🧮 algebra

1. **State the problem:** We need to solve the system of inequalities: $$y < -1$$

1. **State the problem:** We need to find the total length of the course given the distances of Cody and Sarah from the start and finish line, and the fact that Cody is 60 m behind

1. **State the problem:** We need to find the equation of a linear function in slope-intercept form, which is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 2. *

1. **State the problem:** Find the equation of the line in slope-intercept form $y = mx + b$ that passes through the points $(-2, 10)$ and $(5, -4)$. 2. **Formula for slope:** The

1. **State the problem:** Solve the equation $$\frac{v}{3} = \frac{v}{4} - 3$$ for $v$. 2. **Identify the formula and rules:** This is a linear equation with fractions. To solve, w

1. **State the problem:** Solve for $w$ in the equation $$\frac{w}{8} + \frac{w}{12} = \frac{5}{8}$$. 2. **Find a common denominator for the fractions on the left side:** The denom

1. **State the problem:** We want to determine how to check if all solutions of an equation are real numbers. 2. **General rule for polynomials:** For a polynomial equation, the na

1. **State the problem:** Solve the polynomial equation $$16y^3 - 9 = y - 144y^2$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** We need to find the equation of a line in slope-intercept form $$y=mx+b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 2. **Identify given infor

1. **State the problem:** We have a sequence of fractions arranged in pairs: $$\frac{1}{18}, \frac{2}{17}, \frac{\boxed{\phantom{0}}}{16}, \frac{4}{\boxed{\phantom{0}}}, \frac{\box

1. **Stating the problem:** We need to understand what a proportion is and how to solve problems involving proportions. 2. **Definition and formula:** A proportion states that two

1. **State the problem:** We need to find 30% of 0.63 Full-Time Equivalent (FTE) at an annual wage of 24377. 2. **Understand the terms:**

1. **State the problem:** We need to find the positive value of $r$ that satisfies the equation $$r(5 + 2r) - 5(r - 4) = 52$$. 2. **Expand the terms:**

1. समस्या को समझें: हमें दिया गया है कि शब्द 'MATCH' को कूट भाषा में '1381320' लिखा गया है। हमें यह पता लगाना है कि उसी कूट भाषा में 'TROPHY' कैसे लिखा जाएगा। 2. नियम खोजें: पहले श

1. **State the problem:** We need to find the total price of the bag of chips shared by Raymond and Faris. 2. **Define variables:** Let the price Raymond pays be $R = 485$ cents.

1. **State the problem:** We need to find the quadratic function $y = ax^2 + bx + c$ that passes through the points $(-4, 0)$, $(-0.5, 0)$, and $(0, 4)$. 2. **Use the fact that the

1. **State the problem:** We need to find the equation of a quadratic function in standard form $$y = ax^2 + bx + c$$ given points on the graph. 2. **Identify known points:** The v

1. The problem asks to transform the graph of $y = f(x)$ to the graph of $y = f(x - 3) + 1$. 2. The formula for horizontal and vertical shifts is:

1. **State the problem:** We are given the quadratic equation $$x^2 + (3k - 1)x + 10 + 2k = 0$$ and need to find:

1. **State the problem:** We are given the quadratic equation $$x^2 + (3k - 1)x + 10 + 2k = 0$$ and need to find:

1. Let's analyze the relationship between $v$ and $I$ as shown on the graph. 2. Identify the point on the graph where $I=2$.