🧮 algebra

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

1. **State the problem:** We are given the function $f(x) = x^{-2}$ and need to understand its behavior. 2. **Recall the formula and rules:** The function $f(x) = x^{-2}$ can be re

1. The problem states: Given $X=5$ and $Y=6$, find $(XY)^2$. 2. The formula to use is the power of a product: $$(XY)^2 = X^2 Y^2$$ which means you square each factor and then multi

1. **State the problem:** Solve the equation $5X - 10 = -15$ for $X$. 2. **Add 10 to both sides to isolate the term with $X$:**

1. **Problem Statement:** Jacob spends 60 minutes in the gym doing freehand exercises and running on the treadmill. He runs on the treadmill for 30 minutes longer than he does free

1. **State the problem:** We have two functions:

1. The problem asks for the closest distance a person can be to the number 6000. 2. To find the closest distance between two numbers, we use the absolute value of their difference:

1. **State the problem:** We need to find which values among 0, 7, and 6 satisfy the inequality $$-1 - 2x \leq -10$$. 2. **Solve the inequality:**

1. **State the problem:** Given the height function $$h = -5t^2 + 290t + 600$$, find the height at $$t=10$$, the times when height is zero, and rewrite the function in vertex form.