Answer:

Step-by-step explanation:
we know that

Remember the identity

step 1
Find the value of 
we have that
The angle alpha lie on the III Quadrant
so
The values of sine and cosine are negative

Find the value of sine

substitute




step 2
Find the value of 
we have that
The angle beta lie on the IV Quadrant
so
The value of the cosine is positive and the value of the sine is negative

Find the value of cosine

substitute




step 3
Find cos (α + β)

we have




substitute



In an arithmetic sequence:
Tn=t₁+(n-1)d
t₄=t₁+(4-1)d=t₁+3d
t₅=t₁+(5-1)d=t₁+4d
t₆=t₁+(6-1)d=t₁+5d
t₄+t₅+t₆=(t₁+3d) +(t₁+4d)+(t₁+5d)=3t₁+12d
Therefore:
3t₁+12d=300 (1)
t₁₅=t₁+(15-1)d=t₁+14d
t₁₆=t₁+(16-1)d=t₁+15d
t₁₇=t₁+(17-1)d=t₁+16d
t₁₅+t₁₆+t₁₇=(t₁+14d)+(t₁+15d)+(t₁+16d)=3t₁+45d
Therefore:
3t₁+45d=201 (2)
With the equations (1) and (2) we make an system of equations:
3t₁+12d=300
3t₁+45d=201
we can solve this system of equations by reduction method.
3t₁+12d=300
-(3t₁+45d=201)
-----------------------------
-33d=99 ⇒d=99/-33=-3
3t₁+12d=300
3t₁+12(-3)=300
3t₁-36=300
3t₁=300+36
3t₁=336
t₁=336/3
t₁=112
Threfore:
Tn=112+(n-1)(-3)
Tn=112-3n+3
Tn=115-3n
Now, we calculate T₁₈:
T₁₈=115-3(18)=115-54=61
Answer: T₁₈=61
X=4 & y=3
Explanation:
Picture
1 2/3 is the answerrrrrrr
Answer:
14.4
Step-by-step explanation:
1.8 added 8 times = 1.8 * 8
1.8 * 8
use distributive property
1.8 = 1 + 0.8
1.8 * 8 = (1+0.8) * 8
= 1*8 + 0.8*8
anything multiplied by 1 equals itself
1*8 + 0.8*8 = 8 + 0.8 * 8
0.8 = 8/10
0.8 * 8 = (8/10) * 8
= 64/10
= 6.4
8 + 0.8 * 8 = 8 + 6.4 = 14.4 as our answer