🧮 algebra

1. **State the problem:** We need to find the vertical and horizontal asymptotes of the function $$q(x) = \frac{x - 2}{\sqrt{2x - 1}}$$ and then graph it.

1. **Problem statement:** Show that the equation $$3x^2 - 4y^2 + 3x + 16y - 18 = 0$$ represents a hyperbola. Then find its eccentricity and the equations of its asymptotes. 2. **Re

1. **Problem statement:** Show that the equation $$3x^2 - 4y^2 + 3x + 16y - 18 = 0$$ represents a hyperbola, find its eccentricity, and the equations of its asymptotes. 2. **Rewrit

1. The problem asks to find the sum to infinity of a series. 2. The sum to infinity formula for a geometric series is:

1. **State the problem:** Add the polynomials $$-10a^2 + 6a^3 + 3a$$ and $$-6a^3 - 4a + 8a^2$$. 2. **Write the polynomials together:**

1. **Problem Statement:** A. Given an arithmetic progression (AP) where the 6th term $a_6=26$ and the 9th term $a_9=17$, find:

1. **State the problem:** Amari bought 12 mini muffins for 5.40. We want to find out how many mini muffins Amari can buy with 4.00. 2. **Identify the formula:** We use the unit rat

1. **State the problem:** Amari bought 12 mini muffins for 5.40. We need to find the price of 4 mini muffins at the same rate. 2. **Formula used:** To find the price for a differen

1. **Stating the problem:** We have LED points located at specific coordinates in inches on a 200" diagonal image. The display resolution is 1024 x 768 pixels. We want to find the

1. **State the problem:** Simplify the expression $$\frac{5 + 9(1 + 2)^2}{1 + 9}$$. 2. **Recall the order of operations:** Parentheses first, then exponents, multiplication/divisio

1. The problem asks: "Where have we used the range?" in a mathematical context. 2. In mathematics, the "range" of a function is the set of all possible output values (y-values) it

1. **State the problem:** We need to solve the equation where Steven's points equal Isaiah's points: $$80 - 12x = 20 + 3x$$ 2. **Write down the formula and rules:** This is a linea

1. **State the problem:** Solve the equation $6(2y-15) + 2 = 56$ for $y$. 2. **Apply the distributive property:** Multiply 6 by each term inside the parentheses:

1. The problem states that Eric rented a car for 5 days at a total cost of 180. 2. We need to find the cost to rent the car for 3 days at the same rate.

1. Let's clarify the problem first. You seem to be asking if the answer is 48, but we need the original question to verify. 2. Please provide the full problem or equation so I can

1. **Problem Statement:** We are given positive real numbers $x, y, z$ such that:

1. **State the problem:** Matthew saved \(\frac{3}{5}\) of the total amount last year and an additional \(\frac{3}{10}\) of the total amount this summer. We need to find the fracti

1. The problem states Paul completed $\frac{8}{15}$ of his book. Jill's book has 60 pages, and we want to find how many pages Jill must read to have completed the same fraction $\f

1. Задачата е да решим уравнение, подходящо за седми клас. 2. Нека приемем, че задачата е да решим линейно уравнение от вида $ax+b=0$.

1. **Problem statement:** Given the sequence of triangles with numbers 36, 48, and variable $a$ transforming to 24, variable $b$, and 80, find $a$ and $b$. 2. **Understanding the p

1. **State the problem:** Solve the quadratic equation $$3x^2 - 2x - 5 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where the equ