🧮 algebra

1. The problem asks for the net income of Widgets, LTD in 2009 based on the bar graph. 2. From the graph, the bar for 2009 is below zero, indicating a negative net income.

1. **State the problem:** Perform the operation and simplify the expression: $$\frac{7}{21} - \frac{5}{21}$$

1. The problem asks to convert the percentage 22.8% into a decimal. 2. The formula to convert a percentage to a decimal is:

1. The problem asks to convert 22.8% into a decimal. 2. The formula to convert a percentage to a decimal is:

1. The problem asks us to compare the two fractions $\frac{7}{10}$ and $\frac{4}{5}$ and insert the correct inequality symbol ($<$ or $>$) between them to form a true statement. 2.

1. **State the problem:** Simplify the expression $$\left(\frac{3}{5}\right)^2 \div \left(\frac{3}{5} - \frac{1}{14}\right)$$ and find the correct simplified answer. 2. **Write the

1. **State the problem:** Subtract and simplify the expression $$17 \frac{1}{6} - \frac{18}{30}$$. 2. **Convert mixed number to improper fraction:**

1. **State the problem:** We need to find the purchase price of a car given the sales tax amount and the tax rate. 2. **Formula:** Sales tax = Purchase price \times Tax rate

1. **Problem Statement:** During a school fair, tickets for children and adults were sold. Let the number of children tickets be $x$ and adult tickets be $y$. The system of equatio

1. **State the problem:** Find the root(s) of the polynomial equation $$x(x-2)(x+3) = 18$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Find the roots of the polynomial equation $$x^4 + x^2 = 4x^3 - 12x + 12$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equ

1. **Problem statement for Aufgabe 2a:** Berechne $$\sqrt[4]{6^3} \cdot \frac{1}{\sqrt[4]{6^7}}$$. 2. **Formula and rules:** Wurzeln mit gleicher Wurzelzahl können als Potenzen mit

1. The problem asks for the average rate of change of the function $g(t) = \frac{1}{t}$ between $t=1$ and $t=3$. 2. The formula for the average rate of change of a function $g(t)$

1. **State the problem:** We need to find the average rate of change of the water depth $W$ between $x=100$ days and $x=300$ days. 2. **Formula:** The average rate of change of a f

1. Let's start by understanding the concept of Domain and Range in relations and functions. 2. The domain of a relation or function is the set of all possible input values (usually

1. The problem is to graph the piecewise functions \(f(x)\) and \(g(x)\) defined as follows: \[ f(x) = \begin{cases} -2^x, & x < -4 \\ -|x|, & -4 \leq x \leq 0 \\ 4 - x^2, & x > 0

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **Problem:** Do a factoring example. 2. **Formula used:** A common factoring pattern is the greatest common factor rule:

1. El problema nos pide llenar la tabla para la función $$y = 4x - 1$$ usando la regla dada. 2. La fórmula es $$y = 4x - 1$$, donde para cada valor de $$x$$ calculamos $$y$$ multip

1. El problema nos pide llenar la tabla para la función $$y = -2x + 5$$ usando la regla dada. 2. La fórmula es $$y = -2x + 5$$, donde para cada valor de $$x$$ calculamos $$y$$ sust

1. **State the problem:** Simplify the expression $$6 \div 2(1+2)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**