🧮 algebra

1. The problem is to verify if the given equations are correct by filling in the blanks and checking the arithmetic. 2. The general formula for subtraction is $a - b = c$, where $a

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} 2x + 9 & \text{for } x < -3 \\ 2x - 2 & \text{for } x > 4 \end{cases}$$

1. The problem asks to complete the table and graph the pairs of values given in the matrix: $$\begin{matrix}6 & 2 \\ 3 & 4 \\ 6 & 6\end{matrix}$$

1. **State the problem:** A student runs 2 minutes for every 10 minutes she walks. We need to complete the table of running and walking times and find how long she would walk if sh

1. The problem asks for the domain of the difference function $f - g$. 2. The domain of $f - g$ is the intersection of the domains of $f$ and $g$.

1. **State the problem:** Find the difference function $(f - g)(x)$ where $f(x) = 4x + \sqrt{7} - x$ and $g(x) = x^2 - x + 1$.

1. **State the problem:** We need to find the equation that models the proportional relationship between the number of pancakes ($x$) and the amount of flour in cups ($y$). 2. **Un

1. **State the problem:** We need to find which company, Talk-n-Text or Country Connect, charges a lower rate per minute and by how much. 2. **Identify the rates:** For Talk-n-Text

1. **State the problem:** Determine whether the expression $$\frac{2^{4m}}{16}$$ is equivalent to each of the given expressions: $$2^{4m-4}$$, $$4^{2m} \cdot 2$$, $$16^m \cdot 1$$.

1. The problem asks to write the set represented by the number line from 0 to 4, including points 0,1,2,3,4, with a right arrow at 4. 2. This means the set includes all numbers sta

1. **State the problem:** Simplify the expression $$\frac{6b^6 a^{-3}}{36a^{-2} b^{-7}}$$ and write the answer using only positive exponents. 2. **Recall the quotient rule for expo

1. **State the problem:** A bicyclist travels 27 miles in 1.5 hours. We need to find the speed in miles per hour (mph). 2. **Formula used:** Speed is calculated by dividing distanc

1. The problem is to divide the fraction $\frac{5}{6}$ by $\frac{1}{3}$.\n\n2. The formula for dividing fractions is:\n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{

1. **Stating the problem:** We have some bees and flowers. If each bee lands on a different flower, one bee does not get a flower. If two bees share each flower, there is one flowe

1. **State the problem:** We are given the function $f(x) = 9x^2 - 4$ and need to find the value of $f(4) - f(1)$. 2. **Recall the formula:** The function is defined as $f(x) = 9x^

1. **State the problem:** We are given the function $f(x) = 9x^2 - 4$ and need to find the value of $f(-2)$. 2. **Recall the formula:** The function is defined as $f(x) = 9x^2 - 4$

1. **State the problem:** Find the cube root of 27, which is written as $\sqrt[3]{27}$. 2. **Recall the definition:** The cube root of a number $a$ is a number $b$ such that $b^3 =

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. **State the problem:** Simplify or solve the quadratic expression $2x^2 + 4x - 16$. 2. **Identify the formula and rules:** This is a quadratic expression of the form $ax^2 + bx

1. **State the problem:** Simplify or solve the quadratic expression $2x^2 + 4x - 16$. 2. **Identify the formula:** This is a quadratic expression of the form $ax^2 + bx + c$ where

1. The problem asks: Which is greater, $-3.1$ or $-3.01$? 2. To compare two negative decimals, remember that the number closer to zero is greater because negative numbers decrease