🧮 algebra

1. **State the problem:** Simplify the expression $$\left(\frac{x^4}{y^6}\right)^8$$. 2. **Recall the power of a quotient rule:** When raising a quotient to a power, apply the expo

1. **State the problem:** Factor each algebraic expression. 2. **Problem a:** Factor $36x - 9$.

1. **State the problem:** Simplify each algebraic expression by combining like terms. 2. **Recall the rule:** To simplify, add or subtract coefficients of the same variable and com

1. **State the problem:** Simplify the expression $$(3x^6)^3 (2x^2)^4$$. 2. **Recall the exponent rules:**

1. **Problem a:** Evaluate the expression $3(2x - 5) + \frac{x}{4}$ when $x = 8$. 2. **Step 1:** Substitute $x = 8$ into the expression:

1. **State the problem:** We need to find algebraic expressions for each sentence.

1. **State the problem:** Brent is $x$ years old. George is 8 years older than Brent, so George's age is $x + 8$. Joan is 4 times as old as George. We need to find an expression fo

1. **State the problem:** We are given two points $(15,10)$ and $(30,15)$ and need to find the value of $y$ when $x=17.9$ using linear interpolation. 2. **Formula for linear interp

1. **Problem statement:** We are given the function $g(x) = 2x^2 + \frac{1}{x}$ and asked to analyze and plot it. 2. **Function form:** The function is a combination of a quadratic

1. **Problem statement:** Use linear interpolation to find the value of $y$ when $x=26.5$ given points $(30, 51)$ and $(20, 36)$. 2. **Formula for linear interpolation:**

1. **Stating the problem:** We are given the function $$y = 3\sqrt{x^4 + 4x^3 + 5}$$ and we want to understand or analyze it. 2. **Understanding the function:** The function involv

1. **State the problem:** We are given the equation $\frac{w}{p} = \frac{2a}{b} - c$ and need to solve for $w$ step by step. 2. **Understand the equation:** The equation shows $w$

1. **State the problem:** Solve for $b$ in an equation involving $b$. 2. **General approach:** To solve for $b$, isolate $b$ on one side of the equation using algebraic operations

1. **State the problem:** Solve the equation for $w$ given the formula $\frac{w}{p} = \frac{2a}{b} - c$. 2. **Identify the goal:** We want to isolate $w$ on one side of the equatio

1. **State the problem:** Solve for $b$ in the equation $84=4+\frac{8}{b}$. 2. **Isolate the fraction:** Subtract 4 from both sides:

1. **State the problem:** Solve the equation $\beta y = y + \frac{8}{13}$ for $y$. 2. **Rewrite the equation:**

1. **State the problem:** Solve the equation $\frac{w}{p} = \frac{2a}{b} - c$ for $b$. 2. **Isolate the term with $b$:** Add $c$ to both sides to get

1. **State the problem:** Lizzie has 24 feet of fencing to build a square pen. The perimeter $P$ of a square is given by $P = 4s$, where $s$ is the length of one side.

1. **State the problem:** Alex has signed 122 comic books out of 327 total. We want to find how many comic books, $c$, he still needs to sign. 2. **Write the equation:** The proble

1. **State the problem:** We need to complete the table by subtracting 41 from each "In" value to find the corresponding "Out" value. 2. **Formula used:** The rule is:

1. The problem is to complete the table where the "Out" value is found by dividing the "In" value by 4. 2. The rule is: $$\text{Out} = \frac{\text{In}}{4}$$