Answer:
Step-by-step explanation:
There are but a few rules we have to follow when completing the square. However, they are very important rules so we have to be careful. First and foremost, the coefficient on the x-squared term HAS to be a positive 1. If it is not, we have to manipulate the function so it is a positive 1. Then we take half the linear term, square it and add it to both sides (and sometimes this can be very tricky. It is tricky here, so pay attention.)
We begin by separating the x terms from the constant by setting the parabola equal to 0 and moving the constant:
The coefficient on the x-squared is a negative 1, so we factor out the negative:
The linear term is 2. We take half of 2 which is 1, square 1 to get 1 and add it into the left side. BUT don't forget that we have a -1 out front of the ( ) refusing to be ignored. It is a multiplier. That means that we didn't add in a +1, we added in -1(1) which is -1. That is what we add to the right side:
which simplifies to
The reason for this process is that by completing the square you create a perfect square binomial on the left. We rewrite the parabola in terms of that perfect square binomial:
which simplifies to
From this you can now determine that the vertex of the parabola is (-1, -4)
120 because 180 divided by 120 is 1.5 which is 150%
Answer:
Carmen needs 40 oz of strawberry juice and 24 oz of water.
Step-by-step explanation:
The drink needs to be 5/8 strawberry juice and 3/8 water. So you can get the numbers by multiplying the fractions by 8, so that the denominator becomes 64.
Hope this helps!
Answer:
your answer is 18
Step-by-step explanation:
Answer:
lateral area = 180π in²
Step-by-step explanation:
The lateral area is the surface of the cone only.
perimeter of base = 12 x 2 = 24π in
Surface Area = 1/2 perimeter x slant height
SA = 1/2 x 24π x 15 = 180π in²