🧮 algebra

1. Let's start by specifying the problem clearly: solving a typical Class 9 math problem which might involve algebra, geometry, or arithmetic concepts. 2. Since the user didn't spe

1. **Problem statement:** Evaluate the expressions: $$F = -23 - [2 - 5 \times (3 + (-6) \div 2)]$$

1. The problem is to solve the equation $(t + 1)(t + 2) = 0$. 2. According to the zero product property, if a product of two factors equals zero, then at least one of the factors m

1. The problem is to show that the lines $L_1$ and $L_2$ are parallel. 2. The equation of line $L_1$ is given as $$y = 5x + 1,$$ which is in slope-intercept form $y = mx + b$ where

1. The problem involves understanding the graphs described and their equations. 2. We are given two lines related to a variable $x$ and a parameter $\beta t.i-1$:

1. **Problem i:** Solve the system $$\begin{cases} x_1 - 5x_2 = -85 \\ 2x_1 + 4x_2 = 40 \end{cases}$$

1. Solve $0.2x = 7$. Divide both sides by $0.2$: $$x = \frac{7}{0.2} = 35$$

1. The problem is to solve the equation $$(-1 - m)^2 = 12 - m^2 + 1^2$$ for $m$. 2. Start by expanding $(-1 - m)^2$ using the formula $(a+b)^2 = a^2 + 2ab + b^2$:

1. The user presents several calculations involving powers and numbers: 2. The first expression is $5 \times 5 \times 5$, which equals $5^3$. Calculating, $5 \times 5 = 25$ and $25

1. The problem is to evaluate the expression $1 + (-1)^1$. 2. First, calculate the exponentiation: $(-1)^1 = -1$ since any number raised to the power of 1 is the number itself.

1. **State the problem:** We have the matrix equation $$\begin{bmatrix} x \\ y \end{bmatrix} = \frac{1}{5} \begin{bmatrix} 1 & -2 \\ 2 & 1 \end{bmatrix} \begin{bmatrix} 3 \\ 4 \end

1. **State the problem:** Given the equation

1. It seems you want to see the visual of a "through." 2. Assuming you meant the graph of a function looking like a "trough," this corresponds to a quadratic function or a parabola

1. **Problem statement:** Find the value of the determinant $D$ of the matrix $$A=\begin{bmatrix}1 & -2 \\ 2 & 1\end{bmatrix}.$$ 2. The determinant of a $2\times 2$ matrix $$\begin

1. **State the problem:** We are given the system of equations: $$-7x + 2y = 12$$

1. Let's recall that a matrix is lower triangular if all entries above the main diagonal are zero. 2. For matrix (a):

1. The problem asks us to identify the position of the value -17 in the matrix resulting from adding two given 3x3 matrices. 2. We start by adding the matrices element-wise:

1. The problem is to find the determinant of matrix \( D = \begin{bmatrix} 3 & 4 \\ 6 & ? \end{bmatrix} \).\n\n2. Since the user provides elements 3, 4, and 6, we assume the matrix

1. **State the problem:** We need to multiply a 1x3 matrix $A = [65\ 80\ 30]$ by a 3x2 matrix $B = \begin{bmatrix}1 & 10 \\ 2 & 15 \\ 8 & 55\end{bmatrix}$.\n\n2. **Recall matrix mu

1. Stating the problem: Simplify the expression $$\frac{3}{4x} - \frac{5}{6x^2}$$. 2. Find the common denominator: The denominators are $$4x$$ and $$6x^2$$. The least common denomi

1. Simplify $\frac{3}{4}x - \frac{5}{6}x^2$. - The terms share no common factors, so the expression remains as is: $$\frac{3}{4}x - \frac{5}{6}x^2$$.