🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{(11 \times 2 \times 3) \times 12 \times 11 \times 9 \times \sqrt{9}}{2 \times 7 \times (12 \times 1) \times 2 \times 11 \t

1. **State the problem:** Simplify the expression $$\frac{(11 \frac{1}{2})^{12} \times 11^{19} \times \sqrt{9}}{27 \times 12^2 \times 11^{11}}$$. 2. **Rewrite mixed number:** Conve

1. **Stating the problem:** Mark and Tony had the same weight before vacation. Mark's weight increased by $\frac{1}{16}$ and Tony's by $\frac{1}{20}$. Together, their combined weig

1. Stated problem: Izračunajte izraz $-81 - \frac{5}{3}$.\n\n2. Prvo, izrazimo oba broja u zajedničkom obliku da bismo mogli da ih saberemo ili oduzmemo. Broj $-81$ možemo napisati

1. **Stating the problem:** You have 18,000,000 Rp and want to convert all of it into Ge, then find out how much $ it would take to buy that amount of Ge. 2. **Given:**

1. Postavimo problem: Neka je broj $x$. Sabiranjem tog broja sa 5 dobijamo $x+5$. 2. Zbir $x+5$ množimo sa $\frac{1}{3}$, što daje izraz $$\frac{1}{3}(x+5)$$.

1. نبدأ بحل السؤال الأول: "أقل من مثلي عدد بمقدار خمسة يساوي 12". 2. نترجم الجملة إلى معادلة:

1. نبدأ بترجمة الجملة: "أقل من مثلي عدد بمقدار خمسة يساوي 12". 2. لنفترض أن العدد هو $ن$.

1. **State the problem:** Multiply the fractions $\frac{2}{3}$ and $4 \frac{1}{2}$.\n\n2. **Convert mixed number to improper fraction:**\n$4 \frac{1}{2} = \frac{4 \times 2 + 1}{2}

1. **State the problem:** Solve the equation $\frac{m}{3} = -12$ for $m$. 2. **Formula and rule:** To isolate $m$, multiply both sides of the equation by 3, because $m$ is divided

1. **State the problems:** Solve the linear equations from question 9 to 13. 2. **General formula and rules:** For linear equations of the form $ax + b = c$, isolate $x$ by subtrac

1. The problem asks to convert 3.2 million to a fraction of a million. 2. We start with the number 3.2 million, which means 3.2 times 1,000,000.

1. **State the problem:** Simplify the expression $$2 k^5 \times k^4 \times \frac{1}{2} k^7$$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying te

1. **State the problem:** We need to put the fractions $\frac{7}{10}$, $\frac{8}{15}$, and $\frac{3}{5}$ in ascending order. 2. **Find a common denominator:** To compare fractions,

1. **State the problem:** We need to put the fractions $\frac{47}{100}$, $\frac{9}{20}$, and $\frac{4}{10}$ in ascending order. 2. **Find a common denominator:** To compare fractio

1. **State the problem:** Simplify the expression $$- \frac{1}{2} n^2 \times - \frac{1}{2} n^6 \times n^7$$. 2. **Recall the rules:** When multiplying powers with the same base, ad

1. **State the problem:** Find all functions $f : \mathbb{Z} \to \mathbb{Z}$ such that $$f(f(n)) + f(n+1) = 2n + 3$$

1. The problem is to find the roots of the quadratic function $f(x) = -2x^2 - 8x - 3$ and describe its graph. 2. The roots of a quadratic function $ax^2 + bx + c = 0$ are found usi

1. Problema: Determinar el dominio y bosquejar la gráfica de la función \(h(x) = \sqrt{1 - x^3}\). 2. Para funciones con raíz cuadrada, el radicando debe ser mayor o igual a cero p

1. **State the problem:** Simplify the expression $$12\sqrt{10} \div 2$$. 2. **Recall the rule:** Division can be written as multiplication by the reciprocal. Here, dividing by 2 m

1. **State the problem:** Find the positive solution of the equation $$7x^{\frac{5}{3}} + 27 = 54459$$. 2. **Isolate the term with the variable:** Subtract 27 from both sides: