🧮 algebra

1. **State the problem:** We need to find the graph that represents the system of inequalities: $$y < x + 2$$

1. **State the problem:** We need to find a system of inequalities representing the number of ushers ($x$) and tech crew members ($y$) based on hours worked and uniforms available.

1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} -3x - 9 & \text{for } -4 < x \leq -1 \\ -x - 3 & \text{for } -1 < x \leq 5 \end{cases}$$

1. **State the problem:** We need to graph the piecewise function:

1. **State the problem:** We are given a piecewise function:

1. **State the problem:** We need to write a piecewise function $T(x)$ that gives the tax owed based on taxable income $x$ for $x < 117950$. 2. **Given tax brackets:**

1. **State the problem:** We have a piecewise function for filing income taxes $T(x)$ based on adjusted gross income $x$:

1. **State the problem:** Solve for $m$ in the equation $$9m - (6m - 7) = 2(m - 3)$$. 2. **Apply the distributive property and remove parentheses:**

1. **Problem 7: Write the piecewise function for** $$f(x) = \begin{cases} -x^2 + 5, & x < 2 \\ 5, & x = 2 \\ -3, & 2 < x < 5 \\ x - 2, & 5 \leq x \leq 8 \end{cases}$$

1. The problem asks us to find two consecutive whole numbers between which the value of $\sqrt{75}$ lies. 2. Recall that $\sqrt{n}$ is the number which, when squared, equals $n$.

1. The problem asks for the best estimate of the amount of money in the jar at the end of the first month, given the line of best fit equation $$B = 0.45m + 1.93$$ where $m$ is the

1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the equation that represents the relationship between $x$ and $y$. 2. **Given table:**

1. **State the problem:** Find the equations of the vertical asymptotes of the function $$f(x) = \frac{x^2 + 2}{(x^2 - 9)(x^2 - 25)}$$. 2. **Recall the rule for vertical asymptotes

1. **Problema (a):** Risolvere $\log_2(x + 3) + \log_2(x) = 2$. Usiamo la proprietà dei logaritmi: $\log_b(m) + \log_b(n) = \log_b(m \cdot n)$.

1. **State the problem:** Find the equations of the vertical asymptotes of the function $$f(x) = \frac{x^2 + 3}{(x^2 - 1)(x^2 - 25)}.$$\n\n2. **Recall the rule for vertical asympto

1. **Problema (a):** Risolvere $\log_2(x + 3) + \log_2(x) = 2$. Usiamo la proprietà dei logaritmi: $\log_b(m) + \log_b(n) = \log_b(m \cdot n)$.

1. **State the problem:** Find the vertical asymptotes of the function $$f(x) = \frac{x^2 + 3}{(x^2 - 1)(x^2 - 25)}.$$\n\n2. **Recall the rule for vertical asymptotes:** Vertical a

1. **State the problem:** Find the horizontal asymptote(s) of the function $$f(x) = \frac{3x^4 + 4x + 4}{2x^4 + 3x - 3}$$. 2. **Recall the rule for horizontal asymptotes:**

1. **State the problem:** Find the horizontal asymptote(s) of the function $$f(x) = \frac{3x^4 + 2x + 2}{5x^4 + 2x - 4}$$. 2. **Recall the rule for horizontal asymptotes of rationa

1. **State the problem:** We are given a graph of a polynomial function with x-intercepts near $x \approx -9, -6, 4, 8$ and local extrema at $(-8,-5)$ (minimum), $(-2,9)$ (maximum)

1. The problem asks to find the value of $y$ for $y = f(4)$ using the graph of the function $f$. 2. From the description, the graph is a cubic curve crossing the x-axis near $-5$,