🧮 algebra

1. **State the problem:** Solve the system of equations: $$X + m - t = 150$$

1. Muammo: Berilgan ifodalardan eng kattasini toping: A) $\log_2 18 - \log_2 9$

1. The problem is to understand the mathematical constant $e$. 2. The number $e$ is an irrational and transcendental constant approximately equal to 2.71828.

1. **State the problem:** Solve the equation $X + m - t = 150$ for $X$. 2. **Formula and rules:** To isolate $X$, we need to move the terms $m$ and $-t$ to the other side of the eq

1. **Problem 15:** Given $f(x - 1) = (x + 2)^2 - 3$, find the vertex coordinates of $y = f(x - 2) + 1$. 2. First, rewrite $f(x)$ from $f(x - 1)$:

1. Problem: Determine if the function $f: \mathbb{R} \to \mathbb{R}^+$ defined by $f(x) = x^2$ is invertible. 2. To check invertibility, a function must be one-to-one (injective) a

1. **Problem statement:** Simplify the expression $$\frac{6}{2 - \sqrt{10}} + \frac{5\sqrt{2} - 2\sqrt{5}}{\sqrt{5} - \sqrt{2}} - \sqrt{7 - 2\sqrt{10}}$$. 2. **Rationalize denomina

1. **Problem Statement:** Determine which statement about the graph of $$y = (3 - 2x)^2 + 1$$ is true. 2. **Rewrite the function:** Expand the square to get the quadratic in standa

1. **State the problem:** Solve the system of equations using Cramer's rule: $$3x - 2y = 4$$

1. **State the problem:** We have three lines L₁, L₂, and L₃ with given intercepts and relationships: L₁ has x-intercept -6 and y-intercept 4, L₁ is perpendicular to L₂, and L₁ is

1. **Stating the problem:** We have two lines $L_1: x + \alpha y + b = 0$ and $L_2: x + cy + d = 0$ with constants $\alpha, b, c, d$. We want to determine which of the statements I

1. **Problem statement:** Given two lines $L_1: 3x + ky - 2 = 0$ and $L_2: 6x + y + k = 0$, where $k$ is a non-zero constant, find the $y$-intercept of $L_2$ if the lines are perpe

1. **State the problem:** Solve the system of equations using the elimination method: $$\begin{cases} x + y = 7 \\ x - y = 1 \end{cases}$$

1. **Stating the problem:** We are given a quadratic function $y = f(x)$ with a graph of a downward-opening parabola. 2. **Given information:**

1. **Stating the problem:** We want to understand the sum of the first 8 natural numbers: $$1 + 2 + 3 + \dots + 7 + 8$$ and explore the approximations involving expressions like $$

1. **Stating the problem:** We are given the quadratic function $$y = a(x + h)^2 + k$$ with constants $a$, $h$, and $k$. The graph is a parabola opening downwards with vertex at $(

1. **Problem Statement:** We are given the quadratic function $$y = a(x + h)^2 + k$$ where $$a$$, $$h$$, and $$k$$ are constants. The graph is a parabola opening downwards with ver

1. The problem states that the graph of $y = (mx + n)^2 - 1$ passes through the origin $(0,0)$ and we need to determine which statements about $m$ and $n$ are true. 2. Since the gr

1. **State the problem:** Solve the equation $$9^x = 3^{2x+1}$$ for $x$. 2. **Rewrite the bases:** Note that $9$ can be written as $3^2$, so rewrite the equation as $$\left(3^2\rig

1. **Problem 8:** Given the polynomial $f(x) = 8px^3 + 4qx^2 - 6x$, where $p$ and $q$ are constants, and $f(x)$ is divisible by $2x + 3$. We need to find the remainder when $f(x)$

1. The problem asks to simplify the expression \( \frac{5:2}{3} \).\n2. First, interpret the colon ":" as division, so \(5:2 = \frac{5}{2}\).\n3. Now the expression becomes \( \fra