🧮 algebra

1. The problem is to verify if $$\left( \frac{4}{5} \right)^2 = \frac{25}{16}$$ is true. 2. The formula for squaring a fraction is $$\left( \frac{a}{b} \right)^2 = \frac{a^2}{b^2}$

1. **Problem:** Find the domain and range of the rational function $$f(x) = \frac{x+3}{x-4}$$. 2. **Domain:** The domain of a rational function is all real numbers except where the

1. **State the problem:** Solve the equation $$2x^4 - 3x^2 + 1 = 0$$ for $x$. 2. **Identify the type of equation:** This is a quartic equation but can be treated as a quadratic in

1. **Problem:** Determine if the statement "The solution set for $x^2 = 81$ is \{9\}" is true or false. 2. **Formula and rules:** To solve $x^2 = 81$, we use the property that if $

1. **State the problem:** Simplify the expression $$\frac{3x + 6}{8} \div \frac{5x + 10}{6}$$. 2. **Recall the rule for dividing fractions:** Dividing by a fraction is the same as

1. **Problem statement:** Transform the conic given in polar coordinates $$r = \frac{4}{4 - 2 \cos \theta}$$ into rectangular coordinates and show it reduces to the ellipse equatio

1. **State the problem:** Solve the quadratic equation $$x^2 - 25 = 0$$. 2. **Formula and rules:** This is a difference of squares equation, which can be factored using the identit

1. **State the problem:** Simplify the expression $ (3054 - 741) \times 12 + 36 $.\n\n2. **Apply the order of operations:** First, perform the subtraction inside the parentheses.\n

1. **State the problem:** Simplify the expression $\frac{8520}{5} - 524 + 21$. 2. **Apply division first:** Calculate $\frac{8520}{5}$.

1. The problem is to simplify the expression \(\sqrt{x}6\). 2. The expression \(\sqrt{x}6\) can be interpreted as \(6\sqrt{x}\) since multiplication is commutative.

1. The problem is to solve the equation $$2x^2 - 4x - 6 = 0$$ for $x$. 2. We use the quadratic formula to solve equations of the form $$ax^2 + bx + c = 0$$, which is:

1. The problem is to solve the equation $$2x^2 - 4x - 6 = 0$$ for $x$. 2. We use the quadratic formula to solve equations of the form $$ax^2 + bx + c = 0$$, which is:

1. The problem is to solve the equation $$2x^2 - 4x - 6 = 0$$ for $x$. 2. We use the quadratic formula to solve equations of the form $$ax^2 + bx + c = 0$$, which is:

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then

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:** Calculate the value of the expression $-4(-1)(-14)$. 2. **Recall the multiplication rules for signs:**

1. The problem is to simplify the expression $5^1 \times 2^x$. 2. Recall that $5^1$ means 5 raised to the power of 1, which is simply 5.

1. The problem is to arrange the fractions $\frac{7}{12}$, $\frac{1}{2}$, and $\frac{2}{3}$ in ascending order, i.e., find $a < b < c$ where $a$, $b$, and $c$ are these fractions.

1. **Stating the problem:** We want to arrange fractions in order of size, from smallest to largest or vice versa. 2. **Formula and rules:** To compare fractions, we can use the co

1. Muammo: Kompleks sonni darajaga ko'tarish formulasi va misollar bilan tushuntirish. 2. Kompleks sonni darajaga ko'tarish formulasi De Moivre teoremasiga asoslanadi:

1. **State the problem:** We need to determine which of the given equations is true for all positive values of $x$ and $y$. 2. **List the equations:**