🧮 algebra

1. **State the problem:** We need to find the value of the function $b(x) = \sqrt[3]{2x - 1}$ at $x = \frac{9}{2}$. 2. **Recall the formula:** The cube root function is defined as

1. The problem asks to find the value of the function $a(x) = 4x^2 + 2x - 5$ at $x = -2$. 2. To solve this, substitute $x = -2$ into the function:

1. State the problem: The binary operation $*$ is defined on the set $\mathbb{R}$ by $a * b = \frac{ab}{4}$ and we are to find $\sqrt{2} * \sqrt{6}$.\n2. Formula and rules: Use the

1. Stating the problem: A binary operation $*$ is defined on the set $\mathbb{R}$ of real numbers by $a * b = \frac{ab}{4}$. Find $\sqrt{2} * \sqrt{6}$.\n2. Formula and rules: Use

1. **State the problem:** Simplify the algebraic expression $4d + 4a - 3a - 2c$. 2. **Group like terms:** Combine terms with the same variables.

1. **State the problem:** Simplify the expression $11x + 7 + 5 : 6 - 7x + 20x$. 2. **Clarify the expression:** The colon $:$ is often used to denote division. So the expression is

1. **State the problem:** Simplify the expression $6m - 6 + 8m$. 2. **Identify like terms:** The terms $6m$ and $8m$ are like terms because they both contain the variable $m$.

1. **State the problem:** Solve the system of equations to find the value of $y$: $$4x + 19y = 25$$

1. **State the problem:** Simplify the expression $$\left(\frac{w^{-15} y^{12}}{-64 x^{3}}\right)^{-\frac{1}{3}}$$. 2. **Recall the exponent rules:**

1. We are given the system of equations: $$4x + 19y = 25$$

1. **State the problem:** A dirt bike requires 15 liters of gas mixed with 4 liters of oil. We need to find how much oil is needed if 20 liters of gas are used. 2. **Set up the rat

1. **State the problem:** We are given the equation $3x = 2y + 3$ and asked to find the expression $\frac{8^x}{4^y}$.

1. **State the problem:** We have a corn chowder recipe with 3 cups of corn, 2 cups of water, and 1 1\/2 cups of cream. We want to find how much corn is needed if the cream is incr

1. **State the problem:** Solve the equation $3x = 2y + 3$ for $x$ in terms of $y$. 2. **Formula and rules:** To isolate $x$, we need to divide both sides of the equation by 3. Rem

1. **Stating the problem:** We want to find all possible equations of the form $5 \; \square \; 3 = \square \square$ where the operation is either multiplication or division, and t

1. **State the problem:** Tyler's family took a taxi that charged $3.00 per mile plus a $3.00 tip, paying a total of $16.50. We need to find the distance to the museum. 2. **Set up

1. **State the problem:** We are given the function $$y = \frac{1}{4} |x|$$ and asked to understand its graph and properties. 2. **Formula and explanation:** The absolute value fun

1. **Problem:** Factor the expression $5n^2 + 20n - 60$ completely. 2. **Step 1: Identify the greatest common factor (GCF).**

1. **State the problem:** We need to find the circumference of the circle traversed by wheel 12 in a wheel line irrigation system. 2. **Identify the radius of the circle for wheel

1. **State the problem:** Solve for $x$ in the equation $$\frac{x-3}{3} = \frac{4 - x - 2}{2}.$$\n\n2. **Simplify the right side:** Combine like terms inside the numerator on the r

1. **State the problem:** Add the fractions $\frac{1}{6}$ and $\frac{1}{10}$. 2. **Formula used:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd