🧮 algebra

1. The problem asks to identify the graph of the absolute value function $$y = |x - 2|$$. 2. The absolute value function $$y = |x - a|$$ produces a V-shaped graph with its vertex a

1. The problem is to identify the graph of the absolute value function $$y = |x| - 3$$. 2. The general form of an absolute value function is $$y = |x - h| + k$$, where $$(h, k)$$ i

1. The problem is to identify the graph of the absolute value function $$y = |x - 3|$$ from three given graphs. 2. The general form of an absolute value function is $$y = |x - h|$$

1. **State the problem:** Simplify the expression $2\frac{1}{2} - 1\frac{1}{5}$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} -4, & x \leq -2 \\ x - 2, & -2 < x < 2 \\ -2x + 4, & x \geq 2 \end{cases}$$

1. **Problem statement:** Find the square roots of the numbers: $$10^{12}, 2^6, 4 \times 10^8, 0.0001, 10^{-6}, \frac{9}{49}, 25 \times 10^{-8}, 3^4.$$\n\n2. **Formula and rules:**

1. The problem asks us to determine which inequality is represented by a given number line. 2. To solve this, we need to identify the critical points and the shaded region on the n

1. **State the problem:** Solve the equation $-0.255 = -12 + \frac{(x+12) \times 100000}{115000}$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** We are given the equation $$y=0.003x$$ which models the number of inches of rain $$y$$ after $$x$$ minutes of rainfall. 2. **What is asked?** Find the num

1. **State the problem:** We need to express $x$ in terms of $n$ from the equation:

1. The problem states that the number of inches of rain, $y$, after $x$ minutes of rainfall is modeled by the equation $$y = 0.003x$$ and asks how many inches of rain fall in 2 min

1. **Problem Statement:** We need to identify the graph of the absolute value function $$y = -\frac{1}{2} |x|$$ from the three given graphs. 2. **Understanding the function:** The

1. **State the problem:** Solve the inequality $x + 2x \leq 36$. 2. **Combine like terms:** Since $x$ and $2x$ are like terms, add them together:

1. **State the problem:** We are given the inequality $$100 + 25x < 150 + 20x$$ where $x$ represents the number of hours a moving job takes. We want to find for which values of $x$

1. **State the problem:** Solve for $x$ in the equation $$-0.255 = -12 + \frac{(x+12) \times 15000}{115000}$$

1. **State the problem:** Simplify the expression $$\frac{x^2 - 4}{\frac{4x^2 - 7x - 2}{x}} - 2x$$ and express the answer in the form $$\frac{ax^2}{bx + c}$$ where $a$, $b$, and $c

1. **State the problem:** Simplify the expression $\left(2x^{\frac{3}{2}} y\right)^4$. 2. **Recall the power of a product rule:** For any expressions $a$, $b$ and exponent $n$, we

1. Let's start by stating the problem: We want to understand when a function $a$ is one-to-one (injective). 2. A function $f$ is one-to-one if and only if for every pair of inputs

1. **State the problem:** Determine which of the given functions is one-to-one. 2. **Recall the definition:** A function is one-to-one (injective) if each output corresponds to exa

1. The problem is to simplify the expression given by the user. However, no specific expression was provided, so I will explain the general approach to simplification. 2. Simplific

1. **Problem Statement:** Understand what one-to-one functions and inverse functions are, and how to determine if a function is one-to-one and find its inverse. 2. **One-to-One Fun