🧮 algebra

1. **Problem statement:** Given the binary operation $x * y = 5y - 3x$, find the value of $3 * 2$. 2. **Formula used:** The operation is defined as $x * y = 5y - 3x$.

1. **State the problem:** We need to divide the polynomial $a^3 - 6a^2 + 10a - 3$ by the binomial $a - 3$. 2. **Formula and rule:** Polynomial division can be done using long divis

1. **Problem:** Given the binary operation $x * y = 5y - 3x$, find the value of $3 * 2$. 2. **Formula:** The operation is defined as $x * y = 5y - 3x$.

1. **State the problem:** Simplify the expression $$\frac{m^2 + m - 6}{m + 4}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor the numerator and de

1. **Problem:** Find $f(\frac{3}{2}) + g(-9)$ given $f(x) = 2x - 9$ and $g(x) = 3x^2 - 5x + 2$. 2. **Step 1:** Calculate $f(\frac{3}{2})$.

1. **Problemstellung:** Löse die Gleichung $$\frac{1}{3x^2} - 1 = \frac{1}{6x}$$ mit der Bedingung $$x \neq 0$$. 2. **Formel und Regeln:** Um Bruchgleichungen zu lösen, multiplizie

1. The problem is to convert the mixed number $-14\frac{1}{2}$ into an improper fraction. 2. Recall that a mixed number consists of a whole number and a fraction. To convert it to

1. **State the problem:** Clara needs to pay a security deposit that equals the first and last month's rent plus $75 per pet. She has 1 dog and 1 cat. 2. **Identify the known value

1. The problem asks: What is 22.11% of 50? 2. To find a percentage of a number, use the formula:

1. **State the problem:** Find what is $6 \frac{4}{5}\%$ of 33. 2. **Convert the mixed number percent to an improper fraction:**

1. The problem is to simplify the expression $-43 + (x - 6)^2$. 2. The formula for squaring a binomial is $ (a - b)^2 = a^2 - 2ab + b^2 $.

1. **State the problem:** Express the quadratic expression $7 - 12x + x^2$ in the form $p + (q + x)^2$, where $p$ and $q$ are integers. 2. **Recall the formula:** The expression $(

1. The problem asks for the first four terms of the sequence defined by the formula for the $n^{th}$ term: $$a_n = 8(3 - n)$$ 2. To find the first four terms, substitute $n = 1, 2,

1. **Stel het probleem vast:** Los de vergelijking op $$ (x-1)(x-6) = 3(x-6) $$. 2. **Gebruik de distributieve eigenschap:** Vermenigvuldig de haakjes aan de linkerkant uit.

1. **State the problem:** Solve for $r$ in the equation $$\frac{r - 9}{3} = 3.$$\n\n2. **Formula and rules:** To solve for $r$, we want to isolate $r$ on one side. Since $r - 9$ is

1. The problem asks whether the cost of purchasing cookies from Tasty Sweets, which is $3.00 per cookie plus $5.50 for the box, represents a proportional or non-proportional relati

1. **Problem Statement:** Determine whether the equation $y = 6h + 2x$ represents a proportional or non-proportional relationship. 2. **Understanding Proportional Relationships:**

1. **State the problem:** We have three sets:

1. **Stating the problem:** Determine the coordinates of the point B, which is the intersection of the graphs of two functions: \(f\), a function of inverse proportionality, and \(

1. **State the problem:** Simplify the expression $$15x - 8x - 9$$ and determine the sign of the terms in the answer. 2. **Identify like terms:** The terms $$15x$$ and $$-8x$$ are

1. **State the problem:** We need to find the ratio of gold to silver to bronze medals won by Sweden in the 1988 Winter Olympic Games and simplify it. 2. **Identify the values:** F