🧮 algebra

1. **State the problem:** Simplify and solve the equation $$30 = \frac{x^2 - 9}{3 - x} + \frac{x}{2} \cdot \frac{x - 3}{x - 3}$$ where the second fraction simplifies to 1 since num

1. **State the problem:** Simplify and understand the expression $$62.5 \cos(2\pi 60 t) \left( \frac{2\pi 60 e^{-t} \cos(2\pi 60 t) - e^{-t} \sin(2\pi 60 t)}{1 + (2\pi 60)^2} - \fr

1. **Problem statement:** (a) Determine which carton size of Smiley Orange Juice is the better buy based on cost per ml.

1. The problem asks to write the domain of the given graph as an inequality. 2. The domain of a function is the set of all possible input values (x-values) for which the function i

1. **State the problem:** Tamika wants to find when the total cost to fish at Floyd's Catfish Farm equals the total cost at Miller's Catfish Farm.

1. Énonçons le problème : Résoudre l'équation $$-1,5x^2 + 45x + 20 = 5$$ et arrondir les solutions aux centièmes. 2. Simplifions l'équation en ramenant tout à zéro :

1. **State the problem:** Solve the equation $x + 5 = \sqrt{5x + 21}$ for $x$. 2. **Recall the formula and rules:** To solve equations involving square roots, we isolate the square

1. **State the problem:** Solve the equation $x + 5 = \sqrt{5x + 21}$ for $x$. 2. **Recall the formula and rules:** To solve equations involving square roots, isolate the square ro

1. **Stating the problem:** We are given a table of height $y$ in meters versus time $x$ in seconds: $$\begin{array}{c|c}

1. The problem asks to write an equation in the form $y = mx + b$ for the given graph. 2. The graph shows a line passing through the origin $(0,0)$ and points increasing by 20 unit

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. **Problem statement:** We have a rectangular enclosure divided by a fence parallel to two of its sides, using a total of 600 meters of fencing. We want to find the dimensions th

1. The problem states that the 3rd graph is not a function because it passes through 2 points with the same x-coordinate. 2. A function is defined as a relation where each input (x

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