🧮 algebra

1. The problem is to convert a given equation into standard form. 2. Standard form for a linear equation is usually written as $$Ax + By = C$$ where $A$, $B$, and $C$ are integers,

1. **Problem Statement:** Find the roots and factored form of the function $f(x)$ given its roots and graph description. 2. **Roots of $f(x)$:** The roots are the values of $x$ whe

1. The problem involves analyzing the graph of the piecewise function $$f(x) = \begin{cases} -x + 1 & x < 0 \\ x - 2 & 0 \leq x \end{cases}$$ and identifying the error in the graph

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} -x + 1, & x < 0 \\ x - 2, & x \geq 0 \end{cases}$$

1. **State the problem:** Francis is hiking up Killington Hill. After 1 hour, his elevation is 100 feet, and after 5 hours, it is 360 feet. We need to find the slope of the line re

1. **Problem:** Given $3^s = \sqrt{3} \times 3\sqrt{7} \sqrt{9}$, find the value of $(13 + 24x)^4$. 2. **Step 1: Simplify the right side of the equation for $3^s$**

1. **State the problem:** Simplify the expression $$\frac{\sqrt[5]{\frac{1}{10000}} \times \sqrt[5]{-0.00032}}{\sqrt[4]{(-4)^4}}.$$ 2. **Recall the rules:**

1. The problem states that Francis is hiking up Killington Hill and we know two points on his elevation path: after 1 hour, elevation is 100 feet, and after 5 hours, elevation is 3

1. The problem asks to identify the order of transformations applied to the function $f(x) = x^2$ to get $f(-x + 4) + 3$. 2. The original function is $f(x) = x^2$.

1. **State the problem:** Solve the inequality $ (x-2)(x+1) \leq 3(x+1) $. 2. **Rewrite the inequality:** Expand the left side and keep the right side as is:

1. **State the problem:** Calculate the average rate of change of the function $f(x) = \sqrt{x} + 2$ over the interval $[2,7]$. 2. **Formula:** The average rate of change of a func

1. The problem states that we have a parabola passing through the points $(-2,9)$, $(-1,3)$, $(0,1)$, $(1,3)$, and $(2,9)$. We want to create a table of values for the function ref

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

1. The user states "its not nehative," which likely means "it's not negative." 2. This implies the value or expression in question is either zero or positive.

1. **State the problem:** We have a system of equations arranged in a grid with unknowns represented by question marks (?). The goal is to find the value of the unknowns. 2. **Writ

1. **Stating the problem:** We have a 3x3 grid with arithmetic operations and numbers, some missing values represented by ellipses (...). The goal is to find the missing numbers so

1. We are given the equation $? + 16 \times 18 = 247$ and need to find the value of $?$. 2. First, calculate the product $16 \times 18$.

1. **State the problem:** Leo has $\frac{2}{3}$ cups of flour, which is $\frac{4}{5}$ of the flour needed for 1 batch of dinner rolls. We need to find how many cups of flour Leo ne

1. The problem is to find the next number in the sequence: 8, 2, \frac{1}{3}, \frac{1}{24}, ? 2. Let's analyze the pattern by looking at the relationship between consecutive terms.

1. **State the problem:** Solve for $x$ in the equation $$2(3x + 6 - x^2) = 7x + 5$$ to 3 significant figures. 2. **Expand and simplify:** Distribute the 2 on the left side:

1. The problem is to find the value of the missing number $?$ in the equation $1 + ? - ... = -1$ given the other rows and columns. 2. From the first row: $2 - 3 + 5 = 4$.