🧮 algebra

1. **State the problem:** Solve the quadratic equation $4n^2 + 4n + 36 = 0$ by completing the square. 2. **Write the equation:**

1. **State the problem:** We want to factor the expression $$(x-7)^7 + 7x(x-7)^6$$ into the form $$(x-7)^6((x-7) + 7)$$. 2. **Identify common factors:** Notice that both terms cont

1. **Problem statement:** Schreibe den Term ohne Klammern und fasse so weit wie möglich zusammen. 2. **Formel und Regeln:** Verwende das Distributivgesetz: $a(b+c) = ab + ac$.

1. Problem: Schreibe den Term ohne Klammern und fasse nach Möglichkeit zusammen. 2. Wir betrachten den ersten Term:

1. The problem is to express the repeating decimal $0.5\dot{8}\dot{8}$ as a fraction in simplest form. 2. Let $x = 0.5\dot{8}\dot{8}$, which means $x = 0.588888\ldots$ where the di

1. **State the problem:** Find the greatest common factor (GCF) of the terms $-18x^3$ and $-6x^2$. 2. **List the terms:** The terms are $-18x^3$ and $-6x^2$.

1. **State the problem:** Find the greatest common factor (GCF) of the terms $$8a^4 + 24a^3 - 40a^2$$. 2. **Identify each term's factors:**

1. The problem asks us to find the first three terms of the sequence defined by the formula $T(n) = 5n - 7$. 2. The formula for the $n^{th}$ term of the sequence is given as:

1. Problem: Løs ligningen med brøker: $$\frac{2x}{2} = 3$$ 2. Formel: Når vi har en ligning med en brøk, kan vi multiplicere begge sider med nævneren for at fjerne brøken.

1. The problem states that $y = f(x) = \log_m(x)$ with $m > 1$ and asks to find a point that the graph of $y = g(x) = \log_m(0.5x)$ could pass through. 2. Recall the logarithm prop

1. **State the problem:** Calculate the value of the expression $$80 \div \left(4^2 \div \frac{2}{5}\right) + 3.75$$. 2. **Recall the order of operations:** Parentheses first, then

1. **Stating the problem:** Beräkna arean av botten på en läskburk som är en cirkel med radien $r=3$ cm.

1. Stating the problem: Solve the equation $6 + x = 3x - 12$ for $x$. 2. Write down the equation:

1. Planteamos el problema: Queremos saber si el vector $\vec{w} = (5,7)$ puede expresarse como combinación lineal de los vectores $\vec{a} = (2,1)$ y $\vec{b} = (1,3)$, es decir, s

1. **State the problem:** We are given the expression $2 + 6 \div 2 + 4 \times 3$ and asked to:

1. **State the problem:** We are given a sequence starting with the first term unknown, and the term-to-term rule is "Multiply by a number then subtract 2". The sequence provided i

1. **State the problem:** Simplify the expression $(+4ab-5ab)\times(+3ab+5a^2-3-5ab)$.\n\n2. **Simplify inside the parentheses:**\n\nFirst, simplify $+4ab-5ab$:\n$$+4ab-5ab=\cancel

1. **State the problem:** Factor the quadratic polynomial $$2x^2 + 9x + 7$$ into the form $$(ax + b)(cx + d)$$. 2. **Recall the factoring method:** For a quadratic $ax^2 + bx + c$,

1. We are given the system of equations: $$2+3x=-7$$

1. The problem is to find the value of the function $h(x) = -3x - 2$ at $x=3$. 2. The formula given is $h(x) = -3x - 2$.

1. **State the problem:** We need to find the value of $g(2) \cdot h(3)$ given the function $g(x) = 5x - x^2$. However, the function $h(x)$ is not provided, so we can only evaluate