🧮 algebra

1. **State the problem:** Find the 8th term of the arithmetic progression (A.P.) with the first three terms given as $-3, -1, 1$. 2. **Identify the formula:** The $n$th term of an

1. **State the problem:** Find an open interval about $c=4$ such that for all $x$ in this interval, the inequality $|f(x) - L| < \varepsilon$ holds, where $f(x) = x + 1$, $L = 5$,

1. **State the problem:** Calculate the value of $-2 \frac{7}{10} \div \frac{12}{7}$. 2. **Convert mixed number to improper fraction:** $-2 \frac{7}{10} = -\left(2 + \frac{7}{10}\r

1. **State the problem:** Find the slope of the line passing through the points $(-3, -1)$ and $(2, 2)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1

1. Let's start by understanding the general form of a sinusoidal function: $$y = a \sin(bx + c) + d$$ or $$y = a \cos(bx + c) + d$$. 2. In this formula, the amplitude is the absolu

1. **State the problem:** We need to divide the mixed number three and one-half by the mixed number four and two-thirds. 2. **Convert mixed numbers to improper fractions:**

1. 题目：求解方程 $2x + 3 = 7$ 的解。 2. 公式和规则：

1. **State the problem:** Solve the equation $$5x + 2 - 3x = 8 + 2x - 10$$ for $x$. 2. **Simplify both sides:** Combine like terms on each side.

1. **State the problem:** Solve the equation $$3x + 2x - 1 = 4 + 5x - 5$$ for $x$. 2. **Combine like terms:** On the left side, combine $3x$ and $2x$ to get $5x$.

1. **State the problem:** Find the slope of the line passing through the points $(8, -4)$ and $(4, -6)$. 2. **Formula for slope:** The slope $m$ of a line passing through two point

1. The problem asks to find $f(-x)$ and $-f(-x)$ for the function $f(x)$, then compare these with $f(x)$ to determine if the function is even, odd, or neither. 2. Recall the defini

1. **State the problem:** Solve the equation $$2(x + 3) = x + 3 + x$$ for $x$. 2. **Write down the equation:** $$2(x + 3) = x + 3 + x$$

1. **State the problem:** Find the 8th term of the arithmetic progression (A.P.) with the first three terms given as $-3, -1, 1$. 2. **Identify the formula:** The $n$th term of an

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **Problem Statement:** We are given a table of time $t$ (in seconds) and distance $D(t)$ (in meters) driven by Salma's racecar. We need to find the average rate of change of dis

1. **State the problem:** We need to write an equation in slope-intercept form to represent the amount of gas $y$ in the tank after $x$ minutes of pumping gas. 2. **Recall the slop

1. **State the problem:** Simplify the expression $$36^{\frac{1}{2}} \times 64 - \frac{1}{3} \times 5^0$$. 2. **Recall important rules:**

1. **State the problem:** Find the slope of the line passing through the points $(-7, 2)$ and $(9, 6)$. 2. **Formula:** The slope $m$ of a line passing through points $(x_1, y_1)$

1. **State the problem:** Simplify the expression $$36^{\frac{1}{2}} \times 64 - \frac{1}{3} \times 5^0$$. 2. **Recall the rules:**

1. **State the problem:** Solve for $y$ in the proportion $$\frac{924}{396} = \frac{658}{y}.$$\n\n2. **Formula and rule:** In a proportion $\frac{a}{b} = \frac{c}{d}$, the cross pr

1. **State the problem:** We are given the proportion $$\frac{h}{235} = \frac{20}{5}$$ and need to solve for $h$. 2. **Formula and rule:** In a proportion $\frac{a}{b} = \frac{c}{d