Recall that a rational function:

has a vertical asymptote at x₀ if and only if:

Also, the roots of the above rational function are the same as P(x).
Since the rational function has a vertical asymptote at x=-1, we get that its denominator must be:

Since the rational function has a double zero at x=2 we get that its numerator must be of the form:

Finally, since the rational function has y-intercept at (0,2) we get that:

Simplifying the above equation we get:

Dividing the above equation by 4 we get:

Therefore, the rational function that satisfies the given conditions is:

Answer:
The numerator is:

The denominator is:
Answer:
55 because if u take the 6 and 3 and multiply then subtract 4 and whatever you get that's your answer same with the others
3x+15 , this expression correctly combines the like terms
Answer:
The price of one gallon of gasoline is $3.15
Step-by-step explanation:
If the lady buys 2.4 gallons of gasoline for a total of $7.56, then as the problem suggests, one can find the unknown price of gasoline per gallon (p) by solving the equation for the unknown "p":
2.4 p = 7.56
then divide both sides by 2.4 to isolate the unknown "" on one side of the equal sign:
p = 7.56/2.4
p = $3.15
so this is the price per gallon of gasoline.
Answer: the length of Maria's piece of string is 45 inches.
the length of Katy's piece of string is 39 inches
Step-by-step explanation:
Let x represent the length of Maria's piece of string.
Let y represent the length of Katy's piece of string.
When they put the two pieces of string together end to end, the total length is 84inches. This means that
x + y = 84 - - - - - - - - - - - -1
Maria's string is 6 inches longer than Katy's. This means that
x = y + 6
Substituting x = y + 6 into equation 1, it becomes
y + 6 + y = 84
2y + 6 = 84
2y = 84 - 6 = 78
y = 78/2 = 39
x = y + 6 = 39 + 6
x = 45