Part A:
I have attached the graph of this system of inequalities.
Part B:
Plug in (8,10) into both equations
10 > 3(8) + 10
10 > 24 + 10
10 > 34
This is false!
10 < (-3/4)(8) - 1
10 < (-3)(2) - 1
10 < -6 - 1
10 < -7
This is also false!
So,
(8,10) is not included in the solution area for the system.
The sum of any arithmetic sequence is the average of the first and last terms times the number of terms.
Any term in an arithmetic sequence is:
a(n)=a+d(n-1), where a=initial term, d=common difference, n=term number
So the first term is a, and the last term is a+d(n-1) so the sum can be expressed as:
s(n)(a+a+d(n-1))(n/2)
s(n)=(2a+dn-d)(n/2)
s(n)=(2an+dn^2-dn)/2
However we need to know how many terms are in the sequence.
a(n)=a+d(n-1), and we know a=3 and d=2 and a(n)=21 so
21=3+2(n-1)
18=2(n-1)
9=n-1
10=n so there are 10 terms in the sequence.
s(n)=(2an+dn^2-dn)/2, becomes, a=3, d=2, n=10
s(10)=(2*3*10+2*10^2-2*10)/2
s(10)=(60+200-20)/2
s(10)=240/2
s(10)=120
3) 180-32= 148°
4) x = 142°
5) 3x+2x = 90°
5x =90°
x= 90/5
x = 18°
6) 180 = 6x + x
180 +2 = 7x
182/7 =x
26° = x
Answer:
x = 5
Step-by-step explanation:
6 - 8x = 6x - 8x - 24
(add the x's on each side)
6 - 8x = -2x - 24
(pass -2x on the other side (adding))
6 - 6x = -24
(pass the 6 to the other side (subtracting))
- 6x = - 30
(divide by -6 on both sides)
x = 5