Algebra Semester Review Part 3 24-25

Front

What is the slope of a line parallel to the line represented by the equation 8x - 10y = -2?

Back

The slope of the line is \frac{8}{10} = \frac{4}{5}.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope.

Front

What is the equation of a line in slope-intercept form?

Back

The equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the process to simplify the expression \frac{45x^6y^7}{(3x^2y^4)^2}?

Back

First, simplify the denominator: (3x^2y^4)^2 = 9x^4y^8. Then, divide: \frac{45x^6y^7}{9x^4y^8} = \frac{5x^2}{y}.

Front

What does it mean to simplify an expression?

Back

To simplify an expression means to reduce it to its simplest form, making it easier to understand or work with.

Front

What is the result of simplifying \frac{25a^{-6}b^{12}}{5}?

Back

The result is \frac{5b^{12}}{a^6}.

Front

What is the power of a product rule in exponents?

Back

The power of a product rule states that (ab)^n = a^n * b^n.

Front

What is the equation of a line that is parallel to y = 2x + 6 and passes through the point (-4, -7)?

Back

The equation is y = 2x + 1.

Front

What is the square of a product rule in exponents?

Back

The square of a product rule states that (ab)^2 = a^2 * b^2.

Front

How do you simplify the expression (5a^4b^3)^2?

Back

You apply the power of a product rule: (5a^4b^3)^2 = 25a^8b^6.