🧮 algebra

1. **State the problem:** Given a point $(m,n)$ on the graph of $y = f(x)$, find the corresponding point on the graph of $y = f(x - 11) + 4$. 2. **Recall the transformation rules:*

1. **State the problem:** A company buys inkjet printers, LCD monitors, and memory chips. Total items bought: 41.

1. **State the problem:** We need to write a system of linear equations to represent the purchase of inkjet printers, LCD monitors, and memory chips.

1. **State the problem:** We are given the function $$f(x) = -2|x-7| + 8$$ and want to understand its behavior and graph. 2. **Recall the absolute value definition:** The absolute

1. The problem is to simplify the fraction $\frac{3}{4}$. 2. The fraction $\frac{3}{4}$ is already in its simplest form because 3 and 4 have no common factors other than 1.

1. **State the problem:** Simplify the expression $$\left(\frac{-4 a^4 b^5 c^0}{2 a^2 b^3 c^6}\right)^{-3}$$. 2. **Recall the rules:**

1. Stating the problem: Simplify the expression $$\frac{10 x^6}{4 y^2} \times \frac{-4 a^4 b^5 c^0}{2 a^2 b^3 c^6} \times (-3) \times 9^{-2}$$. 2. Recall the rules:

1. **Problem statement:** Jason observes that the amount of money donated each hour increases by 15 compared to the previous hour, starting with 40 in the first hour. We need to: a

1. **State the problem:** We need to find $n(A)$, the number of elements in the set $A = \{127, 128, 129, 130, \ldots, 141\}$. 2. **Recall the formula:** For a set of consecutive i

1. The problem involves solving and understanding the system of inequalities: $$y < -\frac{3}{2}x + 5$$

1. **State the problem:** We are given three functions: $f(x) = x^2$, $g(x) = 2x$, and $h(x) = x^2 - 2x$. We need to fill in the table of values for $f(x)$ and $g(x)$ at $x = -2, -

1. **Problem statement:** Find the condition for which the line $y=mx+c$ touches the ellipse $$\frac{x^2}{25} + \frac{y^2}{16} = 1.$$ Then find the equation of the tangents with sl

1. Vamos a empezar explicando cómo resolver ejercicios de álgebra básicos, que suelen ser muy comunes en los exámenes. 2. Un problema típico es resolver una ecuación lineal, por ej

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