Answer:
I believe it's Division property
Step-by-step explanation:
Since 8m = -16
You divide both sides by 8. So -16 divided by 8 will equal to -2. m=-2
Hope this helpsʕ•ᴥ•ʔ
Answer:
Step-by-step explanation:
8 earth years
Answer:
the common ratio is either 2 or -2.
the sum of the first 7 terms is then either 765 or 255
Step-by-step explanation:
a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.
so,
a1
a2 = a1×f
a3 = a2×f = a1×f²
a4 = a3×f = a1×f³
the problem description here tells us
a3 = 4×a1
and from above we know a3 = a1×f².
so, f² = 4
and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).
again, the problem description tells us
a2 + a4 = 30
a1×f + a1×f³ = 30
for f = 2
a1×2 + a1×2³ = 30
2a1 + 8a1 = 30
10a1 = 30
a1 = 3
for f = -2
a1×-2 + a1×(-2)³ = 30
-10a1 = 30
a1 = -3
the sum of the first n terms of a geometric sequence is
sn = a1×(1 - f^(n+1))/(1-f) for f <>1
so, for f = 2
s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765
for f = -2
s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =
= -1×-255 = 255
Answer:
t=40
Step-by-step explanation:
The sum of all angles in a triangle will always equal 180°. This means that:
(2t-42)+(4t-49)+(2t-49) = 180°
Let's solve this equation!
(2t-42)+(4t-49)+(2t-49) = 180
First we simplify what's on the left side:
2t-42+4t-49+2t-49 = 180
2t+4t+2t-42-49-49 = 180
8t-140 = 180
*Add 140 to both sides
8t = 180+140
8t = 320
Divide both sides by 8 to know what t means:
t = 320/8
t = 40
