🧮 algebra

1. **State the problem:** We need to find the value of the piecewise function $f(x)$ at $x = -5$. 2. **Identify the correct piece:** The function is defined as:

1. **State the problem:** A trader sold a Mathematics textbook for Le4940 and made a profit of 30%. We need to find the price at which he bought the book. 2. **Formula used:** The

1. **State the problem:** We need to find the value of the piecewise function $f(x)$ at $x=6$. 2. **Understand the piecewise function:**

1. The problem is to find the logarithm of 3000 using mathematical tables. 2. We use the property of logarithms: $$\log(ab) = \log a + \log b$$.

1. 問題陳述：計算 $\exp(-24.65)$ 的近似值。 2. 公式與規則：

1. The problem is to identify the graph of the absolute value function $$y = |x + 1|$$. 2. The general form of an absolute value function is $$y = |x - h|$$, where the vertex is at

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 $$-0.255 = -12 + \frac{(x+12) \times 15000}{115000}$$