🧮 algebra

1. **State the problem:** We have a total of 380 tickets sold for a school play. Adult tickets cost 12 each and student tickets cost 8 each. The total revenue from ticket sales is

1. **State the problem:** Find the point of intersection of the two lines given by the equations: $$y = -3x + 20$$

1. **State the problem:** Solve the system of linear equations: $$y = 4x + 13$$

1. Das Problem lautet: Löse die Gleichung für den Fall 4 a. 2. Da keine konkrete Gleichung angegeben ist, nehme ich an, dass es sich um eine algebraische Gleichung handelt, die gel

1. **State the problem:** Find the equation of the line passing through the point $(5,3)$ with an undefined slope. 2. **Recall the concept:** A line with an undefined slope is a ve

1. **State the problem:** Find the equation of the line passing through the point $(2, -1)$ and perpendicular to the line given by $2x - y = 4$. 2. **Rewrite the given line in slop

1. **Problem statement:** Solve the equation $2x + 3 = 11$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable on one side by performing inverse ope

1. **Problem statement:** Find the number of intersection points of the graphs of the functions for each case. 2. **General approach:** To find the number of intersection points of

1. **State the problem:** We need to find an equation that models the relationship between the cost $c$ in dollars and the number of gallons $g$ of gasoline Allen buys, given that

1. **State the problem:** Determine if the relationships described are proportional. 2. **Recall the definition:** Two quantities are proportional if their ratio is constant.

1. **Problem:** Solve the first equation using the Quadratic Formula: $4x^2+11x-20=0$. 2. **Formula:** For $ax^2+bx+c=0$, the Quadratic Formula is $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a

1. The problem is to find the value of the function $g(x)$ at $x=3$, i.e., find $g(3)$. 2. To solve this, you need the definition or formula of the function $g(x)$. Without the for

1. **State the problem:** We are given a function $g(x)$ defined on the interval $-2 \leq x \leq 3$ and asked to find specific values and transformations based on its graph. 2. **P

1. The problem asks to identify the graph of the inequality $y < -x - 3$ in the standard $(x, y)$ coordinate plane. 2. The boundary line for this inequality is $y = -x - 3$. This i

1. **State the problem:** We are given the vertices and foci of a conic section and need to identify and analyze it.

1. **State the problem:** Simplify the expression $$\left(\frac{125}{64}\right)^{\frac{2}{3}}$$ and find which of the given options matches the result. 2. **Recall the exponent rul

1. **State the problem:** A town has a population of 8,000 and grows at 2% every year. We want to find the population after 14 years, rounded to the nearest whole number. 2. **Form

1. **State the problem:** Graph the inequality $x \geq -3 \cdot 2$ for three different sets: integers ($\mathbb{Z}$), natural numbers ($\mathbb{N}$), and real numbers ($\mathbb{R}$

1. **State the problem:** Solve the simultaneous equations: $$x + 2y = 1$$

1. **State the problem:** We have a budget of $9600 for a product launch event. Various expenses reduce this budget, and we want to determine if the event cost was more than $200 u

1. **State the problem:** We need to find the greatest and smallest expenses from the given budget decreases for a product launch event. 2. **List the expenses:** Venue (-2400), Ca