🧮 algebra

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 $y$:**

1. **State the problem:** Graph the inequality $x - y < -1$ on the coordinate plane with axes ranging from -10 to 10. 2. **Rewrite the inequality:** Start by isolating $y$.

1. The problem is to graph the inequality $y \geq \frac{4}{3}x - 8$ on a Cartesian coordinate system. 2. The boundary line is given by the equation $y = \frac{4}{3}x - 8$. This lin

1. **State the problem:** Simplify the expression $$-2x(4x + 6x^2 - 5x^3 + 12) - 5(x - 2) + (7 - 2x)(5 - 3x^2)$$. 2. **Distribute terms:**

1. **State the problem:** We need to graph the inequality $$y \geq -\frac{1}{2}x - 2$$ on the coordinate plane. 2. **Understand the inequality:** This inequality represents all poi

1. **State the problem:** We are given a quadratic sequence: 8, 16, 26, 38, 52, ... and need to find the formula for the $n^{th}$ term. 2. **Recall the formula for a quadratic sequ

1. **State the problem:** We need to graph the inequality $y \geq \frac{3}{4}x - 4$ on the coordinate plane. 2. **Understand the inequality:** The inequality $y \geq \frac{3}{4}x -

1. **State the problem:** We are given the quadratic sequence 9, 20, 33, 48, 65, ... and need to find the formula for the $n^{th}$ term. 2. **Identify the type of sequence:** Since

1. **State the problem:** We need to understand and graph the inequality $x - y < -5$. 2. **Rewrite the inequality:** To analyze it better, isolate $y$:

1. **State the problem:** We are given the cost function for selling $x$ volleyball uniforms as $$c(x) = 1200 + 14x + 0.045x^2.$$ We want to understand or evaluate this function, p

1. The problem states that David starts with 50 cards and adds 45 cards each month. 2. We want to write an equation for $y$, the total number of cards after $x$ months.

1. **State the problem:** We need to graph the inequality $$y \leq 3x - 6$$ on the coordinate axes. 2. **Understand the inequality:** The inequality $$y \leq 3x - 6$$ means that th