🧮 algebra

1. **State the problem:** We need to find how many miles are in 48 kilometers using the formula: $$\text{distance in miles} = \frac{5}{8} \times \text{distance in km}$$

1. **State the problem:** We need to find the output when the input fraction $\frac{6}{7}$ is multiplied by 35. 2. **Formula used:** The operation is multiplication of a fraction b

1. The problem is to calculate $3 \div \frac{17}{5}$ and express the answer in simplest form. 2. Recall the rule for dividing by a fraction: dividing by $\frac{a}{b}$ is the same a

1. **State the problem:** Simplify the expression $$(5x + \sqrt{5})^2 (5x - \sqrt{5})^2$$. 2. **Recall the formula:** The expression is a product of two squares. We can rewrite it

1. **Problem Statement:** We are given the export function of Avocados from Indonesia as $$E(P) = P - 10000$$ where $$P \geq 10000$$ and $$P$$ represents production in thousands. 2

1. **Problem Statement:** We want to find the volume $V(x)$ of an open-top box formed by cutting out squares of side length $x$ from each corner of a $12 \times 12$ inch square she

1. **State the problem:** Simplify the expression $$(5x + \sqrt{5})^2 (5x - \sqrt{5})^2$$. 2. **Recall the formula:** The expression is a product of squares of binomials. We can us

1. The problem is to simplify the expression or equation given by the user. 2. Simplification involves combining like terms, reducing fractions, and applying algebraic rules.

1. **State the problem:** Simplify the expression $$(5x + \sqrt{5})^2 (5x - \sqrt{5})^2$$. 2. **Recall the formula:** The expression is a product of two squares. We can use the ide

1. **State the problem:** Simplify the expression $$(4x^4y^8 + 49)(2x^2y^4 + 7)(2x^2y^4 - 7).$$ 2. **Identify the formula and rules:** Notice that the last two factors are of the f

1. **Problem Statement:** Show that the equation $$x^3 + 3x + 1 = 0$$ has exactly one real solution. 2. **Define the function:** Let $$f(x) = x^3 + 3x + 1$$.

1. **State the problem:** Evaluate the expression $$-\frac{2}{3}xyz$$ given $$x = -8.4$$, $$y = 0.25$$, and $$z = 3 \frac{4}{5}$$. Write the answer as a mixed number in simplest fo

1. **State the problem:** We need to find the value of $C$ in the equation $C + C + 88 = 180$. 2. **Write the equation:** The equation can be simplified by combining like terms: $$

1. **State the problem:** Evaluate $\frac{1}{2} yz$ given $y = \frac{3}{5}$ and $z = -1 \frac{7}{8}$. Write the answer as a fraction in simplest form. 2. **Convert mixed number to

1. **Simplify** $\frac{2}{a+1} + \frac{3}{2a+2}$. - Note $2a+2 = 2(a+1)$.

1. The problem appears to involve evaluating or simplifying the expression: $$\frac{5000 \times e^{4.5 \times 20}}{4.5 \times 1.5}$$. 2. First, recognize that $e$ is the base of th

1. **State the problem:** We need to evaluate $\frac{a}{b}$ where $a = -\frac{1}{4}$ and $b = 0.02$. Then, write the answer as a mixed number in simplest form. 2. **Write the expre

1. **Problem Statement:** Identify the domain and range of the given graph and determine if it represents a function and if it is one-to-one.

1. **State the problem:** Evaluate $\frac{1}{4}xy$ given $x = -\frac{2}{3}$ and $y = \frac{3}{5}$. Write the answer as a fraction in simplest form. 2. **Formula used:** The express

1. **State the problem:** We need to find the value of $8 \frac{1}{3} \div \left(-\frac{5}{9}\right)$ and write the answer in simplest form. 2. **Convert mixed number to improper f

1. **State the problem:** We need to find the value of $-3 \frac{4}{9} \div -2 \frac{1}{3}$ and express the answer as a mixed number in simplest form. 2. **Convert mixed numbers to