Answer:
Step-by-step explanation:
To find the population density of any state:
We must divide the population number by the area
Thus Washington state's population density equals 7,705,281 / 71297.95
Which equals 108.1
Hope that helps!
Notice that the given equation is a parabola.
a) VERTEX
We need to find out where the parabola opens. You can predict the equation by tabulating any values of x and f(x). The table is shown:
x f(x)
_____
0 -7
1 -2
2 1
3 2
4 1
5 -3
As you plot it, the parabola opens downward. The vertex is (3,2) because that is the maximum point. The rest of the values are lesser than 2.
However, there is an easier technique to find the opening parabola and vertex rather than you plot it.
b) AXIS OF SYMMETRY
The axis of symmetry is a line that divides the parabola into two congruent halves. There is a formula for the axis of symmetry which is x = -b/2a.
Note: That is only applied if the parabola opens upward or downward and their axis of symmetry is a vertical line.
To get a and b, arrange the given equation first.
f(x) = -(x - 3)^2 + 2
= -(x^2 - 6x + 9) + 2
= -x^2 + 6x - 7 + 2
= -x^2 + 6x -5
The general form of the quadratic equation is ax^2 + bx + c. Setting a = -1, b = 6, c = -5, the axis of symmetry is
x = -6/(2*-1) = 3.
But anyway, you find it out the table above. We know that the coordinate of the vertex is (3,2). For instance, that is x = 3.
c) MAXIMUM or MINIMUM
Remember that the maximum refers to a vertex where the parabola opening downward. Otherwise, it is a minimum if the parabola opens upward. The maximum or minimum must have a certain value.
We know the answer will be a maximum. Since the axis is symmetry is a vertical line, the value for a maximum is 2.
d) DOMAIN and RANGE
Based on the given equation, the domain will be (-∞, ∞) because all values of x, the parabola continually spreads out.
The range will be (-∞, 2] because the maximum point is 2 and the rest of the values goes negative.
Here, in the given figure. Angle y° forms vertical opposite angle pair with Angle 163°, therefore they have equal values.
that means ~
There are a couple of ways you can solve this. You can write it out like
(K-3)(K-3)(K-3)(K-3)(K-3)(K-3)(K-3)
And pretty much use the foil method
Or you can use the binomial theorem (google it if you dont know)
The solution should be:
(K^7) - 21(k^6) + 189(k^5) - 945(k^4) + 2835(k^3) - 5103(k^2) + 5103k - 2187
9514 1404 393
Answer:
111 1/9 pounds
Step-by-step explanation:
The given relationship is ...
delivered = ground × (1 -10%)
Then ...
ground = delivered/0.90 = 100 lb/0.90 = 111 1/9 lb
It is necessary to grind 111 1/9 pounds of grain to have exactly 100 lb after a 10% payment.
