🧮 algebra

1. **Problem:** Use laws of logarithms to combine the expression $$4\log 6 - 3\log 2 + 3\log 5 + 8\log 12 + \log 9$$. 2. **Formula and rules:**

1. **Problem:** Use laws of logarithms to combine the expression $$4\log 6 - 3\log 2 + 3\log 5 + 8\log 12 + \log 9$$. 2. **Formula and rules:**

1. **Problema:** Verificar el límite $\lim_{x \to 2} (5x^5 - 3x^3 + x - 2)$ para confirmar si el resultado es 136. 2. **Fórmula y regla:** Para límites de polinomios, se puede eval

1. Problemi kërkon të zëvendësojmë variablat $zv$, $t$, dhe $dt$ në një shprehje të dhënë. 2. Për të zëvendësuar variablat, duhet të dimë vlerat ose shprehjet që ato përfaqësojnë.

1. Lahenda võrrand a) \((2x + 1)^2 + 3(2x + 1) = 0\).\n\n2. Märkame, et \(y = 2x + 1\), siis võrrand saab kujule \(y^2 + 3y = 0\).\n\n3. Kirjutame võrrandi ümber: \(y^2 + 3y = 0\).

1. **State the problem:** Felicia buys a motorcycle for 3985. Each year its value depreciates by $x\%$. After 7 years, its value is 3269. We need to find $x$ to 2 decimal places. 2

1. **Stating the problem:** Simplify or understand the expression $(x+a) \sqrt{2x+1}$. 2. **Formula and rules:** The expression involves a binomial $(x+a)$ multiplied by a square r

1. **Stating the problem:** Given the function $$R(x) = (4 + a) \sqrt{2x + 1} - x + 3 - y$$ and the condition $$P(4) = 7$$, we want to find the value of $$a$$ assuming $$y$$ is a c

1. **State the problem:** Solve the system of linear equations: $$6x - y = 25$$

1. The problem asks for the answer of the expression involving variables 10, a, b, c, d, and e. 2. Assuming the expression is the product $10 \times a \times b \times c \times d \t

1. **State the problem:** We need to estimate the value of

1. Stating the problems: - Problem 8a: Solve for $a$ in the equation $8a = 0$.

1. **State the problem:** Mario bought four headphone sets and sold them for €320. The exchange rate is £1 = €1.1701. We need to find the profit Mario made and express it as a perc

1. **State the problem:** We are given a triangle with sides $x$, $x+2$, and $x+4$ and a perimeter of 24 cm. We need to find the value of $x$ and determine the type of triangle.

1. **Stating the problem:** We have four numbers: $1.5 \times 10^4$, $4.8 \times 10^6$, $3.2 \times 10^2$, and $7.5 \times 10^3$.

1. **Stating the problem:** We have four numbers in standard form: $1.5 \times 10^4$, $4.8 \times 10^6$, $3.2 \times 10^2$, and $7.5 \times 10^3$.

1. **State the problem:** Find the slant (oblique) asymptote of the function $$h(x) = \frac{x^2 - 9}{x}$$. 2. **Recall the rule for slant asymptotes:** A slant asymptote occurs whe

1. **State the problem:** Find the zeros of the function $$f(x) = \frac{x^2 + 14x + 49}{x^2 + 1}$$. 2. **Recall the rule for zeros of a rational function:** The zeros occur where t

1. **Problem statement:** Given functions $f(x) = \frac{x+1}{x-3}$ and $g(x) = x + 3$, find the composition $(f \circ g)(x)$ and determine its domain. 2. **Formula and rules:** The

1. **State the problem:** We are given a rectangle BCDE with side BC labeled as $4t - 17$ and side DE labeled as $6t - 29$. We need to find the length of side DE. 2. **Recall prope

1. The problem asks for the 6th term of a geometric sequence with the first few terms 1, 5, 25, ... 2. A geometric sequence has terms where each term is found by multiplying the pr