🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{a}{2x+2y} = \frac{3x+3y - b}{3x+3y}$$ and understand the relationship between the terms. 2. **Rewrite the denominators:**

1. The problem is to find the equation of the ellipse given its center and axes. 2. The ellipse is centered at $(3,2)$.

1. The user asked for an equation but did not specify the type or context. 2. A simple example of an equation is a linear equation, which can be written as $$y = mx + b$$ where $m$

1. **State the problem:** Mindy and Troy together ate 9 pieces of cake. Mindy ate 3 pieces, and Troy ate \(\frac{1}{4}\) of the total cake. We need to find the total number of piec

1. The problem is to add $x$ to $x$. 2. The formula for addition of like terms is $a + a = 2a$.

1. The problem asks to find the equation representing the cost $c$ of using a carpooling service for $d$ days based on the graph. 2. From the graph, the cost starts at $0$ when $d=

1. The problem states: For every $\frac{1}{4}$ mile Pascal walks, Lucien runs $\frac{2}{3}$ mile. We want to find how many miles Pascal walks for every 1 mile Lucien runs. 2. To fi

1. **Problem a:** Solve the equation $$\frac{6}{x - 1} = \frac{x}{x^2 + 2x + 1}$$ 2. **Step 1:** Recognize that $$x^2 + 2x + 1 = (x + 1)^2$$.

1. The problem is to find the decimal value of the fraction $\frac{11}{20}$. 2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator: $\text

1. The problem is to find the value of the fraction $\frac{1}{4}$. 2. A fraction $\frac{a}{b}$ represents the division of $a$ by $b$.

1. **State the problem:** We have a rational function which is a quotient of linear functions. It has a vertical asymptote at $x=-4$, a horizontal asymptote at $y=3$, and an $x$-in

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides to undo the

1. Problem 2.98: Klient banku spłacił pożyczkę w wysokości 13923 w czterech ratach, z których każda następna była o 10% większa od poprzedniej. Oblicz kwotę pierwszej i czwartej ra

1. The problem asks if the ratios 6 staff members to 10 campers and 3 staff members to 5 campers are equivalent. 2. To check if two ratios are equivalent, we can write them as frac

1. **State the problem:** We need to determine if the ratios 10 large bookmarks to 4 small bookmarks and 15 large bookmarks to 6 small bookmarks are equivalent. 2. **Formula and ru

1. **Problem Statement:** Given the function $f(x) = -x^2 - 3x + 28$, we need to find: a) The $x$ and $y$ intercepts.

1. **Problem Statement:** Given the function $f(x) = -x^2 - 3x + 28$, find the X and Y intercepts, compute the vertex coordinates and its nature, plot the function, and draw the ax

1. **State the problem:** We need to divide the polynomial $6x^3 - 5x^2 - 2x + 1$ by a divisor using long division. Since the divisor is not specified, we assume the divisor is $x

1. The problem asks for the rate of change in boxes of cookies sold between Thursday and Friday. 2. The rate of change formula is:

1. **State the problem:** We need to find the rate of change in the number of sandwiches sold between Thursday and Friday. 2. **Formula:** The rate of change between two points is

1. **State the problem:** Solve the system of equations: $$3x - 8y = 24$$