🧮 algebra

1. The problem states that a farmer bought material for 325000 after a 35% discount. 2. Let the marketed price be $x$.

1. Problem: Setze für ■ eine passende Zahl bzw. einen passenden Term ein, sodass unter der Wurzel eine binomische Formel entsteht, und ziehe dann die Wurzel. 2. a) Gegeben: $$\sqrt

1. **State the problem:** Solve the quadratic equation $x^2 - 7x + 5 = 0$. 2. **Identify coefficients:** Here, $a = 1$, $b = -7$, and $c = 5$.

1. **State the problem:** We need to find the cost of linoleum to cover a dining room described by the region bounded by the y-axis ($x=0$), x-axis ($y=0$), the line $y=25-5x$, and

1. State the problem: Simplify the expression $$32 - [36 - 2\{5 \times 2 + 7 - 6\}]$$. 2. Simplify inside the curly braces first: Calculate $$5 \times 2 + 7 - 6$$.

1. **State the problem:** We sell an article for 216 resulting in a loss. If sold for 300, the gain is 2.5 times the loss. We need to find the cost price (CP).

1. The problem asks to find the product of 2 and the square root of 3. 2. We write this mathematically as $2 \times \sqrt{3}$.

1. **Problem statement:** We consider the lattice formed by the divisors of 105, denoted as 105D, with the partial order defined by divisibility. We need to (i) draw the Hasse diag

1. The problem is to simplify the expression $-2\sqrt{x}27 - 3\sqrt{x}45$. 2. First, rewrite the terms by separating the constants and the square roots:

1. To help you simplify further, please provide the specific expression or equation you want to simplify. 2. Simplification depends on the form and terms of the expression.

1. The problem is to analyze the function $z8(x) = -4x$ and $y = -4x$, which are linear functions. 2. Both functions have the form $y = mx + b$ where $m$ is the slope and $b$ is th

1. The problem involves understanding and manipulating the function $f(x) = 5x^2 - 10$. 2. Given $y = 5x^2 - 10$, we want to express $x$ in terms of $y$.

1. **State the problem:** Solve the quadratic equation $x^2 - 6x - 3 = 0$. 2. **Identify coefficients:** Here, $a = 1$, $b = -6$, and $c = -3$.

1. **State the problem:** Solve the system of equations using Gauss-Elimination Method: $$\begin{cases} x + y + z = 6 \\ 2x + 3y + z = 14 \\ x - y + 2z = 7 \end{cases}$$

1. Let's start by stating the problem: A quadratic equation is a polynomial equation of degree 2, generally written as $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are constants a

1. **State the problem:** We are given the original ratio of workers to supervisors as 8:2. 2. **Express the original numbers:** Let the number of workers be $8x$ and the number of

1. **State the problem:** The original ratio of students to teachers is 5:1. After 10 more teachers join, the ratio changes to 5:2. We need to find the original number of students.

1. Find the domain of each rational expression. 1.a. Expression: $$\frac{x^2 - 4}{x^2 + 3}$$

1. **State the problem:** Simplify the expression $$6.2 \div \left[ 3.8 + \left\{ 10.6 - \left( 30 - 25 - \frac{4}{5} \times 3.5 + 4.0 \right) \right\} \right]$$. 2. **Calculate th

1. Let's start by understanding the problem: you want a step-by-step explanation for solving a math problem. Since no specific problem was given, I'll demonstrate solving a simple

1. The problem states that the mice population starts at 25,000 and decreases by 20% each year. 2. To model this, we use an exponential decay function: $$P(t) = P_0 (1 - r)^t$$ whe