🧮 algebra

1. **State the problem:** Mr. Wells has two copiers. The first copier makes 1,000 copies in 30 minutes, and the second copier makes 1,000 copies in 20 minutes. We want to find how

1. **Problem:** Clayton can sweep the gym floor in 24 minutes, and Morgan can do it in 40 minutes. How long will it take if they work together? 2. **Formula:** When two people work

1. **State the problem:** Simplify or factor the quadratic expression $x^2 + 4x + 4$. 2. **Recall the formula:** A quadratic expression $ax^2 + bx + c$ can be factored using the fo

1. **State the problem:** An element with an initial mass of 640 grams decays by 27.5% per minute. We want to find how much of the element remains after 5 minutes, rounded to the n

1. **State the problem:** We need to find the value of a car after 11 years if it depreciates at 9.5% per year from an initial value of 20300. 2. **Formula used:** The value after

1. Let's clarify the question: "Why do we ignore the 2 in the division?" This usually happens when simplifying fractions or expressions where a factor cancels out. 2. Consider an e

1. **Stating the problem:** We are given the equation $35,45 = 26,497 + A_2 \times 24,72\%$ and need to solve for $A_2$. 2. **Rewrite the equation:** Convert the percentage to deci

1. **State the problem:** Solve the equation $$\sqrt{4x+36}+2=10$$ for $x$. 2. **Isolate the square root term:** Subtract 2 from both sides:

1. **State the problem:** Solve the equation $$\sqrt{5x-34} - 17 = -16$$. 2. **Isolate the square root term:** Add 17 to both sides to isolate the square root.

1. **State the problem:** We are given the equation $-4(2n + 8) = -12$ and need to find the value of $n$. 2. **Write the equation:**

1. El problema nos da el foco $F = (2, -\frac{111}{16})$ y la directriz $y = -\frac{113}{16}$ de una parábola. 2. La fórmula estándar para una parábola con eje vertical es:

1. **State the problem:** Solve the exponential equations in Set 2 by expressing both sides with common bases and then equate the exponents. 2. **Recall the rule:** If $a^m = a^n$

1. **Stating the problem:** Solve the inequality $$\frac{1}{2}\left(x-\frac{2}{3}\right)^2 + x\left(x-\frac{2}{3}\right)\left(x+\frac{2}{3}\right) - x^3 \ge \frac{x}{2}\left(x-\fra

1. The problem asks to find the value of $f(7) + 9 \cdot g(-1)$.\n\n2. We need to find the values of $f(7)$ and $g(-1)$ from the given graphs.\n\n3. From the solid blue graph (whic

1. **State the problem:** We are given that the measure of an angle is five times the measure of its complementary angle. We need to find the measures of both angles. 2. **Recall d

1. **State the problem:** We are given that the measure of an angle is forty-four times the measure of its supplementary angle. We need to find the measure of each angle. 2. **Reca

1. **State the problem:** Solve the inequality $4 - 2x \leq 14$ for $x$. 2. **Write the inequality:**

1. **State the problem:** Solve the inequality $$2(x - 1) + 4x \leq 10$$. 2. **Expand and simplify:** Apply the distributive property to expand $$2(x - 1)$$:

1. Il problema è risolvere l'equazione fratta: $$\frac{x - 1}{x} = \frac{1}{x+1} + \frac{2 + x}{x^2 + x}$$

1. **Problem:** Divide the polynomial $x^3 - 7x - 17$ by $x - 8$. 2. **Formula and Rules:** Polynomial division is similar to long division with numbers. We divide the highest degr

1. **Stating the problem:** We are given a table showing the amount of a drug in a person's system over time and asked to determine if the relationship is linear or exponential, an