🧮 algebra

1. **State the problem:** We need to find how many milligrams of vitamin C are in 1 serving of orange juice and cranberry juice. 2. **Formula:** To find the amount of vitamin C per

1. **State the problem:** Simplify the expression $$\left(-\frac{3}{7} + \frac{1}{3}\right) - \left[ 2 - \left(3 - \frac{1}{7}\right) + \left(1 - \frac{7}{3}\right) \right].$$ 2. *

1. **State the problem:** Darin mows 90 lawns in 45 hours. We want to find how many hours it will take to mow 12 lawns at the same rate. 2. **Identify the formula:** Since the lawn

1. **State the problem:** Howard has golf lessons for Driver every 5 days, Putter every 6 days, and Sand Bunker every 8 days. He had all three lessons on the same day. We need to f

1. **State the problem:** Solve the equation $2x + 5 = 9$ for $x$. 2. **Write the formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 5 fr

1. **State the problem:** Calculate the percentage of the pizza that is cheese. 2. **Formula:** Percentage of a part = $\frac{\text{part}}{\text{whole}} \times 100$%

1. The problem asks which of the three curves (green, red, blue) is NOT a function. 2. Recall the definition of a function: For each input $x$, there must be exactly one output $y$

1. **State the problem:** Simplify and solve the expression $3x(3x+3)$. 2. **Use the distributive property:** Multiply $3x$ by each term inside the parentheses:

1. **State the problem:** Simplify or analyze the expression $$(0.4\log(x) + 0.88)^2$$ where $\log$ is the logarithm base 10. 2. **Recall the formula:** The square of a binomial $(

1. We start with the first problem: find for which values of $x$ the graph of $f(x)$ lies below the graph of $g(x)$. 2. For (a), the functions are $f(x) = x^2$ and $g(x) = -4x + 5$

1. **State the problem:** Express the rational function $$\frac{x^2 + 4}{x^3 + 2x}$$ in partial fractions. 2. **Factor the denominator:**

1. **State the problem:** Solve the system of equations: $$x + 2y = 1$$

1. **State the problem:** We want to express the rational function $$\frac{x - 2}{x^2 - 2x + 1}$$ in partial fractions.

1. Planteamos el problema: Encontrar la función inversa de $$f(x) = \frac{2x}{x-1}$$. 2. Para hallar la función inversa, intercambiamos $$x$$ y $$y$$ en la ecuación y despejamos $$

1. Das Problem lautet: Faktorisiere die Gleichung $$0=5x^4-198x^2+800$$. 2. Wir erkennen, dass es sich um ein Polynom vierten Grades handelt, das nur gerade Potenzen von $x$ enthäl

1. **State the problem:** We have two functions:

1. The problem is to solve the equation given by the user. However, no specific equation was provided, so I will demonstrate solving a simple algebraic equation as an example: $2x

1. Das Problem lautet: Finde die Nullstellen der Funktion $5x^4 - 198x^2 + 800 = 0$ durch Faktorisieren. 2. Wir verwenden die Substitution $y = x^2$, damit die Gleichung zu einer q

1. The problem is to find the value of $c$ given some context where the answer key states $c=20$. 2. Since the user only mentioned the answer key's value for $c$, we need to verify

1. **State the problem:** We have a rectangle QRST with sides QR = $x$, QT = $3x - 10$, RS = $2y$, and TS = $4y$. Since QRST is a rectangle, opposite sides are equal in length. 2.

1. **State the problem:** Multiply the fraction $\frac{4}{6}$ by the mixed number $3 \frac{3}{5}$. 2. **Convert the mixed number to an improper fraction:**