🧮 algebra

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

1. **State the problem:** Calculate $8 + 3$. 2. **Recall the addition rule for integers:** When adding two positive integers, simply add their absolute values.

1. **State the problem:** Creed wants to find the cost of 1 kg (1000 g) of Halloween Treats when 450 g costs 3.75. 2. **Formula used:** To find the cost per gram, use the unit rate

1. The problem is to solve the proportion $$\frac{x}{78} = \frac{8}{13}$$ and find the value of $x$. 2. The formula for solving proportions is to cross multiply: $$a/b = c/d \impli

1. **State the problem:** We are given a line passing through points $(-7, -8)$ and $(1, 6)$ and asked to find the y-intercept of this line. 2. **Formula and rules:** The y-interce

1. **State the problem:** Find the gradient (slope) of the line passing through points $(-2, -5)$ and $(1, 4)$.\n\n2. **Formula for gradient:** The gradient $m$ of a line through p

1. **Problem statement:** Identify the degree, leading coefficient, and end behavior of each polynomial function. 2. **Key concepts:**

1. Problem: Bestimme zu jedem Graphen die Funktionsgleichung der drei Geraden g1, g2 und g3. 2. Allgemeine Formel für eine lineare Funktion: $$y = mx + b$$ wobei $m$ die Steigung u

1. **State the problem:** We need to find an expression that represents the total profit from selling $h$ hot dogs, $p$ pretzels, and $d$ drinks. 2. **Identify the profit per item:

1. State the problem: Simplify and factorise the expression b) $3x^2 - 11 + x^2 - 7$. 2. Formula and rules: Combine like terms by adding coefficients of the same power, e.g. $ax^n

1. **State the problem:** Jade is twice as old as Sara. If Sara is $y$ years old, find an expression for Jade's age. 2. **Understand the relationship:** "Twice as old" means Jade's

1. **State the problem:** We want to find the largest whole number $x$ such that $8 + x$ is larger than $2x$. 2. **Write the inequality:**

1. **State the problem:** Simplify the expression $$\frac{m^{x+9}}{m^3}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same base, s

1. **State the problem:** Solve the equation $$\frac{6}{x+2} = \frac{5x-1}{2-3x}$$ for $x$. 2. **Understand the formula and rules:** To solve an equation with fractions, we can cro

1. **State the problem:** We are given a cubic function $$f(x) = x^3 - 14x^2 + 61x - 84$$ and told that one factor is $$(x - 7)$$. We need to find all zeros of the function. 2. **U

1. The problem is to simplify the expression $\frac{4}{ }$, but the denominator is missing. 2. A fraction requires both a numerator and a denominator to be defined.

1. **State the problem:** Solve the quadratic equation $$x^2 + x - 6 = 0$$ using the graph of the function $$y = x^2 + x - 6$$. 2. **Formula and rules:** The solutions to $$x^2 + x