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
<span>3x = y + 7
</span><span> y =3x-7
</span>
<span>8x = 2y + 5
</span><span>8x = 2(3x-7) + 5
8x=6x-14+5
8x-6x=-9
2x=-9
x=-4.5
</span><span>8x = 2y + 5
</span>8(4.5)=2y+5
36=2y+5
2y=31
y=15.5
The line will remain unchanged because you are just and only dilating the rectangle. I hope this helps :).-
Divide 40 and 5 and multiply the answer by 3. That should give you your answer.
It’s should be 30 if the triangle is drawn to scale
It would absolutely not be 180 because that’s the sum of all angles of the triangle
It could be 75 but if the triangle is drawn to scale then the two isosceles angle should be greater than angle U, so it won’t be reasonable if angle U is 75
