🧮 algebra

1. We are given a system of two equations with variables $m$ and $n$: $$\frac{m}{2} + \frac{n}{3} - \frac{13}{6} = 0$$

1. Stating the problem: We know the battery was charged from 23% to 89% over 30 minutes.

1. Mari kita nyatakan harga sebuah pensil sebagai $x$. 2. Karena harga sebuah buku adalah 3 kali harga sebuah pensil, maka harga sebuah buku adalah $3x$.

1. **State the problem:** Solve for $b$ in the equation $$2b - 7 = \frac{1}{3}b + 3$$. 2. **Isolate variable terms:** Subtract $\frac{1}{3}b$ from both sides to get all $b$ terms o

1. We are given the function $p(u) = u^3 - 3u^2 + 4u$ with $u$ in meters. The problem involves understanding this cubic function and its interaction with the factor $(u - 2)$, whic

1. The problem is to define the region shaded on the graph which is bounded by the curve $y^2 = 4x$, the line $x=1$, and the x-axis ($y=0$). 2. First, understand the curve. The equ

1. The problem is to factorize the quadratic expression $$x^2 + 5x + 6$$. 2. Start by breaking the middle term into two terms whose coefficients add up to 5 and multiply to 6. Here

1. Solve $5r^2 + 10r = 80$ by completing the square. Step 1: Divide the entire equation by 5 to simplify:

1. Stating the problem: Solve the equation $34 = 4 + 6x$ for $x$. 2. Subtract 4 from both sides to isolate the term with $x$:

1. **State the problem:** Solve the equation $$38 = 10h + 7$$ for $h$. 2. **Isolate the term with $h$:** Subtract 7 from both sides:

1) Calculate the following: &i. Calculate $1^2 - 2^3 \times 3 + 8 \div 4 - (3^3 + 2)$:

1. State the problem: Solve the linear equation $$10.5 = 3x - 1.5$$ for $x$. 2. Add $1.5$ to both sides to isolate the term with $x$:

1. Stating the problem: Solve the linear equation $$3x - 1.5 = 13.5$$. 2. Add 1.5 to both sides to isolate the term with $$x$$:

1. The problem is to solve the equation $$\frac{n - 5}{3} = 6$$ for $n$. 2. To eliminate the fraction, multiply both sides of the equation by 3:

1. State the problem: Solve the equation $\frac{y + 1}{2} = 6$ for $y$. 2. Multiply both sides of the equation by 2 to eliminate the denominator:

1. **State the problem:** Find the domain and range of the functions: - $$y = x^2$$

Problem statement: Solve the listed algebra and matrix problems as given by the user. 1. a) Problem 1(a): If the demand and supply laws are $2p^2+q^2=3$ and $p+q=2$ find the equili

1. مسئلہ بیان کریں: 4n² اور 5n³ کا حاصل ضرب نکالیں۔ 2. حاصل ضرب:

1. The problem involves finding values of $a$ and $b$ for the polynomial $f(x) = ax^3 - 15x^2 + bx - 2$ where $2x - 1$ is a factor and the remainder when divided by $x-1$ is 5. 2.

1. The problem asks for the sum of the powers of 2 and 3 in the prime factorization of 8640. 2. Find prime factorization of 8640:

1. Problem 1: Given a 3x3 matrix \(A=\begin{bmatrix}1 & 0 & 0 \\ 2 & -3 & 0 \\ 1 & 4 & 2\end{bmatrix}\), - We know the sum of two eigenvalues equals the trace of \(A\).