🧮 algebra

1. **State the problem:** We are given the equation of a circle: $$x^2 + y^2 + 6x - 2y + 9 = 0$$ and we want to find its center and radius. 2. **Formula and rules:** The general fo

1. **State the problem:** We are given the function $f(x) = 1.5x + 4$ and another function $g(x) = f(x) + k$. We need to find the value of $k$ that transforms the graph of $f$ into

1. Simplify $x^{4/3} \cdot x^{2/3}$. Using the rule $a^m \cdot a^n = a^{m+n}$, add the exponents:

1. Masalah: Selesaikan persamaan kuadrat $x^2 - 5x + 6 = 0$. 2. Rumus yang digunakan adalah rumus kuadrat: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ di mana $a$, $b$, dan $c$ adal

1. **State the problem:** Given the variables $a = -3$, $q = 5$, and $t = 6$, we need to solve an algebraic expression involving these values. 2. **Identify the expression:** Since

1. **Problem Statement:** Find the equation of a line parallel to the line given by $$y = -3x + 4$$ and containing the point $$(3, -1)$$. 2. **Recall the formula for the slope-inte

1. The problem is to simplify the expression $17 - 4x^3 + 7x^2$. 2. This is a polynomial expression with terms involving powers of $x$ and constants.

1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula or factorization to solve quadratic equations. The quadratic formula is $$x = \frac{-b \

1. The problem asks us to compare the distance from sea level of the fish and the toad using their elevations on the number line. 2. The elevations given are:

1. The problem asks for the squirrel's vertical distance from sea level. 2. Elevation is given in feet relative to sea level, which is at 0 feet.

1. **Problem Statement:** We are given the elevations of four animals by a lake and need to interpret their positions on a vertical number line. 2. **Given Data:**

1. **State the problem:** We are comparing two temperatures: Vancouver at $-1.5$ degrees and Chicago at $-5$ degrees. 2. **Understanding negative numbers:** On the number line, num

1. The problem asks for the temperatures in two cities, Berlin and Paris, based on thermometer readings. 2. Each thermometer scale ranges from -5 to 5 degrees, with zero in the mid

1. **State the problem:** Solve the quadratic equation $$20 - 12u + u^2 = 0$$. 2. **Rewrite the equation in standard form:** The standard form of a quadratic equation is $$au^2 + b

1. **State the problem:** We are given the inequalities:

1. **State the problem:** Solve the quadratic equation $$10y^2 - 11y - 6 = 0$$. 2. **Formula used:** For a quadratic equation $$ay^2 + by + c = 0$$, the solutions are given by the

1. **Stating the problem:** We need to graph the system of inequalities:

1. **State the problem:** We have a box where the height is 1 cm longer than the width, and the length is twice the width. The volume is 346 cm³. We need to find the dimensions: wi

1. **State the problem:** Joe's average running speed is 0.5 km/h greater than Bob's. In a 5-km race, Bob finishes 3 minutes (which is 0.05 hours) behind Joe. We need to find their

1. **Problem Statement:** We are given the function $f(x) = -\frac{1}{x^2 + 6x - 7}$. We need to sketch the graph, label key points, find the domain and range, equations of asympto

1. **Problem Statement:** We are given the function $f(x) = (x-2)(x-5)(x+2)$. We need to sketch the graph, label key points, find the domain and range, equations of asymptotes, end