🧮 algebra

1. Das Problem lautet: Berechne den Ausdruck $\frac{7n}{\epsilon} + \frac{1}{5}$.\n\n2. Die Formel für die Addition von zwei Brüchen mit unterschiedlichen Nennern ist: $$\frac{a}{b

1. The problem is to simplify an expression and write it using only positive exponents. 2. The general rule is that any negative exponent $a^{-n}$ can be rewritten as $\frac{1}{a^n

1. **State the problem:** Simplify the algebraic expressions and write the answers with positive exponents only. 2. **Expression 1:** $4q^2 \times 4p^4 q^{-3}$

1. The problem involves analyzing the polynomial function $$f(x) = (x - 3)(x + \sqrt{5})(x - \sqrt{5})$$ and understanding its properties. 2. First, expand the function by multiply

1. **State the problem:** Simplify the expression $ (6b^2 - 4b^4) - (7b^2 - b^4) $. 2. **Rewrite the expression by distributing the minus sign:**

1. **State the problem:** Simplify the expression $$(1 - 4x^3) - (5 - 3x^3)$$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to each

1. **State the problem:** Find the points of intersection of the two parabolas given by the equations: $$y = x^2 - 2x + 2$$

1. **State the problem:** We are given that Jiahao and Raju have stamps in the ratio 3 : 1.

1. **Stating the problem:** Sam's savings and Ali's savings relate as follows: $\frac{3}{5}$ of Sam's savings equals $\frac{1}{4}$ of Ali's savings.

1. **State the problem:** Solve for $x$ in the equation $4x + 1 - 2x + 2 = 0$. 2. **Combine like terms:** Group the $x$ terms and the constants.

1. **State the problem:** Find the equation of the line passing through the points $(-8,8)$ and $(8,-4)$ in slope-intercept form $y=mx+b$. 2. **Formula for slope:** The slope $m$ i

1. **State the problem:** We need to find the equation of a line in slope-intercept form, which is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 2. **Identify g

1. The problem is to write the number 862 in scientific notation. 2. Scientific notation expresses a number as $a \times 10^n$ where $1 \leq |a| < 10$ and $n$ is an integer.

1. The problem asks to find the equation of the line in the form $y=mx$ that models the relationship between the number of weeks ($x$) and the number of books ($y$) based on the gi

1. **State the problem:** Solve for $x$ in the equation $$\frac{0.853}{0.972} = \frac{x}{0.0750} \times \frac{0.642}{0.972} + \frac{x}{0.188}.$$\n\n2. **Rewrite the equation clearl

1. **State the problem:** Solve for $x$ in the equation $$\frac{0.853}{0.972} = 0.0750 \times \frac{0.642}{0.972} + \frac{x}{0.188}.$$\n\n2. **Rewrite the equation:** \n$$\frac{0.8

1. The problem asks to find an equation to determine how much taller Noah is than Elena, given Noah's height is $64 \frac{3}{4}$ inches. 2. Let $d$ represent Elena's height in inch

1. The problem is to find an equation that represents how much taller Noah is than Elena. 2. Let $d$ represent the difference in height between Noah and Elena.

1. The problem asks to find the value of $x$ squared when $x=10$. 2. The formula for squaring a number is $x^2 = x \times x$.

1. **State the problem:** We need to find the values of the expressions when $x=6$ and match them to the given options. 2. **Expressions and evaluation:**

1. The question asks why the variable $C$ is different from $b$. 2. In algebra and mathematics, variables like $C$ and $b$ represent different quantities or constants.