🧮 algebra

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.

1. State the problem: Calculate \( \frac{2.45 \times 10^{-5} \times 4.76 \times 10^{12}}{8.06 \times 10^{3}} \) and express the answer in standard form to 3 significant figures. 2.

1. We are given the expression $$\frac{2.45 \times 10^{-5} \times 4.76 \times 10^{12}}{8.06 \times 10^{3}}$$ and asked to simplify it and express the answer in standard form with 3