🧮 algebra

1. Diberikan fungsi $f(x) = 5^{x+1}$ dan nilai $f(k) = 125$. Kita diminta mencari nilai $k$ yang memenuhi. 2. Substitusikan $k$ ke dalam fungsi:

1. State the problem: Find the value of $x$ if $\frac{3}{4} = \frac{x}{8}$.\n\n2. Use the formula for proportions: $\frac{a}{b} = \frac{c}{d} \implies ad = bc$. This means the prod

1. State the problem: Create two similar algebraic problems without solutions. 2. Problem 1: Solve for $x$ in the equation $$3x + 5 = 20$$.

1. The problem is to analyze the quadratic function $$f(x) = 2x^2 - 5x + 1$$ and understand its properties. 2. The general form of a quadratic function is $$f(x) = ax^2 + bx + c$$

1. Тодорхойлж эхэлье: Илэрхийлэл нь $\frac{4}{3} \times \frac{4}{4}$ байна. 2. Хуваарьлах дүрмийг ашиглана: Хуваарьлах үед тоонуудыг үржүүлж, дараа нь хуваана.

1. Planteamos el problema: Resolver la ecuación cuadrática $2x^2 - 4x - 6 = 0$. 2. Usamos la fórmula general para ecuaciones cuadráticas: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

1. **Problem statement:** David divided his collection of stamps into equal groups of 9, and there are 112 groups. We need to find the total number of stamps in David's collection.

1. The problem asks to convert the decimal numbers 2.167 and 0.867 into fractions. 2. To convert a decimal to a fraction, write the decimal number over its place value and simplify

1. The problem is to convert a decimal number to a fraction. 2. The general formula to convert a decimal to a fraction is to write the decimal number as the numerator and the place

1. **State the problem:** Solve the equation $$x - 1 = \sqrt{x + 1}$$ for $x$. 2. **Recall the formula and rules:** To solve equations involving square roots, we isolate the square

1. **State the problem:** Solve the equation $$\sqrt{x^2 - 6x + 36} = 10$$. 2. **Formula and rules:** To solve an equation with a square root, first isolate the square root express

1. **Problem statement:** Simplify the expressions: (i) $ (4\sqrt{3} - 2\sqrt{2})(3\sqrt{2} + 4\sqrt{3}) $

1. **Problem statement:** Find the maximum and minimum values of the function $$f(x) = \frac{2x^2 + 4x + 5}{x^2 + 1}$$ for all real numbers $x \in \mathbb{R}$. 2. **Formula and rul

1. **State the problem:** Solve the inequality $$9x^2 + 3x - 2 \geq 0$$ and graph the solution set on a real number line. 2. **Formula and rules:** To solve a quadratic inequality,

1. **State the problem:** Evaluate the determinant of the matrix $$D = \begin{vmatrix} 1 & 2 & -1 \\ 3 & 0 & 0 \\ 2 & -2 & -1 \end{vmatrix}$$

1. **State the problem:** Find the value of $$k^2 + \frac{1}{k^2}$$ where $$k = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$$.

1. **Problem:** Simplify the expression $$11\sqrt[3]{x^4 y^7} - 5xy \sqrt[3]{8xy^4} + y^2 \sqrt[3]{27x^4 y}$$ and verify it equals $$4xy^2 \sqrt[3]{xy}$$. 2. **Formula and rules:**

1. **Stating the problem:** We are given several expressions involving variables $x$, $u$, and $u_1$, and we want to understand and solve for $u$ and $u_1$ based on the given equat

1. **Problem:** Mahi, Lara, and Maivi participated in a quiz contest. Mahi and Lara scored 45 and 18 points respectively. Find how many points Maivi scored. 2. **Write an equation:

1. **Stating the problem:** We want to find the equation of the curve outlining the trophy shape, which is given as a parabola segment $$y = -(0.16x - 2.109)^2 + 4.28$$ for $$1.963

1. **Stating the problem:** We are given several algebraic expressions and equations to build up and undo, and to solve for variables. 2. **Building and undoing expressions:**