🧮 algebra

1. Problem c) Solve the equation $|3x + 4| = |2x + 6|$. 2. Recall that for absolute values, $|A| = |B|$ implies either $A = B$ or $A = -B$.

1. **Problem c)** Solve the equation $|3x + 4| = |2x + 6|$. 2. The absolute value equation $|A| = |B|$ implies either $A = B$ or $A = -B$.

1. The problem asks to use the graph in the first question, but since no explicit function or graph details were provided, I will assume a general approach to analyzing a graph of

1. The problem is to write the piecewise function for $f(|x|)$ given a function $f(x)$. 2. Recall that the absolute value function $|x|$ is defined as:

1. **State the problem:** We need to find a four-digit number $ABCD$ where each digit is a perfect square (0, 1, 4, 9). 2. **Given conditions:**

1. **State the problem:** We are given the function $f(x) = x^2 - 4x$ and want to analyze it. 2. **Formula and rules:** This is a quadratic function of the form $ax^2 + bx + c$ whe

1. **Problemstellung:** Überprüfe, ob die Punkte P(2 | 14) und Q(3 | 49) auf dem Graphen der Funktion $f(x) = 2 \cdot 3^x - 4$ liegen. 2. **Formel:** Für einen Punkt $(x,y)$ liegt

1. Stwierdzenie problemu: Mamy dopasować wyrażenia opisujące pole do odpowiednich figur oznaczonych literami A, B, C oraz wyrażeniami I, II, III. 2. Przypomnienie wzorów na pola fi

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