🧮 algebra

1. **Problem Statement:** A theatre group models revenue with $R = -50(t - 2)(t - 3)$ where $t$ is ticket price. They know revenue is maximized at $t=3$ with $R=450$ and $R=400$ at

1. **State the problem:** Simplify the expression $(1,4:5+19:20)*2-1,5$. 2. **Clarify notation:** The commas likely represent decimal points, so rewrite as $(1.4 \div 5 + 19 \div 2

1. **State the problem:** Calculate the value of the expression $\left(1,\frac{4}{5}+\frac{19}{20}\right)\times 2 - 1.5$. 2. **Clarify the expression:** The comma seems to separate

1. The problem is to find the inverse of a function, which means finding a function that "undoes" the original function. 2. The general formula for finding the inverse of a functio

1. **Stating the problem:** Solve question 5 (assuming it is an algebraic equation or expression to solve). 2. **Formula and rules:** Since the exact problem is not provided, I wil

1. The problem is to write the expression minus(bminus2c)minus3a without brackets. 2. First, understand that "minus" means a negative sign, so the expression is:

1. The problem is to solve the equation given by the user, but since no specific equation was provided, let's consider a general approach to solving algebraic equations. 2. The gen

1. El problema pide encontrar la ecuación de una recta que tiene ordenada al origen $-4$ y es paralela a la recta dada por $5x - 2y + 4 = 0$. 2. Para resolverlo, recordemos que dos

1. **Problem:** Convert the decimal 0.5 into a fraction. 2. **Formula and rules:** A decimal can be converted to a fraction by writing it over a power of 10 depending on the number

1. Planteamos el problema: Encontrar la ecuación de la recta que pasa por el punto $\left(\frac{1}{2}, -\frac{2}{3}\right)$ y es perpendicular a la recta dada por $9x - 5y = 1$. 2.

1. Problem 14: Find values of $a,b,c,d$ such that the line $y=x+1$ is a common tangent to the curves $$x^2 + y^2 + ax + by = 1$$

1. **Problem 13:** Find the possible values of $a$ and $b$ such that the curves $$x^2 + y^2 = 10$$ and $$x^2 + y^2 + ay = b$$ intersect at right angles where $x=3$. 2. **Step 1: Un

1. **State the problem:** We want to prove that for positive numbers $x$ and $y$, if $x^2 < y^2$, then $x < y$. 2. **Recall the properties:** Since $x$ and $y$ are positive, both $

1. The problem is to determine if the point $(1, -1)$ satisfies the inequality $y > x - 5$. 2. The inequality is $y > x - 5$.

1. The problem is to solve the equation $$\frac{2x+3}{x-1} = 4.$$\n\n2. We use the formula for solving rational equations: multiply both sides by the denominator to eliminate the f

1. Problema este să calculăm $e$ la puterea 1, adică $e^1$. 2. Formula generală pentru puterea unui număr este $a^b$, unde $a$ este baza și $b$ exponentul.

1. **State the problem:** Solve the equation $8(2x+3)-4=120$ for $x$. 2. **Apply the distributive property:** Multiply 8 by each term inside the parentheses.

1. **State the problem:** Solve the linear equation $ (2x + 3) - 4 = 120 $ for $ x $. 2. **Simplify the equation:** Combine like terms inside the parentheses and constants outside.

1. The problem is to simplify the expression $\frac{625}{100} \times 100$. 2. The formula used here is basic arithmetic multiplication and division.

1. **State the problem:** Solve the system of equations: $$2x + 38y = 252$$

1. The problem is to convert the mixed number $1\frac{3}{4}$ into an improper fraction or decimal. 2. Recall that a mixed number consists of a whole number and a fraction. To conve