🧮 algebra

1. Problem statement: A pump fills a tank in 2 hours, but with a leak, it takes 2.5 hours to fill the tank. Find the time in hours for the leak alone to empty the full tank. 2. Def

1. The user asks a question about the certainty of a sum. 2. To clarify, please provide the exact sum or problem you are referring to.

1. The problem states that 12 sheets of thick paper weigh 40 grams, and we want to find how many sheets weigh 1 gram. 2. First, find the weight of one sheet by dividing the total w

1. The problem is to simplify the fraction $\frac{405}{36}$ to its lowest terms. 2. First, find the greatest common divisor (GCD) of 405 and 36.

1. Stating the problem: We know 3 lambs finish eating the grass in 5 days. We want to find how many days 2 lambs will take to finish the same grass. 2. Understand that the work don

1. The problem is to understand the linear equation $y = mc + x$ and explore its components. 2. Here, $y$ is the dependent variable, $m$ and $c$ are constants, and $x$ is the indep

1. Stating the problem: We need to find the two possible values of $x$ that satisfy the equation $$\frac{54}{2x} = 3x.$$\n\n2. Start by simplifying the equation: $$\frac{54}{2x} =

**Problema:** Expande y simplifica los siguientes cuadrados de sumas usando la fórmula $ (a + b)^2 = a^2 + 2ab + b^2 $.\n\n1. Para $ (x + 2)^2 $:\n- Identificamos $ a = x $ y $ b =

1. The problem is to simplify the expression $$(\sqrt{2}+3)(\sqrt{2}-3)-2+9$$. 2. Start by expanding the product using the difference of squares formula: $$(a+b)(a-b) = a^2 - b^2$$

1. Задача: Розглянемо рівняння лінійної функції $y = 2x + 3$. Потрібно знайти значення $y$ при $x = 4$. 2. Підставляємо $x = 4$ в рівняння:

1. Given the expression to simplify: $$ (36c^6 d^4)^{\frac{1}{2}} $$. 2. Recognize that raising to the power of $\frac{1}{2}$ means taking the square root: $$ \sqrt{36c^6 d^4} $$.

1. Stated problem: Solve the cubic equation $2x^3 - 2x^2 - 4 = 0$. 2. Factor out the common factor of 2:

1. On considère la suite $S_n = \sum_{k=1}^n \frac{k}{2^{k-1}} = 1 + \frac{2}{2} + \frac{3}{2^2} + \cdots + \frac{n}{2^{n-1}}$ définie pour $n \in \mathbb{N}^*$. 2. Montrons la for

1. **State the problem:** Simplify the expression $$\frac{4x^{18} y^8 \times 6x^9 y^{16}}{(2xy^2)^3}$$ and express it in the form $$ax^b y^c$$ where $a$, $b$, and $c$ are constants

1. We are given the matrix equation: $$\begin{pmatrix} x & s - x^2 \\ -3 & 1 \end{pmatrix} \begin{pmatrix} x - 2 & 1 \\ 2 & 1 \end{pmatrix} = \begin{pmatrix} 2 & 9 \\ 6 & c \end{pm

1. **State the problem:** We need to find the average amount of money spent per customer in May. 2. **Given data:**

1. State the problem: Simplify and solve the equation $$\frac{4x^2}{40x} = 3$$. 2. Simplify the left-hand side by dividing numerator and denominator:

1. We are given the equation $(2x^3)^a = bx^{12}$ and need to find the values of $a$ and $b$. 2. First, apply the power to both the coefficient and variable inside the parentheses:

1. Stating the problem: Simplify the expressions for $A$, $B$, and then calculate $C = A(\sqrt{6} - B)$, where $A = \sqrt{150} - 2\sqrt{24} + \sqrt{36}$ and $B = 3\sqrt{8} \times \

1. **State the problem:** Simplify expressions for $A$, $B$, and $C$ given: $$A = \sqrt{150} - 2\sqrt{24} + \sqrt{36}$$

1. We start with the problem: a) Calculate $ (1.8 \times 10^9) + (6.2 \times 10^7) $ in standard form.