Test 6

Front

What is the standard form of a hyperbola?

Back

Front

How do you write the standard form equation of an ellipse?

Back

Front

What is the relationship between the vertices and foci of an ellipse?

Back

Front

How do you solve exponential equations?

Back

To solve exponential equations, you can set the bases equal to each other or take the logarithm of both sides.

Front

What is the value of x in the equation 3^3 = 3^(4x + 2)?

Back

x = \frac{1}{4}.

Front

How do you solve the equation 7^{-x} = 49?

Back

Convert 49 to a power of 7: 49 = 7^2. Thus, -x = 2, leading to x = -2.

Front

Back

Front

Back

Front

What is the definition of a hyperbola?

Back

A hyperbola is a type of conic section that is formed by the intersection of a plane and a double cone, characterized by two separate curves.

Front

What is the difference between a hyperbola and an ellipse?

Back

A hyperbola consists of two separate branches, while an ellipse is a closed curve.