🧮 algebra

1. Let's start with a simple algebra problem: Solve for $x$ in the equation $2x + 3 = 7$. 2. To isolate $x$, subtract 3 from both sides: $$2x + 3 - 3 = 7 - 3$$ which simplifies to

1. Stating the problem: We are given the system of equations: $$X + \sqrt{Y} = 11$$

1. **Stating the problem:** Determine which among the sets A, B, or C have points that lie on the same straight line. 2. **Approach:** Points are collinear if the slope between any

1. Posons le système S donné : $$\begin{cases} 2x + y - 3 \leq 0 \\ x - y + 2 \geq 0 \\ x > -3 \\ y > -4 \end{cases}$$

1. You asked for material suitable for Class 9 level. 2. Class 9 math typically covers algebra, geometry, statistics, and number systems.

1.\ نبدأ بكتابة نظام المعادلات في صورة مصفوفة موسعة: $$\begin{bmatrix}1 & 9 & -1 & | & 27 \\ 1 & -8 & 16 & | & 10 \\ 2 & 1 & 15 & | & 37\end{bmatrix}$$

1. The problem is to find the equation of the column (vertical line) that passes through the point (3,2) and also intersects the line described by equation $y=1$. 2. A vertical lin

1. The problem asks for a line parallel to the vertical line $x=1$ passing through the point $(3,2)$. 2. Lines parallel to $x=1$ are also vertical lines, meaning they have the equa

1. The problem is to solve the equation $$\frac{3}{4}a + \frac{4}{5}b = 54$$ for $b$. 2. We want to isolate $b$, so start by subtracting $$\frac{3}{4}a$$ from both sides:

1. **State the problem:** We are given the function $F(x) = x \sqrt{x} - 1$. We want to understand and simplify this function. 2. **Rewrite the function:** Recall that $\sqrt{x} =

1. Problem: Solve the system \{3u - 2v = 9, 7u - 5v = 28\} and find $u - v$. Step 1: Multiply the first equation by 5 and the second by 2 to eliminate $v$:

1. **State the problem:** Calculate the CGPA (Cumulative Grade Point Average) for the given marks using the scale where 85 out of 100 corresponds to a GPA of 4.00. 2. **Understand

1. **Problem A: Find a closed-form for $a_n$ and determine $a_{100}$.** Given $a_1=1$ and recursive relation

1. The problem is to solve a quadratic equation of the form $ax^2+bx+c=0$ using the quadratic formula. 2. The quadratic formula states that the solutions for $x$ are given by:

1. The problem is to solve the quadratic equation $$3y^2 - 2y + 5 = 0$$. 2. Identify coefficients: $$a=3$$, $$b=-2$$, $$c=5$$.

1. **State the problem:** Given the equation $2 \log x + \log(y-2) = 0$, find $y$ in terms of $x$. 2. **Use logarithm properties:** Recall that $a \log b = \log b^a$. So rewrite $2

1. First, state the problem: Solve the equation $$0\cdot 3y^2 - 2y + 5 = 0$$. 2. Notice that $$0\cdot 3y^2 = 0$$, so the equation simplifies to $$-2y + 5 = 0$$.

1. We are asked to solve the quadratic equation $3y^2 - 24y + 5 = 0$ using the quadratic formula. 2. Recall the quadratic formula for an equation $ay^2 + by + c = 0$ is:

1. The problem is to find $y$ in terms of $x$. 2. Since no specific equation or relation between $y$ and $x$ is given, the problem is incomplete as stated.

1. Stating the problem: We are given the equation $2 \log x + \log (y-2) = 0$. 2. Use the logarithm power rule to simplify $2 \log x$ as $\log x^2$.

1. Solve $3(2x - 1) - 2(x + 4) = 6$. Expanding: $6x - 3 - 2x - 8 = 6$.