🧮 algebra

1. The problem is to solve the equation or expression given before, but now we will explain it in simple words. 2. First, we use the formula or rule that helps us solve this kind o

1. **Stating the problem:** We want to create a fairer speeding fine system combining elements from New York and Massachusetts systems.

1. **Problem Statement:** We want to compare the New York and Massachusetts speeding fine systems based on miles per hour (mph) over the speed limit.

1. **State the problem:** We need to find which values of $x$ from the given list make the function $f(x) = x^2 - 5x - 36$ equal to zero. 2. **Formula and rule:** A zero of the fun

1. **State the problem:** Simplify the expression $10c + c^2 - 3c^3$. 2. **Identify terms:** The expression contains three terms: $10c$, $c^2$, and $-3c^3$.

1. **State the problem:** Simplify the expression $$\frac{10c + c^2 - 3c^3}{5c^2 - 6c - 8}$$. 2. **Rewrite the expression:** Arrange terms in descending powers of $c$ for clarity:

1. **State the problem:** We need to find an expression for the function $$y = 6x^3 - \frac{4}{x^2}$$. 2. **Understand the components:** The function consists of two terms: a polyn

1. **State the problem:** We need to find an expression for the area of a rectangular field. 2. **Given:** The length of the field is $4x + 2$ meters.

1. **Work out the multiplications and simplify each:** **a.** $\frac{3}{5} \times \frac{6}{7}$

1. Problem: Simplify the expression \((15^{\frac{3}{8}})(81^{\frac{1}{34}})(15^{\frac{4}{3}})(81^{\frac{1}{7}})(15^{\frac{7}{8}})(81^{\frac{1}{7}})\). 2. Use the property of expone

1. **State the problem:** Simplify the expression $$\frac{1}{\sqrt{5} - 2} \times \frac{1}{\sqrt{5} + 2}$$. 2. **Recall the formula:** When multiplying expressions with conjugates

1. **Problem:** Simplify the expression $$ (15^{\frac{3}{8}})(81^{\frac{1}{34}})(15^{\frac{3}{4}})(81^{\frac{1}{7}})(15^{\frac{5}{8}})(81^{\frac{1}{7}}) $$ 2. **Formula and rules:*

1. **State the problem:** Simplify the expression $$\frac{36 \pi}{5} \times \frac{8}{20} = \frac{1}{\pi} - \frac{1}{\pi} \times \frac{5}{8}.$$\n\n2. **Simplify the left side:** Mul

1. Let's create a real-life situation involving algebra. 2. Problem: Suppose you are buying apples and oranges. Apples cost $2 each and oranges cost $3 each. You buy a total of 10

1. **State the problem:** Solve the equation $2x + 5 = 9$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. We do this by per

1. **State the problem:** Given the system of equations $$2x + y = \frac{1}{\sqrt{5 - 2}}, \quad 2x - y = \frac{1}{\sqrt{5 + 2}}$$

1. We are asked to find the composition \((g \circ f)(x)\), which means we substitute \(f(x)\) into \(g(x)\). 2. Given functions:

1. **Stating the problem:** Evaluate the expression $7\log 4 \cdot 2\log 5 + 7\log \frac{49}{25}$.

1. **Stating the problem:** We want to express $\log_6 18$ in terms of $x = \log_6 6$ and $y = \log_2 2$. 2. **Recall the given values:**

1. 문제: 식 $$(x+y)^2 - 9(x+y)(2x - y) + 20(2x - y)^2$$ 을 인수분해하시오. 2. 치환: $x + y = A$, $2x - y = B$ 로 치환하면 식은 $$A^2 - 9AB + 20B^2$$ 가 됩니다. (㉠, ㉡)

1. **State the problem:** Simplify the expression $$\frac{X^{-4} \cdot X^{3}}{X}$$. 2. **Recall the laws of exponents:**