🧮 algebra

1. **State the problem:** Solve for $y$ in the equation $$125y^3 = 8$$. 2. **Formula and rules:** To solve for $y$, isolate $y^3$ by dividing both sides by 125, then take the cube

1. The problem is to simplify the expression $\frac{1}{2}\ln((x-4)^2) + 16$. 2. Recall the logarithm power rule: $\ln(a^b) = b\ln(a)$.

1. The problem asks to identify expressions that represent the verbal phrase: "The difference of 12 and 20% of a number x". 2. The phrase "difference of 12 and 20% of a number x" m

1. The problem asks for the expression representing the difference of 12 and 20% of a number $x$. 2. "Difference of 12 and 20% of $x$" means subtracting 20% of $x$ from 12.

1. **State the problem:** Factor the expression $$\frac{8}{3} - \frac{2}{3}x$$ using the greatest common factor (GCF). 2. **Identify the GCF:** Both terms $$\frac{8}{3}$$ and $$\fr

1. **State the problem:** Subtract the expression $(3.5x - 10)$ from $(4.5x - 5)$, i.e., compute $(4.5x - 5) - (3.5x - 10)$. 2. **Recall the subtraction rule:** When subtracting ex

1. **State the problem:** We need to find which expressions are equivalent to $$- \frac{2}{5}(15 - 20d)$$. 2. **Use the distributive property:** Multiply $$- \frac{2}{5}$$ by each

1. **Solving quadratic equations by completing the square:** The method involves rewriting the quadratic equation in the form $$a(x-h)^2 + k = 0$$ where $h$ and $k$ are constants.

1. **State the problem:** Simplify and evaluate the expression $$\left(\frac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{\sqrt{3}+\sqrt{2}-\sqrt{5}} + \frac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{\sqrt{3}+\s

1. **Stating the problem:** We are given several expressions and equations involving arithmetic operations, fractions, and a function with a square root in the denominator. We need

1. **State the problem:** We need to find Camilla's unit rate of speed, which is the distance she drives per hour, using the graph that shows time in hours and distance in miles. 2

1. **State the problem:** We need to find the rate at which Sebastian and Gabriel complete math problems per minute and then compare these rates to determine who works faster. 2. *

1. We are asked to perform synthetic division on the given polynomials by the specified binomials. 2. Synthetic division is a shortcut method for dividing a polynomial by a binomia

1. The problem is to express $\tan \alpha$ in terms of slopes $m$ and $m_1$ where $m_1 = \frac{dy}{dx}$. 2. The formula for the tangent of the angle between two lines with slopes $

1. The problem is to substitute values directly into an expression involving $m_1$ without solving for $m_1$. 2. When substituting directly, you replace the variable $m_1$ with the

1. Let's start by understanding what a word problem is: it is a math problem presented in a story or real-life context. 2. The first step is to carefully read the problem and ident

1. **State the problem:** Solve the equation $$\frac{1}{n^2} + \frac{1}{n} = \frac{1}{2n^2}$$ for $n$. 2. **Rewrite the equation:** To solve for $n$, first get a common denominator

1. **Stating the problem:** We need to find the missing denominators in the equivalent fractions: a) $\frac{8}{24} = \frac{21}{\_}$

1. **Convert mixed numbers to improper fractions and improper fractions to mixed numbers:** - For mixed numbers $a \frac{b}{c}$, the improper fraction is $\frac{a \times c + b}{c}$

1. **State the problem:** Convert the given fractions to decimals and decimals to fractions in lowest terms. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $[(3 - 4^2) \times (3^2 - 7)] - 6$. 2. **Recall the order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and