🧮 algebra

1. **State the problem:** We have a function $f(x) = \sqrt{x - 5}$ and we want to find the equation of its reflection $g(x)$ about the line $y = x$. 2. **Recall the reflection rule

1. **Problem statement:** We start with a function $y=f(x)$ and apply three transformations: - Vertical reflection about the x-axis

1. **State the problem:** Add the fractions $\frac{2}{3}$ and $\frac{1}{4}$. 2. **Formula and rules:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc

1. The problem states that the function $y=2x^2 - 4x + 17$ is horizontally translated two units to the right. 2. Horizontal translation of a function $f(x)$ by $h$ units to the rig

1. **State the problem:** We are given a graph with two lines intersecting at the origin. One line passes through points $(-6,-4)$ and $(6,5)$, and the other is the x-axis line $y=

1. The problem asks us to compare the hourly earnings of Jace and Ariana based on their earnings equations and graph. 2. Jace's earnings are given by the equation $y = 25.2x$, wher

1. **State the problem:** We have Aubree's Taxicab Company charges for different miles and total costs, and Bo's company charges given by the equation $y=2.6x+2.5$. We want to find

1. The problem gives a linear equation for the total cost $y$ of a taxi ride based on miles $x$: $$y = 2.6x + 2.5$$ and a table of values for miles and total cost. 2. We want to ve

1. **State the problem:** We need to compare the gas mileage (miles per gallon) of Nachelle's car and Zachary's car. 2. **Calculate Nachelle's miles per gallon (mpg):**

1. **State the problem:** We need to compare the miles per gallon (mpg) of Nachelle's car and Zachary's car to determine who gets more miles per gallon. 2. **Given data:**

1. **State the problem:** We need to find the weekly savings rate for Brody, Avery, and Khalil, then order them from least to greatest savings per week. 2. **Brody's savings:** Bro

1. **State the problem:** We need to find the speed (miles per hour) of Space Explorer A and Space Explorer B, then compare their speeds. 2. **Formula for speed:** Speed is calcula

1. The problem states that Health Club A charges according to the equation $y = 59x + 50$, where $x$ is the number of months and $y$ is the total cost. 2. Health Club B charges a o

1. The problem involves comparing the monthly cost of Health Club A to Health Club B using the linear equation $y = 59x + 50$. 2. Here, $y$ represents the total cost for $x$ months

1. The problem asks us to find the value of $49^{\frac{3}{2}}$. 2. The exponent $\frac{3}{2}$ means we take the square root (denominator 2) and then cube the result (numerator 3),

1. The problem asks to compare the speed (miles per hour) of Space Explorer B to Space Explorer A. 2. Speed is calculated as the rate of change of miles with respect to hours, or s

1. **State the problem:** We need to find the rate of savings per week for Nevaeh, Nasim, and Gabriella, then sort them from greatest to least. 2. **Nevaeh's savings:** She started

1. **State the problem:** We need to find the rate of savings per week for Mariam, Kadeem, and Jose, then sort them from greatest to least. 2. **Mariam's savings:** She started wit

1. **State the problem:** We want to express $\left(5\sqrt{26}\right)^9$ in the form $26^h$ and find the value of $h$. 2. **Rewrite the expression:** Recall that $\sqrt{26} = 26^{\

1. **State the problem:** We need to find values of $n$ and $d$ such that $$18^{\frac{9}{8}} = (\sqrt[n]{18})^d.$$\n\n2. **Recall the formula:** The $n$th root of a number $a$ can

1. The problem is to understand the letter C in a mathematical or algebraic context. 2. Since the letter C alone does not represent a specific mathematical problem, we consider it