🧮 algebra

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 $x^{1/2} = \sqrt{x}$.

1. **State the problem:** Simplify the expression $x^2 \times x^2$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same base, ad

1. The problem involves simplifying algebraic expressions and understanding the floor plan dimensions with tile prices. 2. First, simplify the fraction $$\frac{14x^2 - 63x}{7x}$$.

1. **Stating the problem:** We are given algebraic expressions and a floor plan with dimensions involving $x$. We need to simplify the algebraic fractions and understand the tile d

1. **State the problem:** Expand the expression $ (x+9)(x+8) $. 2. **Formula used:** Use the distributive property (FOIL method) for binomials: $$ (a+b)(c+d) = ac + ad + bc + bd $$

1. **State the problem:** Expand the expression $ (x-3)(x+5) $. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **Problem:** A rectangle has area 6 and perimeter 10. What is the value of its largest side? 2. **Formulas and rules:**

1. **State the problem:** Evaluate the expression $$\sqrt[3]{-8} \times \left(12 - \left(5^2 + \sqrt{9}\right)\right) \div 8$$. 2. **Recall important rules:**

1. The problem asks to factorise the given expressions. 2. Factorisation means expressing an expression as a product of its factors.

1. **State the problem:** Simplify the expression $b \cdot ab^3 \times (-2a^5b)$ where $b = \frac{21m^2n}{7m}$. 2. **Substitute the value of $b$:** Replace $b$ in the expression wi

1. **State the problem:** Calculate the value of $$\sqrt[3]{-8} \times \left(12 - \left(5^2 + \sqrt{9}\right)\right) \div 8$$. 2. **Evaluate the cube root:** $$\sqrt[3]{-8} = -2$$