🧮 algebra

1. **Stating the problem:** We need to simplify and solve the equation $$(120x + 3y + 0.12z) + (200x + 2.5y + 0.12z) = 150000000$$

1. **Stating the problem:** We need to simplify and solve the expression \((120x^{0.3}y^{0.12}z) + (200x^{0.25}y^{0.12}z) = 150000000\).

1. The problem is to simplify the expression $5 - 2\sqrt{7}$. 2. This expression consists of a constant term 5 and a term involving a square root, $2\sqrt{7}$.

1. The problem is to simplify the expression $ (4y - y^2) + (4y^2 + y) $. 2. We use the rule of combining like terms: terms with the same variable and exponent can be added or subt

1. **Problem Statement:** Find the domain and range of the function $f(x) = |x^3 + 1|$. Determine for which values of $x$ the derivative is undefined. Find the inverse function if

1. Muammo: Berilgan sonlar qatorining orasidagi farqni topish: $2 \frac{1}{3}$, $5 \frac{1}{4}$, $\frac{5}{7}$, $5 \frac{6}{7}$.\n\n2. Aralash kasrlarni oddiy kasrlarga aylantirami

1. **State the problem:** We want to find for which values of $a$ the inequality $$a x^2 - 3x + 2 > 0$$ implies $$x^2 + 2(a-2)x + a - 5 > 0.$$\n\n2. **Rewrite the problem:** The im

1. **Problem Statement:** We have bacterial population data over time and assume it follows an exponential growth model $$y = a e^{b x}$$ where $y$ is the population in millions an

1. Let's state the problem: We want to prove a mathematical statement or theorem. 2. A common example is the proof that the sum of the first $n$ natural numbers is given by the for

1. **State the problem:** We want to find for which values of $a$ the inequality $$a x^2 + 2(a-2)x + a - 5 > 0$$ implies $$x^2 - 3x + 2 > 0.$$ 2. **Rewrite the inequalities:** The

1. **Stating the problem:** We are given values for Total Leads (D), Converted (A), Follow up (B), Non-Converted (C), and Refund (0). We need to calculate the Conversion %, Follow

1. The problem asks to write the equation of a line in slope-intercept form given the slope and y-intercept. 2. The slope-intercept form of a line is given by the formula:

1. Diberikan persamaan $x_1 + x_2 + x_3 + x_4 = 20$ dengan batasan bilangan bulat: $1 \leq x_1 \leq 6$, $1 \leq x_2 \leq 7$, $3 \leq x_3 \leq 9$, dan $4 \leq x_4 \leq 11$. 2. Kita

1. The problem is to find the slope and y-intercept of the line given by the equation $y = 6x - 7$. 2. The general form of a linear equation is $y = mx + b$, where $m$ is the slope

1. **State the problem:** Find the slope of the line passing through points $D(-1, 9)$ and $G(4, 9)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $(

1. The problem asks for the slope of the line passing through points $D(-1, 9)$ and $G(4, 9)$. 2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

1. **State the problem:** Find the number of solutions to the equation $$-4(x - 5) - 18 = 8 - 4x - 6$$. 2. **Write the equation clearly:** $$-4(x - 5) - 18 = 8 - 4x - 6$$.

1. **State the problem:** Solve the equation $$2X - 5 = 9X + 2$$ for $X$. 2. **Write down the equation:** $$2X - 5 = 9X + 2$$

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

1. **State the problem:** Simplify the expression $$\frac{9}{13} \times 9 \times 10 \times (2e) \times (24e) \times (5.4 \times 1.6 \times 10) \times r$$. 2. **Rewrite the expressi

1. **Énoncé du problème :** Calculer $U_2$, $U_3$ et $U_4$ pour la suite $(U_n)$ définie par :