🧮 algebra

1. **State the problem:** Simplify the expression $$2(3a + 4b) - (8a - b)$$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside

1. **Problem:** Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. 2. **Recall:** Lines t

1. State the problem: Prove that $$\left\lfloor\frac{x+2}{2}\right\rfloor-2\left\lfloor\frac{x+2}{4}\right\rfloor = 1-\left(\left\lfloor\frac{x}{2}\right\rfloor-2\left\lfloor\frac{

1. The problem is to find 5% of 16. 2. The formula to find a percentage of a number is:

1. **State the problem:** Nadia earns a weekly allowance of $400 plus 5% commission on her sales. We want to find:

1. **Problem:** Simplify the expression $1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \frac{1}{16} - \frac{1}{32}$. 2. **Formula and rules:** This is a finite geometric series wit

1. **State the problem:** Simplify the expression $$\frac{18 - x}{3x - 1} \times \frac{7 - 21x}{2x - 36}$$. 2. **Rewrite each part by factoring where possible:**

1. Il problema chiede se $x = -2$ è soluzione di $x^2 - 4 = 0$ o di $x^2 + 4 = 0$. Verifichiamo sostituendo $x = -2$ in entrambe le equazioni. 2. Per $x^2 - 4 = 0$, sostituiamo:

1. The problem is to identify the slope and y-intercept of the line given by the equation $y = -2x + 11$. 2. The equation is in slope-intercept form $y = mx + b$, where $m$ is the

1. Let's clarify the problem: You asked "where did you get the 3?" which suggests you want to understand the origin of the number 3 in a previous math step. 2. Typically, the numbe

1. The problem asks to express the number 8 in the form $2^x$. 2. Recall the definition: $2^x$ means 2 raised to the power of $x$.

1. The problem asks to find the slope and y-intercept of the line given by the equation $$y = -x + 7$$. 2. Recall the slope-intercept form of a line: $$y = mx + b$$, where $$m$$ is

1. The problem is to apply the zero product property to solve an equation of the form $ab=0$. 2. The zero product property states that if the product of two factors is zero, then a

1. **State the problem:** Solve the quadratic equation $288t^2 - 392 = 0$ for $t$. 2. **Formula and rules:** To solve for $t$, isolate $t^2$ and then take the square root of both s

1. The problem is to find the least common multiple (LCM) of 2 and 3. 2. The LCM of two numbers is the smallest positive integer that is divisible by both numbers.

1. **State the problem:** We need to analyze the function $$y = x^{\frac{3}{2}} + x - 1.3$$ and understand its behavior. 2. **Recall the function form:** The function is a sum of a

1. The problem appears to involve simplifying or evaluating the expression $1xx\sqrt{xx} + xx - 1.3$. However, the expression is unclear due to the use of "xx" and symbols. Assumin

1. **State the problem:** Find the inverse function $f^{-1}(x)$ of the function $$f(x) = \frac{-6x + 11}{8x - 5}.$$\n\n2. **Recall the method to find an inverse:** To find $f^{-1}(

1. **Problem:** Decide if the graphs of the pair of lines are parallel, perpendicular, or neither for (a) $y = -2x + 1$ and $y = 9 - 2x$. 2. **Recall:**

1. Das Problem lautet: Löse die Gleichung. 2. Da keine spezifische Gleichung gegeben ist, kann ich nur allgemeine Schritte zum Lösen von Gleichungen erklären.

1. **State the problem:** Simplify the expression $8x^{1/2}$. 2. **Recall the rule:** The expression $x^{1/2}$ means the square root of $x$, so $x^{1/2} = \sqrt{x}$.