🧮 algebra

1. **State the problem:** Simplify the expression $$(y - 3)(y - 1) - (y + 2)(y - 6)$$. 2. **Use the distributive property (FOIL) to expand each product:**

1. The problem asks to find the unit rate (rate per one unit on the horizontal axis) for each graph. 2. The unit rate formula is $$\text{unit rate} = \frac{\text{change in vertical

1. The problem asks: "It takes Jacob 24 minutes to eat a bucket of ice cream, and Alisha 36 minutes to eat the same amount. If they have 5 buckets to share, how long will it take t

1. **State the problem:** Calculate the area of a square given length $= \frac{x-1}{x+1}$ and width $= \frac{2x}{15}$. 2. **Recall the formula for the area of a square:**

1. **State the problem:** We have an original total cost estimate of 240000 for constructing a house.

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

1. The problem is to identify the graph of the equation $$y=\sqrt[3]{x}+2$$. 2. The cube root function $$y=\sqrt[3]{x}$$ is an odd function with a characteristic S-shaped curve pas

1. The problem is to identify the graph of the equation $$y - 3 = \sqrt{x - 2}$$. 2. This equation can be rewritten as $$y = 3 + \sqrt{x - 2}$$.

1. **State the problem:** Identify the equation of the graph described. 2. **Analyze the given options:**

1. The problem is to identify the equation of the graph given three options: $$y + 1 = \sqrt[3]{x}$$

1. The problem is to identify the graph of the function $$f(x) = \sqrt{x - 4} + 3$$. 2. The general form of a square root function is $$f(x) = \sqrt{x - h} + k$$, where $(h, k)$ is

1. The problem is to identify the graph of the function $f(x) = \sqrt{x - 2} + 3$. 2. The general form of a square root function is $f(x) = \sqrt{x - h} + k$, where $(h, k)$ is the

1. The problem is to identify the graph of the function $f(x) = \sqrt{x - 1} - 4$. 2. The square root function $\sqrt{x}$ starts at $x=0$ and $y=0$ and increases slowly to the righ

1. The problem is to identify the graph of the function $$f(x) = \sqrt{x + 4} + 2$$. 2. The function is a square root function with a horizontal shift and a vertical shift.

1. **State the problem:** We need to identify the graph of the function $$f(x) = \sqrt{x} + 1 - 2$$. 2. **Rewrite the function:** Simplify the expression inside the function:

1. The problem asks to write an equation showing when the costs of Plan A and Plan B are the same. 2. We have the expressions for the costs:

1. Stating the problem: Evaluate the expression $$6^0 + 2^{-3} \cdot \left(\frac{1}{4}\right)^{-1}$$. 2. Recall the rules:

1. **State the problem:** We need to graph the inequality $$y \geq \frac{3}{2}x - 6$$ on a coordinate plane with x and y axes ranging from -10 to 10. 2. **Understand the inequality

1. **State the problem:** Sketch the graph of the linear inequality $y \geq -3x + 4$. 2. **Formula and rules:** The boundary line is given by the equation $y = -3x + 4$. For inequa

1. **State the problem:** We need to graph the inequality $$2x - 5y \leq -10$$ on the coordinate plane. 2. **Rewrite the inequality in slope-intercept form:** To graph, solve for $

1. **State the problem:** We need to graph the inequality $$-3x + 4y < 4$$ on the Cartesian plane with axes from -10 to 10. 2. **Rewrite the inequality in terms of $y$:**