Answer:

Step-by-step explanation:
we are given
sequence is geometric
so, we can use nth term formula

we have


we have to find a9
so, we can plug n=9
we get



Problem 1)
AC is only perpendicular to EF if angle ADE is 90 degrees
(angle ADE) + (angle DAE) + (angle AED) = 180
(angle ADE) + (44) + (48) = 180
(angle ADE) + 92 = 180
(angle ADE) + 92 - 92 = 180 - 92
angle ADE = 88
Since angle ADE is actually 88 degrees, we do NOT have a right angle so we do NOT have a right triangle
Triangle AED is acute (all 3 angles are less than 90 degrees)
So because angle ADE is NOT 90 degrees, this means
AC is NOT perpendicular to EF-------------------------------------------------------------
Problem 2)
a)
The center is (2,-3) The center is (h,k) and we can see that h = 2 and k = -3. It might help to write (x-2)^2+(y+3)^2 = 9 into (x-2)^2+(y-(-3))^2 = 3^3 then compare it to (x-h)^2 + (y-k)^2 = r^2
---------------------
b)
The radius is 3 and the diameter is 6From part a), we have (x-2)^2+(y-(-3))^2 = 3^3 matching (x-h)^2 + (y-k)^2 = r^2
where
h = 2
k = -3
r = 3
so, radius = r = 3
diameter = d = 2*r = 2*3 = 6
---------------------
c)
The graph is shown in the image attachment. It is a circle with center point C = (2,-3) and radius r = 3.
Some points on the circle are
A = (2, 0)
B = (5, -3)
D = (2, -6)
E = (-1, -3)
Note how the distance from the center C to some point on the circle, say point B, is 3 units. In other words segment BC = 3.
Answer:
Multiply both sides by 
Step-by-step explanation:
Given

Required
Get an equivalent of 
To do this, we simply multiply through by 








Answer:
5 chickens, 20 goats
Step-by-step explanation:
We can set up two equations and use substitution
There are 25 total goats and chickens, so

Goats have 4 feet and chickens have two, so

By solving for G in the first equation,

We can now use substitution,

We have 5 chickens, so we have 20 goats.
Let's double check:

It checks out!
Answer:
x = 1 and x = 
Step-by-step explanation:
In this equation, a=5, b=-1, c=-4.
Plug these into the quadratic formula:
x =
and x = 
Now, simplify the equations:
x =
=
=
= 1
and
x =
=
=
= 