🧮 algebra

1. **Stel het probleem vast:** We hebben de uitdrukking $$(ma+1 - 2ma+2 - ma+3 + ma+4)(ma-3 - ma-1 + ma-2)$$

1. **Problem:** Solve the quadratic equation $-3x^2 - 27 = 0$. 2. **Step 1:** Add 27 to both sides:

1. **Problem Statement:** We are given four relations and need to determine which one represents a function. 2. **Definition of a Function:** A relation is a function if every inpu

1. The problem asks to classify each expression as either a percentage increase of 15% or a percentage decrease of 15% for an item costing $p$ dollars. 2. A percentage increase of

1. **State the problem:** We have a data set: 3, 9, 1, 1, 1, 6, 10, and an unknown value $x$. The mean of all these numbers is given as 4.5. 2. **Formula for mean:** The mean of a

1. El problema nos pide calcular el valor numérico de la expresión algebraica $$2x^2 - 5x - 9$$ cuando $$x = 3$$. 2. La fórmula que usaremos es simplemente sustituir el valor de $$

1. Planteamos el problema: Resolver la ecuación $$2x - 5 = 11$$ para encontrar el valor de $$x$$. 2. Usamos la fórmula para resolver ecuaciones lineales: $$ax + b = c \implies x =

1. The problem is to find the value of $k$ given an equation or condition involving $k$. 2. To find $k$, we need the specific equation or expression where $k$ appears.

1. **State the problem:** We have a triangle ABC with vertices A(-2,1), B(6,5), and C(4,k). Angle ABC is the right angle. We need to find the equation of the line passing through p

1. **State the problem:** We are given the polynomial $$U(x) = 6x^4 + 35x^3 + 47x^2 - 15x - 9$$ and asked two questions: a) Identify the list of all possible rational roots of $$U(

1. Vamos resolver a equação $4 (2x - 1)(3 - 6x) = 0$. 2. Para que o produto seja zero, pelo menos um dos fatores deve ser zero. Assim, temos duas equações:

1. **State the problem:** Simplify the expression $$6) \frac{7}{4x^3} \cdot \frac{10x}{2x}$$. 2. **Write the expression clearly:** $$\frac{7}{4x^3} \times \frac{10x}{2x}$$.

1. **State the problem:** Simplify the expression $$\frac{n - 4}{7n^2 - 28n} + \frac{3n}{n - 2}$$ and identify which of the given options it equals. 2. **Factor the denominators:**

1. **State the problem:** Calculate the value of $$4^2 + (5 - 2)^2$$. 2. **Recall the formula and rules:** The expression involves squaring numbers and addition. Squaring a number

1. **State the problem:** Calculate the value of the expression $$4^2 - (13 - 4)$$. 2. **Recall the order of operations:** We first evaluate exponents, then parentheses, and finall

1. **State the problem:** Calculate the value of $2 \times 5^2$. 2. **Recall the order of operations:** Exponents are evaluated before multiplication.

1. The problem is to multiply the variable $d$ by 4. 2. The multiplication operation means adding $d$ to itself 4 times, or simply scaling $d$ by 4.

1. **State the problem:** Calculate the value of the expression $10 \times (6 - (5 - 1))$. 2. **Understand the order of operations:** According to the rules of arithmetic, operatio

1. **State the problem:** Solve the quadratic equation $$x^2 + 16 = 0$$ for $x$. 2. **Formula and rules:** To solve equations of the form $$x^2 + c = 0$$, isolate $x^2$ and then ta

1. Planteamos el problema: calcular el valor de $$\left(-\sqrt[3]{-8} + \sqrt[5]{32}\right) \left(\sqrt[3]{64} - \sqrt{100}\right)$$. 2. Recordemos las propiedades de las raíces:

1. **State the problem:** Find the first 4 terms, in ascending powers of $x$, of the binomial expansion of $ (2 - 5x)^8 $ and simplify each term.