🧮 algebra

1. **State the problem:** Simplify the expression $4x^2$. 2. **Understand the expression:** The expression $4x^2$ means 4 times $x$ squared.

1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$. 2. **Understand the given information:** We know both $a -

1. The problem is to graph the function $y = x^2$. 2. The formula used is $y = x^2$, which is a quadratic function representing a parabola.

1. Stating the problem: We need to expand and simplify the expressions for A, B, C, D, E, and F. 2. Recall the formulas:

1. The problem is to multiply the two variables $A$ and $B$. 2. The multiplication of two variables is expressed as $A \times B$ or simply $AB$.

1. The problem is to understand the relationship or operation involving the letters A, B, and C as given. 2. Since the input is just letters without any explicit operation or equat

1. The problem is to verify if the equation $$p^4 - q^4 = (p - q)(p^3 + p^2q + pq^2 + q^3)$$ is a polynomial identity. 2. Recall the difference of fourth powers factorization: $$a^

1. **State the problem:** The value $Y$ varies inversely with $x$, and we know $y=12$ when $x=5$. We need to find $y$ when $x=4$. 2. **Formula for inverse variation:** When two var

1. **State the problem:** The value $Y$ varies inversely with $x$, meaning $Y$ and $x$ satisfy the relation $Y = \frac{k}{x}$ for some constant $k$. 2. **Given:** $y = 4$ when $x =

1. **State the problem:** Factor the common factor out of the expression $$10 - 15m - m$$ and simplify $$2(5m - 8m)$$. 2. **Analyze the first expression:** $$10 - 15m - m$$.

1. **State the problem:** Factor the expression $-9x + 30$ completely. 2. **Recall the factoring formula:** To factor an expression, find the greatest common factor (GCF) of all te

1. **Problem statement:** Find constants $A$, $B$, and $C$ such that

1. The problem asks to calculate the slope (rate of change) of shoe size with respect to height. 2. The slope formula is $$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$$ where $y$ is

1. The problem asks us to interpret the rate of change of shoe size with respect to height from a linear graph. 2. The graph shows a line starting near (0,1) and ending near (100,8

1. **State the problem:** Solve the equation $2.5 (y - x) = 0$ given $y = 6$ and find $x$. 2. **Write the equation:**

1. **State the problem:** Find the 9th term of a geometric sequence where the first term $a_1=5$ and the common ratio $r=\frac{1}{3}$.\n\n2. **Formula for the nth term of a geometr

1. **State the problem:** Solve the equation $$2.5(x + 4) + x = 38$$ for $x$. 2. **Apply the distributive property:** Multiply $2.5$ by both $x$ and $4$:

1. **Énoncé du problème :** Normand veut que le coût de chaque visite au gym soit exactement 20 $. Le coût total de l'abonnement est de 980 $. On cherche le nombre de visites $x$ p

1. **State the problem:** Determine if the sequence $7, -\frac{7}{3}, \frac{7}{9}, \frac{7}{27}, \ldots$ is geometric. If it is, find the common ratio $r$. 2. **Recall the definiti

1. **State the problem:** Find the slope of the line passing through points near (-7, 8) and (7, -8) and crossing the origin (0,0). 2. **Recall the slope formula:** The slope $m$ o

1. **Problem Statement:** Determine the domain of the function $f$ from the given graph. 2. **Understanding Domain:** The domain of a function is the set of all possible input valu