🧮 algebra

1. **State the problem:** We are given the system of equations: $$2x + 3y = 5$$

1. **State the problem:** Simplify the expression $$\left(\frac{2x^{3} y^{-3}}{3xy^{-2} \cdot 2y^{2}}\right)^{2}$$. 2. **Rewrite the denominator:** The denominator is a product: $$

1. The problem is to find the y-intercept $b$ in the linear equation $y = mx + b$ given a point and the slope. 2. The formula for a line is $y = mx + b$, where $m$ is the slope and

1. **State the problem:** We need to find the equation of line K that passes through the point $(15, 20)$ and is parallel to the line given by $$y = \frac{2}{5}x - 10.$$ 2. **Recal

1. **State the problem:** We want to find how much more expensive a pint of apple juice is per fluid ounce compared to a quart of apple juice. 2. **Given information:**

1. **State the problem:** Find the equation of line W that passes through the point $(2, 11)$ and is parallel to the line $y = 4x + 5$. 2. **Recall the formula:** The general form

1. The problem is to find the y-intercept $b$ of the line given the slope $m=3$ and a point on the line. 2. The equation of a line in slope-intercept form is:

1. **State the problem:** We want to find the slope $m$ of the line passing through the points $(2, -4)$ and $(5, 5)$. 2. **Formula for slope:** The slope $m$ between two points $(

1. **State the problem:** Solve the quadratic equation $$8)\ 2m^2 - 7m - 13 = -10$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero.

1. **State the problem:** We need to sketch the graph of a line with slope $2$ and y-intercept $3$. 2. **Recall the formula:** The equation of a line in slope-intercept form is $$y

1. The problem is to solve an equation using substitution method. 2. Substitution involves replacing a complicated expression with a simpler variable to make the equation easier to

1. **Stating the problem:** You want to solve a linear system where none of the variables have a coefficient of 1. 2. **General approach:** The goal is to isolate variables or elim

1. The problem is to find equivalent fractions for $\frac{5}{6}$ and $\frac{3}{4}$ using the least common denominator (LCD). 2. The LCD is the smallest number that both denominator

1. The problem asks for the least common denominator (LCD) of the fractions $\frac{3}{5}$ and $\frac{1}{10}$.\n\n2. The denominator is the bottom number of a fraction, and the LCD

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 3x - 2y = 5 \\ x - 4y - z = 7 \\ 14x - 6y + z = -13 \end{cases}$$

1. **State the problem:** We want to find the value of $k$ such that the piecewise function $$f(x) = \begin{cases} k^3 + x & \text{if } x < 3 \\ \frac{16}{k^2 - x} & \text{if } x \

1. The problem is to find integer solutions to an equation or system (please specify the exact equation if needed). 2. To find integer solutions, we typically look for values of va

1. **State the problem:** Solve the equation $$104 = 8y^2 + 8$$ for $y$. 2. **Isolate the term with $y^2$:** Subtract 8 from both sides:

1. Stating the problem: Simplify the expression $\frac{a}{b}\left(\frac{c}{d} + \frac{e}{f}\right)$. 2. Use the distributive property and fraction addition rules:

1. **State the problem:** Find the average rate of change of the function $g(x) = 2x^3 + 2$ from $x = -2$ to $x = 3$. 2. **Formula:** The average rate of change of a function $g(x)

1. **State the problem:** Simplify the expression $\sqrt{9x^2+6x-3}$. 2. **Identify the expression inside the square root:** The radicand is $9x^2 + 6x - 3$.