Answer:
(2b-3)²
Step-by-step explanation:
The square of a binomial is ...
(p - q)² = p² - 2pq + q²
The fact that the first and last terms are perfect squares suggests that you might want to look to see if the middle term matches this form. It does.
For p² = 4b², p=2b.
For q² = 9, q = 3.
Then 2pq = 2(2b)(3) = 12b.
So, the factoring is ...
4b² -12b +9 = (2b -3)²
Answer:
$570
Step-by-step explanation:
500 * 1.2 = $600 after 20% pay raise
600 * .95 = $570 after 5% pay cut
The formula for circumference is
C=(pi)d
11304=(pi)d
assume pi is 3.14
rearrange formula
d= c / (pi)
= 11304 / 3.14
d= 3600
The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.
Depending on the formula you know, you can find the length of a side in 1 of 2 ways.
The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.
c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
c^2 = 400 + 400 - 800(cos 45)
c^2 = 800 - 800(cos 45)
c = sqrt(800 - 800(cos 45)
c = 15.31
The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31
We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using
a = S / (2 tan (180 / n)
a = 15.31 / (2 tan (180 / 8))
a = 18.48
Now solve for the area
Area = ap/2
Area = (18.48)(122.48)/2
Area = 1131.72
perimeter = 122.48
area = 1131.72
