🧮 algebra

1. Problema: Calculați radicalii cubici pentru următoarele valori: a) ³√216; b) ³√-512; c) ³√0,027; d) ³√\frac{729}{125}; e) ³√\frac{125}{64}; f) ³√-0,001; g) ³\sqrt{(ab)^5}. 2. Fo

1. **State the problem:** Solve the equation $x - 5 = 8 - 11$ for $x$. 2. **Simplify the right side:** Calculate $8 - 11$.

1. Stating the problem: Solve the equation $$\frac{x}{5} = \frac{8}{11}$$ for $x$. 2. Formula and rules: To solve for $x$ in a proportion $\frac{a}{b} = \frac{c}{d}$, we use cross

1. The problem is to simplify the expression $16x^2 + 4x + 36$. 2. We look for common factors in all terms. The terms are $16x^2$, $4x$, and $36$.

1. The problem asks: What fraction of an hour is 24 minutes?\n\n2. We know that 1 hour = 60 minutes.\n\n3. To find the fraction of an hour that 24 minutes represents, we use the fo

1. **State the problem:** Simplify the expressions $$(2\sqrt{3})^2$$, $$(2 - \sqrt{3})^2$$, and $$(2 + \sqrt{3})(2 - \sqrt{3})$$ and explain how they differ. 2. **Formula and techn

1. **State the problem:** Solve the equation $$\frac{2j}{5} = 6$$ for the variable $j$. 2. **Formula and rules:** To solve for $j$, we need to isolate it on one side of the equatio

1. **State the problem:** We need to divide 121.50 into two parts in the ratio 4:5. 2. **Formula and explanation:** When dividing a quantity in the ratio $a:b$, the total parts are

1. The problem asks for the domain of the profit function $$P(x) = 349x - 39600$$ where $$x$$ is the number of passengers on a 1980-mile flight with a maximum seating capacity of 2

1. **State the problem:** Solve the equation $$x = - \frac{8}{9} y + \frac{5}{8}$$ for the variable $y$. 2. **Write the equation:**

1. **State the problem:** Express $11^4 \div 11$ in index form. 2. **Recall the exponent division rule:** When dividing powers with the same base, subtract the exponents: $a^m \div

1. **State the problem:** Calculate $11^4 \div 11$. 2. **Recall the exponent division rule:** When dividing powers with the same base, subtract the exponents: $$a^m \div a^n = a^{m

1. The problem states that the line $T$ passes through the points $(0, -5)$ and $(1, 3)$ and can be written in the form $y = mx + c$. 2. To find $m$ (the slope), use the formula:

1. **Stating the problem:** Calculate 25% of 58,458. 2. **Formula used:** To find a percentage of a number, use the formula:

1. **State the problem:** Dorothy bought a clutch at a 35% discount and saved 42. We need to find the original price of the clutch. 2. **Formula and explanation:** The discount amo

1. **State the problem:** Winifred bought a bib necklace at a 45% discount, saving $63. We need to find the original price of the necklace. 2. **Formula and explanation:** The disc

1. **Problem statement:** Kürzen Sie so weit wie möglich den Bruch $\frac{9rs}{63st}$. 2. **Formel und Regeln:** Beim Kürzen von Brüchen kürzen wir gemeinsame Faktoren im Zähler un

1. **Problem Statement:** We need to find the total cost for each company (Thunder Cable and Flash Cable) for the first 12 gigabytes of data usage. 2. **Formula:** Total cost for e

1. **Problem Statement:** We are given a function $f(x)$ with inputs and outputs in a table and asked to complete the table for its inverse function $f^{-1}(x)$.

1. **State the problem:** Simplify the expression $$\frac{3f^3}{12f^{18}}$$. 2. **Recall the rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{

1. **Problem statement:** We are asked to explain what a function is and why the composition of two functions is still a function. Then, we will solve the first example: given $f_{