🧮 algebra

1. Planteamos el problema: Ryan tiene 360 metros de valla para construir un jardín rectangular. La longitud lateral del jardín es $x$ metros y queremos encontrar el área $A(x)$ en

1. **State the problem:** A nurse recorded a patient's temperature at different times over two days. We need to answer questions about the frequency of measurements, temperature di

1. The problem asks to convert 5.6% into a decimal. 2. Percent means per hundred, so 5.6% means 5.6 out of 100.

1. The problem is to evaluate the expression $33 \times 33 + 33 - 33$ and then divide the result by 0. 2. The expression is $33 \times 33 + 33 - 33$.

1. **State the problem:** Calculate the value of the expression: $$ (9.48 \times 3.75) + 0.18169 \times 1.364425 + (2.0139 \times 10^{-5}) \times 678357625 + (8.1985 \times 10^{-8}

1. Planteamos el problema: Dadas dos funciones $f$ y $g$, debemos hallar las composiciones $f(g(x))$ y $g(f(x))$ para cada par, y luego determinar si son funciones inversas. 2. Rec

1. Let's restate the problem: We want to solve the equation or expression given previously, but using a different method. 2. Without the original problem explicitly stated here, I'

1. **State the problem:** Solve the equation $$\frac{x + 1000}{2} = 1000$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation.

1. **State the problem:** We are given two functions $g(x) = 4x$ and $h(x) = 3x + 6$. We need to find the expressions for $(g + h)(x)$, $(g - h)(x)$, and the value of $(g \cdot h)(

1. The original problem was solved using a specific method, but there are often multiple ways to approach algebraic problems. 2. For example, if the problem involved solving an equ

1. **Problem 5:** Solve the equation $$\frac{x}{1000} + 544 = -544$$. 2. **Step 1:** Isolate the term with $x$ by subtracting 544 from both sides:

1. **Solve the equation** $10x + 6 = 36$. 2. **Subtract 6 from both sides** to isolate the term with $x$:

1. **Problem 1:** Solve the equation $$\frac{x+1000}{2} = 0$$. 2. To solve for $x$, multiply both sides of the equation by 2 to eliminate the denominator:

1. **State the problem:** Solve the equation $$25^x - 2 \cdot 5^x = 3$$ for $x$. 2. **Rewrite the equation using properties of exponents:** Note that $25 = 5^2$, so $$25^x = (5^2)^

1. **Rounding 50 to three decimal places** The problem asks to round the number 50 to three decimal places.

1. **Problem 45: Solve the equation** $\frac{x}{9} = 4$. 2. The formula used here is to isolate $x$ by multiplying both sides of the equation by 9:

1. **Problem 43: Divide $\frac{30}{60}$ by $\frac{1}{5}$.** 2. The formula for division of fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$

1. **Problem Statement:** You have a current CGPA of 4.0 and you scored a GPA of 4.5 in the next semester. We want to find your new CGPA. 2. **Formula Used:** The CGPA is the cumul

1. **State the problem:** We are given the quadratic function $$y = 4x^2 - 4$$ and asked to analyze it. 2. **Formula and rules:** This is a quadratic function in the form $$y = ax^

1. **Problem statement:** Find the remainder when $f(x) = x^3 - 2x^2 - 5x + 6$ is divided by $x - 1$ and then factorize $f(x)$. 2. **Remainder theorem:** When a polynomial $f(x)$ i

1. **State the problem:** Solve the equation by factoring: $$x^2 - 5x + 6 = 0$$ 2. **Recall the factoring formula:** For a quadratic equation $$ax^2 + bx + c = 0$$, we look for two