🧮 algebra

1. The problem is to find the numbers that fill the blanks in the sequence: 27430 _____ 27459 27459 _____. 2. We observe the sequence and note that 27459 appears twice consecutivel

1. **State the problem:** Find the roots of the quadratic equation $$2x^2 - 12x - 7 = 0$$. 2. **Formula used:** The roots of a quadratic equation $$ax^2 + bx + c = 0$$ are given by

1. The problem is to understand the expression "on 12 it has x" which seems incomplete or unclear. 2. Since the problem is not fully stated, let's interpret it as solving for $x$ i

1. **State the problem:** Find the roots of the quadratic equation $$2x^2 - 12 - 7 = 0$$. 2. **Rewrite the equation:** Combine like terms:

1. **State the problem:** Simplify the expression $x(x - 1)(x + 4) - 2x^2 + 4$. 2. **Expand the product:** First, expand $x(x - 1)(x + 4)$.

1. **State the problem:** Find the points of intersection between the quadratic function and the linear function for the first pair: $$y = 2x^2 - 3x + 1$$ and $$y = x - 1$$. 2. **S

1. **State the problem:** Given the ratio $\frac{x}{y} = \frac{2}{3}$, find the value of $\frac{6x + y}{3x + 2y}$.\n\n2. **Use the given ratio:** From $\frac{x}{y} = \frac{2}{3}$,

1. **State the problem:** We are given the equation $\frac{3m+n}{n-m} = 9$ and need to find the ratio $m:n$. 2. **Write the equation:**

1. সমস্যা: একটি সরলরেখার সমীকরণ $2x + 3y = 6$ থেকে $y$ এর মান বের করুন। 2. সূত্র: সরলরেখার সমীকরণ সাধারণত $Ax + By = C$ আকারে থাকে। এখানে $y$ বের করতে হলে $y$ কে একপাশে রেখে বাকি অ

1. **Problem Statement:** Find the equation of the tangent line to the circle given by $$x^2 + y^2 - 3x + 10y = 15$$

1. The problem is to simplify or understand the expression $x - y + a1$. 2. This expression consists of three terms: $x$, $-y$, and $a1$.

1. **State the problem:** Simplify the expression $4x + 7(4 + y) - 3x$. 2. **Apply the distributive property:** Multiply 7 by each term inside the parentheses:

1. The problem is to find the partial fraction decomposition of the rational expression $$\frac{x^2 + 4}{(x+1)(x^2 + 2)}.$$\n\n2. The formula for partial fraction decomposition whe

1. **State the problem:** We need to subtract $\frac{1}{6}$ from $\frac{7}{12}$.\n\n2. **Formula and rules:** To subtract fractions, they must have a common denominator. The formul

1. **State the problem:** Add the fractions $\frac{3}{4}$ and $\frac{11}{12}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. Find the least commo

1. **State the problem:** We want to analyze and understand the function $$f(x) = \sqrt{2x^2 - 9x - 5}$$ and determine where it is defined and its graph shape. 2. **Domain of the f

1. The problem appears to be a sequence of numbers: 2,400,000; 2,100,000; 1,800,000; 1,500,000; 1,200,000; 900,000. 2. We want to identify the pattern or rule governing this sequen

1. Planteamos el problema: Encontrar la ecuación de la recta que pasa por el punto $\left(\frac{1}{2}, -\frac{2}{3}\right)$ y es perpendicular a la recta dada $9x - 5y = 1$. 2. Pri

1. **State the problem:** We are given a quadratic profit function $P = ax^2 + bx + c$ where $x$ is the number of items produced and $P$ is the weekly profit. We have three data po

1. Stating the problem: Factorize the expression $$E = x^2 - 2x - 15$$. 2. Use the quadratic expression factorization formula: For $$ax^2 + bx + c$$, find two numbers that multiply

1. Problema: Hallar la ecuación de la recta que pasa por el punto $\left(\frac{1}{2}, -\frac{2}{3}\right)$ y es perpendicular a la recta dada por $9x - 5y = 1$. 2. Primero, encontr