🧮 algebra

1. The problem asks: What is a constant? 2. A constant is a value that does not change. In mathematics, it is a fixed number.

1. **State the problem:** Solve for the constant $x$ in the equation $$18 = 3x + 12$$. 2. **Formula and rules:** To isolate $x$, we use basic algebraic operations: subtraction and

1. The user requests a slope graph for "both," but no specific functions or data were provided in the previous message. 2. To create a slope graph, we need explicit functions or da

1. **State the problem:** Find the slope of the line passing through the points (4,1) and (-3,2). 2. **Formula for slope:** The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y

1. The problem involves understanding and analyzing the given equations: - $y = 1 - x$

1. The problem asks to complete the table so it shows a relation that is not a function. 2. A function is a relation where each input $x$ has exactly one output $y$.

1. **State the problem:** We need to find two whole numbers whose squares are closest to 7.9. 2. **Recall the concept:** The square of a whole number $n$ is $n^2$. We want to find

1. **State the problem:** Subtract the fractions $\frac{5}{7}$ and $\frac{2}{7}$. 2. **Formula and rules:** When subtracting fractions with the same denominator, subtract the numer

1. **State the problem:** Add the fractions $\frac{3}{9}$ and $\frac{5}{9}$. 2. **Formula used:** When adding fractions with the same denominator, add the numerators and keep the d

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