🧮 algebra

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 \(A\).

1. **Simplify** $-5x^4 - 9y^3 + 3xy - 2x^2 + 11y^3 - 25xy$. Combine like terms:

1. The problem asks us to expand $ (10+2)^5 $ using the binomial theorem. 2. The binomial theorem states:

1. **State the problem:** Simplify the expression $$-5x^2 - 9y^3 + 3xy = - 2x^2 + 11y^3 - fxy$$ and find the value of $f$ such that both sides are equal. 2. **Collect like terms:**

1. The question seems to ask whether the answer could be $1.5$ or $-1.5$. 2. Without additional context or an equation to verify, we cannot confirm if $1.5$ or $-1.5$ is correct.

1. The problem asks for the average speed of the train between 30 and 40 minutes. 2. Average speed is calculated by the change in distance divided by the change in time: