The fourth vertex would be at (2,5).
It has to be the same x value as (2,3) and the same y value as (-6,5)
Answer:
see attachment
Step-by-step explanation:
We want to sketch the graph of
We want to use tables so we choose some few points and plot.
When x=-6,
y=(-6)²+4(-6)+8=20
When x=-4,
y=(-4)²+4(-4)+8=8
When x=0,
y=(-2)²+4(-2)+8=4
When x=0,
y=(0)²+4(0)+8=8
When x=2,
y=(2)²+4(2)+8=20
The table and graph are shown in attachment.
Answer:
c(x) = –8x^2 + 3x – 5 is a quadratic
Step-by-step explanation:
A quadratic function involves the 2nd power of x: x^2, and may (or may not) involve the 1st and zeroth power of x.
a(x) = -2x^3 is not a quadratic because of that exponent 3; in a quadratic, the highest power is always 2.
b(x) = 5x^3 + 8x^2 + 3 is not a quadratic for the same reason that a(x) is not a quadratic.
c(x) = –8x^2 + 3x – 5 is a quadratic: the highest power of x is x^2, the other powers are x^1 and x^0.
1pint=16oz 1/2 is 16 is 8 so Tawny has a total of 40oz each cup holds 5oz so 40/5=8 so Tawny can fill a total of 8 cups
Answer:
Overall rectangle: 100 ft × 8 16/23 ft ≈ 100 ft × 8.696 ft
Individual pen: 8 16/23 ft × 4 6/11 ft ≈ 8.696 ft × 4.545 ft
Step-by-step explanation:
Half the fence will be used in each of the orthogonal directions to make the pen. That is, the long side of the overall rectangle will be (400 ft/2)/2 = 100 ft. The short side of the overall rectangle will be (400 ft/2)/23 = 8 16/23 ft. (There are 21 partitions between the 22 pens, and 2 end fences, for a total of 23 fence segments of the short length.)
The long (100 ft) side of the overall rectangle is divided into 22 parts by the internal partitions, so each pen will have a short dimension of 100 ft/22 = 4 6/11 ft.
_____
We know half the fence will be used in each direction because we know the total area is a quadratic function of the side length. If the long side of the overall pen is x, then the short side is (400 ft -2x)/23, and the overall area is ...
... A = x(400 ft -2x)/23
The vertex of this quadratic function is halfway between the zeros, at x = 100 ft. That is, the two long sides of the pen total 200 ft, or half the overall length of fence.
