🧮 algebra

1. **Stating the problem:** We are given sequences of tables and chairs and need to identify and correct the incorrect formulas for the number of chairs based on the number of tabl

1. **State the problem:** Find the zeros of a polynomial function. Zeros are the values of $x$ where the polynomial equals zero. 2. **Formula and rules:** To find zeros, solve the

1. The problem is to find the value of $$-0.2 - 1.3$$. 2. Subtraction of a number is equivalent to adding its opposite. So, $$a - b = a + (-b)$$.

1. Masalah: Hitung hasil dari $12^2 \times 5^2 \times 9^2$. 2. Gunakan aturan pangkat: $a^2 \times b^2 \times c^2 = (a \times b \times c)^2$.

1. The problem is to multiply the matrix \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \) by the scalar 3. 2. The formula for scalar multiplication of a matrix is to multiply eac

1. Diberikan fungsi $f(x) = 3x + 4$ dan $g(x) = \frac{x^2 - 2x}{x^2 - 2x}$. Kita diminta mencari nilai $(f \circ g)(-1)$, yaitu $f(g(-1))$. 2. Pertama, hitung nilai $g(-1)$:

1. **State the problem:** Given the system of equations $$x^2 y^3 = 10$$ and $$x^3 y^2 = 8$$, find the value of $$x^5 y^5$$. 2. **Understand the goal:** We want to find $$x^5 y^5$$

1. **State the problem:** Given that $3^x = 10$, find the value of $3^{x-3}$. 2. **Recall the exponent rule:** For any base $a$ and exponents $m$ and $n$, we have $$a^{m-n} = \frac

1. **State the problem:** Given the equation $$\frac{2^x}{2^y} = 2^3$$, find the value of $x$ in terms of $y$. 2. **Recall the exponent rule:** When dividing powers with the same b

1. **State the problem:** Determine if the relation \{(-8, -1), (-7, -7), (-5, 9), (9, -8)\} represents a function. Also, find the domain and range of the relation. 2. **Definition

1. **State the problem:** We are given the linear equation $5x - 3y = 4$ and the function $f(x) = \frac{5}{3}x - \frac{4}{3}$. We want to verify if $f(2) = 2$ is correct. 2. **Rewr

1. **Problem:** Find the L.C.M. of 6, 72, and 120 using the prime factorisation method. 2. **Formula and Rules:**

1. **State the problem:** Solve for $n$ in the equation $$4^{2n+3} = 8^{n+5}.$$ 2. **Rewrite bases as powers of 2:**

1. **State the problem:** We need to find the value of $$n = 1^2 + 1^4 + 1^6 + 1^8 + \ldots + 1^{50}$$. 2. **Understand the terms:** Each term is $$1$$ raised to an even power from

1. The problem asks to find the product of two functions $f(x) = 2x + 1$ and $g(x) = x^2 - 3x$. 2. The formula for the product of two functions is:

1. **State the problem:** Find the value of $a$ given the equation or context (not provided explicitly, so assuming a typical algebraic problem). 2. **Formula and rules:** To find

1. **State the problem:** Given that $a^{-\frac{1}{2}} = 3$, find the value of $a$. 2. **Recall the rule for negative exponents:** $a^{-n} = \frac{1}{a^n}$.

1. **State the problem:** Given that $3^x = 10$, find the value of $3^{x-3}$. 2. **Recall the exponent rule:** For any base $a$ and exponents $m$ and $n$, we have $$a^{m-n} = \frac

1. **State the problem:** We need to express the graphed function as a piecewise function based on the given points and intervals. 2. **Analyze the graph:**

1. The problem is to find the value of 1, which is a straightforward constant. 2. Since 1 is a constant, it does not require any calculation or formula.

1. Bài toán yêu cầu tính giá trị của biểu thức $$\frac{2}{5} + \frac{5}{4} + \left(-\frac{2}{5} + \frac{5}{4}\right) - \frac{5}{2}$$. 2. Ta sẽ thực hiện từng bước tính toán theo th