🧮 algebra

1. **Problem Statement:** We have two functions: - $f : \mathbb{R} \to [0,1]$ defined by $f(x) = \sin x$

1. **State the problem:** Samar has a rectangular garden with length $7 \frac{1}{2}$ meters and width $2.5$ meters. Samar already has $12.5$ meters of fencing and wants to know how

1. **State the problem:** Evaluate the expression $$-\frac{5}{7} \times \left(-\frac{14}{15}\right) - 0.5 \times 1 \frac{3}{5}$$ and select the correct option. 2. **Recall the rule

1. **State the problem:** We need to evaluate the expression $b^2 - ac$ given the values $a = -2 \times \frac{1}{2}$, $b = -0.8$, and $c = \frac{1}{5}$.\n\n2. **Calculate $a$:** Mu

1. **State the problem:** Evaluate the expression $$0.4 + \frac{1}{2} \times \left(-\frac{3}{5}\right)$$. 2. **Recall the order of operations:** Multiplication comes before additio

1. **State the problem:** Calculate the value of the expression $$a b - \frac{c}{b}$$ given $$a = -2 \frac{1}{4}$$, $$b = -0.8$$, and $$c = \frac{1}{5}$$. 2. **Convert mixed number

1. The problem is to evaluate the division of two fractions: $\frac{4}{5} \div \frac{2}{3}$ and write the answer as a mixed number. 2. Recall the rule for dividing fractions: divid

1. **State the problem:** We need to find how many times deeper Karim is compared to Rami based on their depths. 2. **Given data:**

1. The problem is to find the quotient of $2 \frac{1}{5} \div \frac{1}{5}$ and express the answer in simplest form. 2. First, convert the mixed number $2 \frac{1}{5}$ to an imprope

1. The problem is to find the quotient of two fractions: $$\left(-\frac{3}{11}\right) \div \frac{2}{7}$$. 2. The formula for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} =

1. **State the problem:** We need to find the quotient of $-2 \frac{3}{5} \div \frac{2}{5}$ and write the answer as a mixed number in simplest form. 2. **Convert the mixed number t

1. **State the problem:** We need to find the value of $\frac{a}{b}$ where $a = -3 \frac{2}{5}$ and $b = -1.7$. 2. **Convert mixed number to improper fraction:**

1. **State the problem:** We need to find the quotient of $1 \frac{3}{4}$ divided by $\frac{2}{3}$ and write the answer as a mixed number in simplest form. 2. **Convert mixed numbe

1. The problem is to find the quotient of $2 \frac{1}{3} \div \frac{4}{9}$ and express the answer in simplest form. 2. First, convert the mixed number $2 \frac{1}{3}$ to an imprope

1. **State the problem:** We are given two functions $u(x) = 5x + 7$ and $v(x) = 5x + 7$. We need to find the composite functions $(u \circ v)(x)$ and $(v \circ u)(x)$. 2. **Recall

1. **State the problem:** Simplify the expression $$\frac{x^2 + 4x + 20x}{x + 8}$$. 2. **Combine like terms in the numerator:** $$4x + 20x = 24x$$, so the expression becomes $$\fra

1. **State the problem:** Solve the exponential equation $$e^{2x} - 5e^x + 4 = 0$$ for $x$. 2. **Rewrite the equation:** Let $y = e^x$. Then $e^{2x} = (e^x)^2 = y^2$. Substitute to

1. **State the problem:** Find the expression for $x$ to the third power plus 2 times $x$ squared minus 26 times $x$ minus 55. 2. **Write the polynomial:** The expression is $$x^3

1. Problema: Analizar y graficar las funciones dadas: a) $f(x) = \log(x + 3)$

1. **State the problem:** Rewrite the expression $$\ln \left( \frac{x^{16} \sqrt{x - 1}}{3x - 12} \right)$$ using the laws of logarithms so that there are no logarithms of products

1. **State the problem:** Simplify the expression $$\frac{125x^3 - 27}{5x - 3}$$. 2. **Recognize the form:** The numerator is a difference of cubes since $$125x^3 = (5x)^3$$ and $$