🧮 algebra

1. The problem is to understand the meaning and usage of the variable $d$ in a mathematical context. 2. In algebra and geometry, $d$ often represents a distance, difference, or a v

1. **Stating the problem:** The distance going is 5 km with a speed of 40 km/h. The return time is 10 minutes less than the going time.

1. **State the problem:** Calculate the value of $9^{900}$. 2. **Recall the formula:** For any number $a$ and exponent $n$, $a^n$ means multiplying $a$ by itself $n$ times.

1. The problem is to solve the equation or expression given by the user. However, no specific equation or expression was provided. 2. Since no equation is given, we cannot apply an

1. **State the problem:** Solve for all real values of $x$ in the equation $$8^x + 2^x = 130.$$\n\n2. **Rewrite the bases:** Note that $8 = 2^3$, so we can write $$8^x = (2^3)^x =

1. **State the problem:** We are given the polynomial $$40\sqrt{5} x^{3} - 3\sqrt{3} y^{3}$$ and it is factored as $$(2\sqrt{5} x - \sqrt{3} y)(Ax^{2} + Bxy + Cy^{2}).$$ We need to

1. **State the problem:** We are given the polynomial $$405\sqrt{x^3} - 33\sqrt{y^3}$$ and it is factored as $$(25\sqrt{x} - 3\sqrt{y})(Ax^2 + Bxy + Cy^2).$$

1. **State the problem:** Solve the linear equation $3x + 6 = 2x - 7$ for $x$. 2. **Formula and rules:** To solve for $x$, we use the properties of equality: we can add, subtract,

1. **State the problem:** Solve the linear equation $3x + y = 33$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, subtract $3x$ from both sides of the equation.

1. The problem is to find the range of numbers from 0 to 100. 2. This is a simple interval notation problem where the set includes all numbers starting at 0 and ending at 100.

1. **Planteamiento del problema:** Tenemos una parábola con vértice en $(-1,-2)$ y que pasa por varios puntos dados. Queremos encontrar la ecuación de la forma $$y = ax^2 + bx + c$

1. **State the problem:** We need to find another way to express the expression $$12(t - 0.25)$$ where $t$ is the time in hours. 2. **Use the distributive property:** The distribut

1. **State the problem:** Simplify the expression $\sqrt{8^6}$. 2. **Recall the formula:** The square root of a number $x$ is $\sqrt{x} = x^{\frac{1}{2}}$.

1. The problem asks: Which linear equation is written in standard form? 2. The standard form of a linear equation is given by the formula:

1. The problem asks to identify the graph of the slope-intercept equation $$y = -\frac{2}{3}x - 1$$. 2. The slope-intercept form of a line is $$y = mx + b$$ where $$m$$ is the slop

1. **State the problem:** We need to find the equation of the line passing through the points (-5, -1), (0, -3), and (5, -5) in slope-intercept form $y = mx + b$. 2. **Find the slo

1. Das Problem lautet: Löse die linke Seite der Aufgabe, also Nummer 1. 2. Da keine konkrete Gleichung gegeben ist, nehmen wir an, es handelt sich um eine algebraische Gleichung, z

1. **State the problem:** Determine which statements about the function $f(x) = -2\sin(x) - 3$ are true. 2. **Recall the general form and properties:** For a function $f(x) = A\sin

1. **State the problem:** We need to determine which statements are true for the function $$f(x) = -2\sin(x) - 3$$. 2. **Recall the general form and properties:** The general sine

1. **State the problem:** We have a geometric sequence with the first term $a_1 = -2$ and common ratio $r = -\frac{1}{4}$. We need to find the next three terms $a_2$, $a_3$, and $a

1. **State the problem:** Simplify the expression $8x + 9 - 5x$. 2. **Recall the rule:** Combine like terms, which means adding or subtracting coefficients of the same variable.