If
, then you have
By the intermediate value theorem, there will be some number
such that
(i.e.
will have a root in
) if you can guarantee that
or
.
Since the coefficients
are all positive, then you know right away that
, so you need to have
in order for there to be such a
.
This means you need to have
which means (A) must be the answer.
#7) y = - x² + 4
Vertex:
∆=b²-4ac
S(-b/2a , -∆/4a) = (0/-2 , -16/-4) = (0,4)
Axis of symmetry:
x=-b/2a = 0
(we have max here because a is negative) Max:
Max (0,4)
#8) f(x) = x² -4x +4
Vertex:
S(-b/2a , -∆/4a) = (4/2 , 0/4) = (2,0)
Axis of symmetry:
x= -b/2a = 2
(Here it's min because a>0) Min:
Min(2,0)
otal perimeter = 76cm = AB + BC + CD + AD
AD & BC = 13cm
AB = 1.5*(CD)
Solution:
Since we know AD & BC are both 13cm long, plug those numbers into the perimeter equation
76cm+=+AB+%2B+BC+%2B+CD+%2B+AD Place 13cm in for AD & BC
76cm+=+AB+%2B+13cm+%2B+CD+%2B+13cm Combine like terms
76cm+=+AB+%2B+CD+%2B+26cmSubtract 26cm from both sides
50cm+=+AB+%2B+CD Now it is time to substitute the 1.5*(CD) for AB
50cm+=+1.5%2A%28CD%29+%2B+CD rewrite the equation
50cm+=+2.5%2A%28CD%29 Divide both sides by 2.5
20cm+=+CD
To find AB, plug 20cm in for CD in the equation AB = 1.5*(CD)
AB+=+1.5%2A20cm
AB+=+30cm
Answer:
y = -1 + -0.75x
explanation: