🧮 algebra

1. We are given two points: $(5,2)$ and $(-2,-12)$. 2. The goal is to find the equation of the line passing through these points in standard form and general form.

1. The problem is to solve for the variable in the equation labeled as No. 2. Since the exact equation is not provided, please provide the full equation or problem statement for No

1. **Problem:** Convert the line passing through points $(7, -1)$ and $(8, 2)$ into standard form and general form. 2. **Formula:** The slope $m$ of a line through points $(x_1, y_

1. **Problem:** Multiply the equation $2x - 3y = 5$ by 2. Formula: Multiply each term by 2.

1. Stating the problem: Solve the quadratic equation $0 = x^2 - 3x + 2$. 2. Formula used: The quadratic equation $ax^2 + bx + c = 0$ can be solved by factoring, completing the squa

1. **State the problem:** Solve the quadratic equation $x^2 + 8x + 15 = 0$. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the solutions are g

1. The problem is to simplify the expression $$\frac{2}{\sqrt{3}-1}$$ so that there is no square root in the denominator. 2. To remove the square root from the denominator, we mult

1. **Problem Statement:** Write a profit function for producing and selling $x$ thousand notebook computers given the cost function $C(x) = 4000 + 500x$ thousand dollars and the pr

1. **Stating the problem:** We are given the series: A 7 9 H' 9 12 C 12 16 J ? and asked to find the next element. 2. **Analyzing the series:** The series alternates between letter

1. **Stating the problem:** We are given the series: A 7 9 H' 9 12 C 12 16 J ? and asked to find the next element. 2. **Analyzing the series:** The series alternates between letter

1. The problem is to evaluate the expression $120 \div (-15) - 6 \times (-3)$.\n\n2. We use the order of operations (PEMDAS/BODMAS): first division and multiplication from left to

1. Diberikan ekspresi: $1 - \frac{1}{2} + \frac{2}{3} - \frac{3}{4}$. 2. Kita akan menyelesaikan langkah demi langkah dengan menyamakan penyebut agar mudah dijumlahkan.

1. **State the problem:** Solve the quadratic expression $\frac{1}{4}x^2 + 3x + 9$ or simplify it if possible. 2. **Formula and rules:** This is a quadratic expression in standard

1. The problem is to find 49 expressions arranged in a 7x7 grid (cells labeled a to g for rows and columns) such that each expression is a distinct integer and all 49 integers are

1. **Problem statement:** Calculate the value of $A = \frac{\left(-\frac{4}{3}\right)^4}{\left(\frac{4}{5}\right)^2} \times \left(-\frac{2}{3}\right)^{2^2}$ and express it as a pow

1. **Problem statement:** Find a general formula for a 7x7 magic square using 7 variables $a,b,c,d,e,f,g$ such that all 16 sums (7 rows, 7 columns, and 2 main diagonals) are equal.

1. **State the problem:** Solve the system of equations using the substitution method: $$\begin{cases} 4x - 3y + z = -10 \\ 2x + y + 3z = 0 \\ -x + 2y - 5z = 17 \end{cases}$$

1. **State the problem:** We are given a function $f : \mathbb{R}^2 \to \mathbb{R}$ defined by the conditions: $$f(0,y) = y + 1$$

1. **State the problem:** Solve the system of equations using the substitution method: $$\begin{cases} 4x - 3y + z = -10 \\ 2x + y + 3z = 0 \\ -x + 2y - 5z = 17 \end{cases}$$

1. **State the problem:** Solve the system of equations using the substitution method: $$\begin{cases} 4x - 3y + z = -10 \\ 2x + y + 3z = 0 \\ -x + 2y - 5z = 17 \end{cases}$$

1. **State the problem:** Solve the equation $ (2^x)^2 - 3 \times 2^x + 2 = 0 $. 2. **Substitution:** Let $ y = 2^x $. Then the equation becomes: