🧮 algebra

1. Solve the system using elimination method: Given:

1. **Problem statement:** We are given that when a polynomial $P(x)$ is divided by $x+4$, the quotient is $x^2 - x + 7$ and the remainder is $-5$. We need to find $P(x)$. 2. **Reca

1. Problem 1: A human resource officer allocates employees to Accounts, Computer, and Human Resource Management departments in the ratio 3:4:5. Step 1: Let the total number of empl

**Problem:** Solve the exponential equation $$10^x = \frac{1}{10,000}$$. 1. Recognize that 10,000 can be written as a power of 10: $$10,000 = 10^4$$.

1. The problem involves sequences or sets of fractions: (i) $\frac{2}{5}, \frac{2}{5}, \frac{1}{5}$; (ii) $\frac{1}{5}, \frac{1}{2}, \frac{3}{5}$. We analyze each part separately.

1. Masalah yang diberikan: Jika $\sqrt{12} + 8\sqrt{2} = 2\sqrt{b} + a$, tentukan nilai $a+b$. 2. Pertama, kita sederhanakan $\sqrt{12}$. Kita tahu $\sqrt{12} = \sqrt{4 \times 3} =

1. [Yig'indini hisoblash] Berilgan yig'indi: $$ \sum_{k=1}^{2025} \frac{2025!}{(2025-k)!} (-1)^k 2^k $$Bu yig'indi raqamlarni tartib bilan kiritilgan va har bir k uchun ifoda mavju

1. The problem is to summarize the main points of a function concept typically denoted by $f(x)$. 2. A function $f(x)$ is a rule that assigns to each element $x$ in the domain exac

1. A function is a relation where each input has exactly one output. 2. The domain is the set of all possible inputs for the function.

1. Diketahui persamaan: $$7 \div \frac{\sqrt{9}}{2} \times x = 28$$ 2. Ingat bahwa $$\sqrt{9} = 3$$, jadi persamaan menjadi: $$7 \div \frac{3}{2} \times x = 28$$

1. Step 2 typically involves applying a key operation or transformation from the first step's result. 2. To explain thoroughly, identify the exact operation: Are we simplifying, fa

1. **State the problem:** We have a regression equation $$\hat{y} = b_0 + b_1 x$$ where $$b_0=700$$ (y-intercept) and $$b_1=-50$$ (slope). We need to find the predicted value of $$

1. Diberikan persamaan kuadrat $$x^2 - 4x + m = 0$$ dengan akar-akar $$x_1$$ dan $$x_2$$. 2. Menurut rumus jumlah akar-akar dan hasil kali akar-akar persamaan kuadrat, kita punya:

1. **Problem 1.1: Solve the quadratic equation** $$x^2 + 14x + 45 = 0$$ Step 1: Identify coefficients: $$a=1$$, $$b=14$$, and $$c=45$$.

1. Given the quadratic equation $$x^2 + p x + 4 = 0$$ with roots $$\alpha$$ and $$\beta$$. 2. We know from Vieta's formulas:

1. The problem is to evaluate the expression $8 - 11 \times (-6)$.\n2. According to the order of operations, multiplication is done before subtraction.\n3. Multiply $11$ by $-6$: $

1. The problem is to evaluate the expression $8 - 11 \times (-66)$. 2. According to the order of operations, multiplication comes before subtraction. So first, calculate $11 \times

1. The expression given is $8 - 11 x - 6$. 2. Usually, multiplication is implied between a number and a variable, so $11 x$ means $11\times x$.

1. The problem is to simplify the expression $8 - 11 \times -66$. 2. According to the order of operations (PEMDAS/BODMAS), we first perform the multiplication:

1. The problem is to simplify the expression $8 - 11 \times 6$. 2. According to the order of operations, multiplication is performed before subtraction.

1. The problem is to find the equation of the parabola given by $$y = x^2 + 3x + 6$$ after a rotation of 270° about the point $$(-2,4)$$. 2. First, translate the coordinate system