🧮 algebra

1. **State the problem:** We have two functions:

1. **Stating the problem:** We need to find which pairs of ratios are equivalent in each question. 2. **Formula and rule:** Two ratios $a:b$ and $c:d$ are equivalent if their cross

1. **State the problem:** We want to find an equation that models the height $H$ (in cm) of a child as a function of age $A$ (in years) using the given data points: $(2, 84.5)$, $(

1. **Enunciare il problema:** Risolviamo l'equazione esponenziale $$2^x + 2^{x+1} = 2^{x-1} + 7$$. 2. **Formula e regole importanti:** Ricordiamo che per le potenze con la stessa b

1. Énonçons le problème : Calculer $\frac{3}{4}$ divisé par $\frac{5}{8}$.\n\n2. Rappelons la formule pour diviser deux fractions : \n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \

1. **Problem:** Write down the centre and radius length of the circle $$x^2 + y^2 - 6x - 2y - 15 = 0$$. If the line $$3x + 4y + c = 0$$ is a tangent to this circle, find the two va

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle that to isolate $x$, we perform inverse operations to both sides of the equat

1. **State the problem:** We analyze the function's domain, range, intercepts, and asymptotes based on the graph description. 2. **Domain:** The function has a vertical asymptote n

1. **Problem Statement:** Given a graph with two decreasing diagonal lines separated by a vertical dashed red line at $x=1$, answer questions about domain, range, intercepts, and a

1. **State the problem:** We analyze the graph of a rational function to find its domain, range, intercepts, and asymptotes. 2. **Domain:** The domain is all real numbers except wh

1. **Problem Statement:** We analyze a hyperbola-like rational function with two branches, having vertical asymptote at $x=1$ and horizontal asymptote at $y=2$.

1. **State the problem:** We analyze the function's domain, range, intercepts, and asymptotes based on the description of a hyperbola-like rational function with two branches.

1. Das Problem lautet: Wie lange dauert es, bis das nächste Level erreicht wird, wenn die aktuelle Erfahrung (XP) 1.44 \times 10^{304} von 1.65 \times 10^{304} XP ist und die XP-Ra

1. **State the problem:** Write an equation of a parabola with a vertex at the origin and a directrix at $y=5$. 2. **Recall the definition and formula:** A parabola is the set of p

1. **State the problem:** Factor the cubic expression $$2x^3 - 13x - 24$$. 2. **Recall the factoring approach:** For cubic polynomials, try to find rational roots using the Rationa

1. **State the problem:** Sam plans to order a total of 144 items. We need to find how many helmets will be in this new order. 2. **Identify the quantities and relationships:** The

1. **State the problem:** Factor the quadratic expression $$5x^2 + 19x + 18$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two binomials $$(

1. **State the problem:** Find the value of $p^2$ when $p=4$. 2. **Formula used:** The square of a number $p$ is given by $$p^2 = p \times p$$

1. **State the problem:** Find the value of $q^2$ when $q=6$. 2. **Formula used:** The square of a number $q$ is given by $$q^2 = q \times q$$.

1. **State the problem:** Subtract the rational expressions $$\frac{2b - 12y}{7b} - \frac{6b + 5y}{7b}$$ and simplify the result. 2. **Formula and rules:** When subtracting rationa

1. **State the problem:** Simplify the expression $2(5a+8a)-3(4a-8)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.