. **Formula used:** The equation of a lin

1. The problem is to find the 4 roots of the equation for each integer value of $k$ from 0 to 10. 2. Since the original equation is not provided, let's assume a general quartic equ

1. **State the problem:** We need to find the equation of a line passing through point $P(0,0)$ that is perpendicular to the line given by $$y = -9x - 1.$$\n\n2. **Recall the slope