Answer:
x= -2
Step-by-step explanation:
Rational Function can be expressed as:
Where b is our horizontal shift and q is our vertical shift.
For asymptotes, there are two types which are vertical and horizontal.
Vertical Asymtote is the value of -b itself or x = -b.
Therefore, from the functio:
Our vertical asymtote is x = -2
Answer:
see explanation
Step-by-step explanation:
We require 2 equations with the recurring decimal placed after the decimal point.
let x = 0.7272.... (1) ← multiply both sides by 100
100x = 72.7272... (2)
Subtract (1) from (2) thus eliminating the recurring decimal
99x = 72 ( divide both sides by 99 )
x = =
Answer:
Part A)
2nd and 5th choice.
Part B)
Step-by-step explanation:
For the given parabola, our focus is (-3, 2), and our directrix is given by y = 4.
Part A)
We are given a point (x, y) on the parabola.
Since our directrix is an equation of <em>y</em>, the distance from (x, y) to the directrix will simply be the absolute value of the difference in y-values. So:
Recall the distance formula:
Our distance from (x, y) to the focus (-3, 2) can be determined using the distance formula. Let (x, y) be (x₂, y₂) and let our focus (-3, 2) be (x₁, y₁). Therefore:
Hence, for Part A, our answers are the 2nd and 5th choices.
Part B)
Recall that by the definition of a parabola, any point (x, y) on it is equidistant to the directrix and focus. Hence:
Solve for <em>y</em>. Square both sides. We may remove the absolute value since anything squared is positive:
Square:
Rearrange:
Combine like terms:
Divide both sides by -4. Hence, our equation is:
