🧮 algebra

1. **State the problem:** Simplify the expression $$(0.66x) \times \left(\frac{10}{0.77x}\right)$$. 2. **Write the expression clearly:**

1. **State the problem:** Simplify the expression $ (x+4y)(x-5y) $. 2. **Formula used:** Use the distributive property (FOIL method) for multiplying two binomials:

1. **State the problem:** Simplify the expression $-19 + 15 - 4 + 2 - 12 + 6$. 2. **Add and subtract step-by-step:**

1. **State the problem:** Solve the system of linear equations: $$3x + 2y = 49$$

1. The problem is to simplify the expression involving multiplication of fractions and a variable: $$x \times \frac{3}{4} \times \frac{2}{3} \times \frac{3}{7} \times \frac{1}{5}$$

1. **State the problem:** Solve the system of linear equations: $$5p - 5q = 35$$

1. **Problem:** Find the domain and range of the function $f(x) = \sqrt{\frac{x - 1}{x^2 - 4}}$. 2. **Step 1: State the domain conditions.**

1. **State the problem:** Solve the system of linear equations: $$5p - 5q = 35$$

1. **State the problem:** Simplify the expression $$(5x+3)(2x-7) - (3x-2)(4x+1)$$. 2. **Use the distributive property (FOIL) to expand each product:**

1. **Problem:** Given $(f \circ g)(x) = 2x + 5$ and $g(x) = \frac{x}{x+1}$, find $f(x)$. 2. **Recall:** The composition $(f \circ g)(x) = f(g(x))$. So, $f(g(x)) = 2x + 5$.

1. **Problem statement:** Provide two alternative definitions for the set of rational numbers using the idea of ordered pairs. 2. **Definition 1:** Rational numbers can be defined

1. The problem is to analyze and graph the function $$y=\left(\frac{1}{4}\right)^{-x} - 5$$. 2. Recall the rule for negative exponents: $$a^{-x} = \frac{1}{a^x}$$. Applying this to

1. **State the problem:** We want to analyze the function $$y=|x|+\frac{1}{|\sin(4x)|}$$ which involves absolute values and a trigonometric function. 2. **Understand the components

1. Problem: Find the zeros of the function $$f(x) = \frac{(\ln x)^2}{2 - x}$$. 2. To find zeros of a function, set the numerator equal to zero and ensure the denominator is not zer

1. **Problem a:** Simplify $$\left(\frac{a^{2}}{3} \times \left[\frac{a^{3}}{1} \times \frac{1}{a^{4}}\right]\right)^{6 \times \frac{1}{7}}$$. 2. First, simplify inside the bracket

1. **State the problem:** We want to analyze the function $$y = |x| + \frac{1}{|\sin(4x)|}$$ and understand its behavior. 2. **Recall important rules:**

1. **State the problem:** Find the equation of a parabola whose axis is parallel to the x-axis and passes through points (3, 1), (0, 0), and (8, -4). 2. **Recall the form of the pa

1. **State the problem:** Simplify the expression $4x - (3x+2)(4x-1)$. 2. **Use the distributive property:** Expand the product $(3x+2)(4x-1)$ using the FOIL method:

1. The problem involves finding the product of the binomials $(4x + 1)(x + 1)$ and simplifying the expression. 2. The formula for multiplying two binomials is given by the distribu

1. The problem is to understand and analyze the function $y = |x| + \frac{1}{|skn|}$. 2. Here, $|x|$ denotes the absolute value of $x$, which means it is always non-negative regard

1. The problem asks which method is less messy when multiplying two polynomials each with 3 terms: length $x^2 + 2x + 5$ and width $5x^2 + 3x - 7$. 2. The two common methods to mul