Given the expression:
-x^2+18x-99
to solve by completing squares we proceed as follows:
-x^2+18x-99=0
this can be written as:
-x^2+18x=99
x^2-18x=-99.......i
but
c=(-b/2)²
Hence:
c=(-(-18)/2)²=81
adding 81 in both sides of i we get:
x^2-18x+81=-99+81
factorizing the quadratic we obtain:
(x-9)(x-9)=-18
thus
(x-9)²+18=0
the above takes the vertex form of :
y=(x-k)²+h
where (k,x) is the vertex:
the vertex of our expression is:
(9,18)
hence the maximum point is at (9,18)
NOTE: The vertex gives the maximum point because, from the expression we see that the coefficient of the term that has the highest degree is a negative, and since our polynomial is a quadratic expression then our graph will face down, and this will make the vertex the maximum point.
Answer:
3.48/12= .29
Step-by-step explanation:
Answer:
The relationship B is different than the other three, because it has a different proportionality constant.
Step-by-step explanation:
All available options show direct relationships, which are defined as follows:
(1)
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- Proportionality constant, dimensionless.
We proceed to use the following strategy based on the proportionality constant, that is:
A different relationship must indicate a different proportionality constant:
Option A (
, 
)
Option B (
, 
)
Option C (
, 
)
Option D (, 
)
The relationship B is different than the other three, because it has a different proportionality constant.
Answer:
n=2
Step-by-step explanation:
-4n - 8 = 4(-3n + 2)
-4n - 8 = -12n + 8
8n = 16
n = 2
The first thing you have to take into account is the definition of the axis in the complex plane.
We have then:
The vertical axis represents the imaginary part.
The horizontal axis represents the real part.
We then have the following number:
-14 - 5i
Since the real part and the imaginary part are negative, then the number is located in the third quadrant of the complex plane.
Answer:
Quadrant III.
