🧮 algebra

1. **State the problem:** We want to find the value of $n$ such that the polynomial $x^3 + 22x + n$ becomes a perfect square trinomial. 2. **Understand the form of a perfect square

1. **State the problem:** We are given the cubic expression $x^3 + 22x + n$ and need to analyze or solve it depending on the context (e.g., find roots, factor, or determine $n$ for

1. **State the problem:** Solve the equation $$\frac{x}{4} - 2 = 5$$ for $x$. 2. **Add 2 to both sides** to isolate the term with $x$:

1. **State the problem:** We are given the cubic expression $x^3 + 22x + n$ and need to analyze or solve it depending on the context (e.g., find roots, factor, or determine $n$ for

1. **State the problem:** Simplify the expression $-(-2 \frac{1}{5}) - \left(-\frac{13}{5}\right) - 3 \frac{3}{5}$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Solve the system of inequalities: $$ (x + 3)(2 - x) \leq 0 $$

1. **State the problem:** Hillary collects three times more bottles than Morgan, which is expressed as the equation $h = 3m$. 2. **Given:** $m = 6$ (Morgan collected 6 bottles).

1. **Stating the problem:** Solve for $x$ in the proportion $\frac{x}{12} = \frac{5}{10}$. 2. **Formula used:** For proportions $\frac{a}{b} = \frac{c}{d}$, cross-multiply to get $

1. The problem asks to create an equation in point-slope form using a simplified slope and a point from a table. 2. The point-slope form of a line equation is given by:

1. **State the problem:** Calculate the value of the fraction with numerator $-30 - (-16)$ and denominator $12 - 5$. 2. **Write the expression:**

1. **State the problem:** Add the fractions $\frac{2}{3}$ and $\frac{1}{4}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ wh

1. Stating the problem: Simplify the expression $\frac{9}{10} - \frac{3}{5}$.\n\n2. Find a common denominator: The denominators are 10 and 5. The least common denominator (LCD) is

1. The problem asks to simplify the expression $3t \cdot 3(-t)$. 2. The expression involves multiplication of terms. Recall the rule: when multiplying, multiply coefficients (numbe

1. **Problem:** Find the traits algebraically for the function $y = x^3 - x^2 - 9x + 9$ (problem 2). 2. **Formula and rules:** To analyze a cubic function, find:

1. **State the problem:** Marko originally filled out 8 more applications than Henry.

1. **State the problem:** Solve the system of linear equations: $$y = x + 1$$

1. **State the problem:** Meya and Eric's combined ages equal Sam's age, which is 69 years.

1. Problem: Find the factors of $11x^2y$. Factors are numbers or variables multiplied together to get the expression. Here, the factors are $11$, $x$, $x$, and $y$.

1. Problem: Find the common difference in the arithmetic sequence 5, 7, 9, 11, ... The common difference $d$ in an arithmetic sequence is found by subtracting any term from the nex

1. Problem: Find the answers to the given arithmetic expressions involving integers. 2. Formula and rules:

1. **State the problem:** We are given the sequence $35, \frac{35}{3}, \frac{8}{9}, \frac{17}{27}, \ldots$ and asked to find: (a) the common difference or common ratio,