🧮 algebra

1. **State the problem:** Factor the polynomial $$15a - 15a^2$$ using the greatest common factor (GCF). 2. **Identify the GCF:** The terms are $$15a$$ and $$15a^2$$.

1. **State the problem:** Find the greatest common factor (GCF) of $12$ and $60$. 2. **Recall the definition:** The GCF of two numbers is the largest positive integer that divides

1. **Stating the problem:** We are given four systems of inequalities labeled A, B, C, and D. Each system contains two linear inequalities.

1. **State the problem:** We are given a graph of a downward-sloping line crossing the y-axis at about $7$ and the x-axis at about $4.5$, with the shaded region on the lower-left s

1. **State the problem:** Solve the system of linear equations: $$-2x - 9y = -9$$

1. **State the problem:** Solve the system of linear equations: $$-2x + 3y = -5$$

1. **State the problem:** We are given the system of linear equations: $$8x - 3y = -3$$

1. **Problem Statement:** We need to draw the graphs of two functions and analyze the domain and range of a discrete function.

1. **State the problem:** We need to find how long it takes to travel at a speed of $80$ km/h from the point $(32.5, 35.48)$ to the point $(27.03, 27.03)$ (assuming the second coor

1. **State the problem:** Factor the quadratic expression $$X^2 - x - 12$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, find two numbers that multiply t

1. **State the problem:** Simplify or factor the quadratic expression $$X^2 - x - 12$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look f

1. **State the problem:** We are given the function $$y = 3 - 2e^{-2x}$$ and asked two questions:\n\n(a) What happens to $y$ as $x \to \infty$?\n(b) Sketch the graph of the functio

1. **State the problem:** We are given the function $$f(x) = (x - 3)^2$$ and a graph of a parabola with vertex approximately at $$(-1, -2)$$ and x-intercepts approximately at $$(-2

1. **State the problem:** We are given the quadratic function $$f(x) = -\frac{1}{2} x^2 - x - \frac{7}{2}$$ and its graph, a downward-opening parabola with vertex at $(2, -2)$. 2.

1. **State the problem:** We are given the quadratic equation $$y = 3x^2 + 6x + 3$$ and a graph of this parabola. We need to determine which has the smaller minimum value: the equa

1. **State the problem:** We are given the function $$f(x) = 3(x - 1)^2 + 1$$ and a graph of a parabola with vertex at $$(-4, 0)$$. We need to compare the minimum values of the equ

1. **State the problem:** We need to write a piecewise-defined function $M(x)$ that represents the cost of a monthly data plan.

1. **Problem 6:** Given $$g(x) = 3(x + 2)^2$$, apply a shift left by 2 units and stretch vertically by 3. 2. **Step 1:** Understand the transformations.

1. **State the problem:** Identify which three of the given options are equations. 2. **Recall the definition:** An equation is a mathematical statement that asserts the equality o

1. **State the problem:** Solve the equation $$0.15(y - 0.2) = 2 - 0.5(1 - y)$$ and identify any errors in the student's solution. 2. **Distribute terms:**

1. **State the problem:** Solve the equation $$125 = 5^x$$ for $$x$$. 2. **Recall the formula and rules:** We know that $$125$$ can be expressed as a power of $$5$$ because $$125 =