🧮 algebra

1. The problem is to simplify the expression $\frac{0}{x}$ where $x$ is any number except zero. 2. Recall the rule: zero divided by any nonzero number is zero.

1. **State the problem:** The problem is to find the value of $x$ that satisfies the equation $2x + 3 = 7$. 2. **Formula and rules:** To solve for $x$, we use the rule of isolating

1. **State the problem:** Simplify the expression $$ (2^{1}x^{0} y^{2})^{-3} \cdot 2 y x^{3} $$ and then simplify $$ (x^{-3})^{4} x^{4} $$.\n\n2. **Recall the rules:**\n- Any numbe

1. **State the problem:** We are given the equation $s = k - m^2$ and need to make $m$ the subject. 2. **Isolate the term with $m$:** Add $m^2$ to both sides and subtract $s$ from

1. **State the problem:** Solve the equation $$3x^4 - x = x^3 + 3$$ by graphing or algebraic manipulation. 2. **Rewrite the equation:** Move all terms to one side to set the equati

1. Stwierdźmy problem: obliczyć wartość wyrażenia $$\sqrt{75} + \sqrt{12} - \frac{12}{\sqrt{3}} + \frac{3\sqrt{15}}{\sqrt{5}}$$. 2. Przypomnijmy, że pierwiastek z iloczynu to ilocz

1. Stwierdzenie problemu: Oblicz wartość wyrażenia $$\sqrt{75} - \sqrt{12} + \frac{1}{\sqrt{3}} + 3\sqrt{\frac{15}{5}}$$. 2. Rozkład pierwiastków na czynniki pierwsze i uproszczeni

1. El problema es factorizar y descomponer en dos factores la expresión $b + b^2$. 2. Primero, observamos que ambos términos tienen un factor común: $b$.

1. The problem is to understand the function $k(x) = 5 \cdot 3^x$ for $x \geq 0$ and describe its behavior. 2. The function is an exponential function of the form $k(x) = a \cdot b

1. The problem asks for the function whose graph is the same as $y=\frac{1}{x}$ shifted right by 5 units and up by 2 units. 2. The original function is $y=\frac{1}{x}$, a hyperbola

1. The problem is to analyze the function $$f(x) = \frac{5x}{4 - x^2}$$ and understand its behavior. 2. This is a rational function where the numerator is $5x$ and the denominator

1. **State the problem:** Solve for $x$ in the equation $$2.17 = -66.67\left(e^{-0.0003x} - e^{-0.0002x}\right) + 1.17 e^{-0.0002x}.$$\n\n2. **Rewrite the equation:** Distribute an

1. Gaaffii: Gatiin $x$ kan $x < x$ taasisu ni jiraa? Sababa kee ibsi. 2. Hiikkaa: $x < x$ jechuun $x$ tokko gara $x$ isa kaanii xiqqaa ta'uu isaa agarsiisa.

Let's factor the expression $x^2 - 5x - 6$ step by step! 1. Imagine you have $x^2$, which is $x$ times $x$:

1. **State the problem:** We need to determine which of the given linear equations have no solutions. 2. **Recall the rule:** A linear equation has no solution if, after simplifyin

1. The problem is to evaluate the expression $5(9^2 - 7^2) - 35$ and determine which given statements about it are correct. 2. Recall the order of operations: first evaluate expone

1. **State the problem:** Simplify the expression $$\left(-\frac{2}{3} + \frac{1}{6}\right)^2 \div \frac{5}{4}$$ and express the answer as a simplified fraction. 2. **Add the fract

1. **State the problem:** We are given the line $p$ with equation $6x + 3y = 15$. We need to find the equation of a line parallel to $p$ that passes through the point $(-1, 1)$.

1. **State the problem:** Find the equation of the line passing through the points $(2,8)$ and $(5,-6)$.\n\n2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$

1. The problem involves understanding expressions with $x$, $p(x)$, $x^2$, and $x^2 \times p(x)$.\n\n2. Here, $x$ is a variable, and $p(x)$ typically denotes a function of $x$. For

1. **State the problem:** Find the intersection point of the first pair of lines: $$y = -4x + 1$$ and $$y = 4x + 2$$. 2. **Set the equations equal to find the intersection:** Since