🧮 algebra

1. **Stating the problem:** We want to prove that the determinant $$G_2 = \begin{vmatrix} q_1 & q_3 \\ 1 & q_2 \end{vmatrix} = q_1 q_2 - q_3 > 0$$

1. **State the problem:** Given three variables $a$, $b$, and $c$ with the following sums: $$a + b + c = 4$$

1. The problem is to solve the logarithmic equation $\log_x 64 = 3$. 2. Recall the definition of logarithm: $\log_a b = c$ means $a^c = b$.

1. The problem asks to write Boussahia Sayeh's equation as \((x + y) \times (x - y)\). 2. This expression is a difference of squares formula, which states:

1. **State the problem:** Simplify the expression $$\frac{1}{2} + \frac{1}{2 + \frac{12}{7}}$$. 2. **Rewrite the denominator in the second term:** The denominator is $$2 + \frac{12

1. Diberikan fungsi rasional $f(x) = \frac{2x-3}{x+4}$ dengan $x \ne -4$. 2. Tujuan kita adalah mencari fungsi invers $f^{-1}(x)$, yaitu fungsi yang "membalik" $f(x)$ sehingga $f(f

1. **State the problem:** We are given a table showing the distance an object travels over time and asked to find the distance traveled in 5 seconds assuming a constant rate of cha

1. The problem states that an object travels at a constant rate and provides a table of time (s) and distance (m): | Time (s) | Distance (m) |

1. **State the problem:** We are given a table showing the distance an object travels over time and asked to find the distance traveled in 5 seconds assuming a constant rate of cha

1. Diketahui fungsi $f(x) = 3^{2x-4}$. Kita diminta mencari nilai $f(2)$.\n2. Substitusikan $x = 2$ ke dalam fungsi: $$f(2) = 3^{2(2)-4}$$\n3. Hitung eksponen: $$2(2) - 4 = 4 - 4 =

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