🧮 algebra

1. **State the problem:** We need to find which ordered pair $(x,y)$ satisfies the system of equations: $$2x - 12 = -4y$$

1. **State the problem:** We have a geometric sequence with terms given for $n=1,3,6$ as 2, 50, and 6250 respectively. We need to find the 8th term. 2. **Recall the formula for the

1. **Problem 1: Height of the bottom drawer in a geometric progression** The height of the drawers forms a geometric progression with first term $a_1=6$ inches and common ratio $r=

1. **State the problem:** We are given a sequence with terms and their corresponding values: (1, 24), (2, 36), (3, 54), (4, 81). We need to find the rule that determines the consec

1. The first problem asks for the formula to find the nth term of the sequence defined by $f(x) = 3x + 4$ for $x = 1, 2, 3, 4, \ldots$. 2. The general form for the nth term of a se

1. **State the problem:** We need to find the equation that models the distance $y$ (in miles) an athlete runs during week $x$ based on the given data: Week: 1, 2, 3, 4, 5, 6

1. **State the problem:** We are given the tuition costs for years 1, 4, and 5 at Northern Swim School and need to find the costs for years 2 and 3 assuming a constant rate of chan

1. The problem asks to find the factored form equivalent to the expression $$3x^2 - 48$$. 2. First, identify the greatest common factor (GCF) of the terms. Here, the GCF is 3.

1. **State the problem:** Claudio's revenue from ticket sales is modeled by the quadratic equation $$R = 15000 + 200x - 10x^2$$ where $x$ is the number of $1 increases in ticket pr

1. **State the problem:** Claudio sells 500 tickets at 30 each. For every 1 increase in price, 10 fewer tickets are sold. The revenue function is given by $$R = 15000 + 200x - 10x^

1. The problem is to convert meal prices from Mexican pesos to U.S. dollars using an exchange rate. 2. The formula to convert currency is:

1. **State the problem:** Simplify the expression $$\frac{2x^3 + 4x^2}{3x^2 + 2x}$$. 2. **Write the formula and rules:** To simplify a rational expression, factor numerator and den

1. **State the problem:** We need to find the factored form equivalent to the quadratic expression $$2x^2 - 10x - 48$$. 2. **Write the expression:** $$2x^2 - 10x - 48$$.

1. **Planteamiento del problema:** Resolver la ecuación $\frac{2x+3}{4} = \frac{5x-1}{6}$. 2. **Fórmula y reglas importantes:** Para resolver ecuaciones con fracciones, multiplicam

1. **State the problem:** We need to find which of the given expressions is a factor of the quadratic polynomial $$2x^2 - 3x - 35$$. 2. **Recall the factoring method:** To factor a

1. **Problem Statement:** Describe the transformations J and K on parallelogram EFGH and find images of points P and Q under these transformations. 2. **Transformation J:** Given m

1. The problem is to factor the trinomial $2x^2 + 13x + 6$. 2. We use the factoring method for trinomials of the form $ax^2 + bx + c$.

1. **State the problem:** Factor the expression $9x^2 - 16$. 2. **Formula used:** This is a difference of squares, which follows the rule:

1. The problem is to factor the expression $9x^2 - 16$. 2. Recognize that this is a difference of squares, which follows the formula:

1. **State the problem:** We need to find which binomial is a factor of the quadratic expression $$2x^2 + x - 1$$. 2. **Recall the factoring method:** To factor a quadratic $$ax^2

1. **State the problem:** Simplify the expression $$\frac{2x \cdot x^2}{(x - y)^2}$$. 2. **Write the formula and rules:** When multiplying powers with the same base, add the expone