🧮 algebra

1. **State the problem:** Solve the equation $4b = 24$ for $b$. 2. **Formula and rule:** To isolate $b$, divide both sides of the equation by 4. The rule is that whatever you do to

1. **State the problem:** We have an arithmetic sequence: -9, -2, 5, 12, ... We need to find the first term $f(1)$ and the common difference $d$.

1. **Problem Statement:** Determine which statement about the ball's motion is not true based on the graph of height vs. time. 2. **Given Information:** The graph is a downward-ope

1. **State the problem:** We have three sequences and need to order them by their common ratios from least to greatest. 2. **Recall the formula for the common ratio in a geometric

1. The problem asks to identify which quadratic function matches the given graph. 2. The options are:

1. The problem is to solve for $v$ in the equation \frac{v - 78}{2} = 6. 2. The formula used here is to isolate $v$ by undoing the division by 2. Multiply both sides of the equatio

1. **State the problem:** We want to understand the relationship between the number of batteries $x$ and the total cost $y$ based on the given data and equation. 2. **Identify the

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. We can

1. **State the problem:** Simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. **Formula and rules:** To simplify a rational expression, factor numerator and denominator and cancel

1. **State the problem:** Expand and simplify the expression $$(5x+3)(-4x-3)$$. 2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by e

1. The problem is to expand and simplify the expression $(x + 5)(x - 5)$. 2. Use the distributive property (FOIL method) to expand: $ (x + 5)(x - 5) = x \cdot x + x \cdot (-5) + 5

1. **State the problem:** Simplify the expression $$2^{13} \cdot 15^{-3} \cdot 7^{5}$$. 2. **Recall the rules:**

1. **State the problem:** Evaluate the expression $$\left( \frac{1}{4} \right)^{-3}$$. 2. **Recall the property of negative exponents:** For any nonzero number $a$ and integer $n$,

1. **State the problem:** We need to determine which values from the set \{7, 2, 0, 5, -1\} satisfy the inequality $x < 5$. 2. **Recall the inequality rule:** The inequality $x < 5

1. **State the problem:** Simplify the expression $$\frac{3f^3}{12f^{18}}$$. 2. **Recall the rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{

1. **State the problem:** Find the product of the functions $c(x) = -2x + 5$ and $a(x) = x^2 - 4$, i.e., compute $(c \cdot a)(x) = c(x) \times a(x)$. 2. **Write the expression:**

1. The problem asks to find the function $(f+g)(x)$, which means we need to add the functions $f(x)$ and $g(x)$ together. 2. Given:

1. **State the problem:** Solve for $x$ in the equation $$\frac{96}{4x} + 11 = 14$$. 2. **Isolate the fraction:** Subtract 11 from both sides to get $$\frac{96}{4x} = 14 - 11$$.

1. The problem asks to solve two separate questions (not specified in the prompt), so we will assume two algebraic problems. 2. For each problem, we use the appropriate algebraic f

1. State the problem. Problem: Simplify the expression $ (5 + 5n^3) - (1 - 3n^3)$.

1. **State the problem:** Solve the system of linear equations: $$3x - y = 4$$