If we now that 4y equals to x, that means we can replace x with 4y.
Therefore we can write: 4y+2y = 12
We can summarize that to 6y = 12.
If we divide both sides with 6, you get y = 2
In order to solve for x, we can use the second equation and just replace y with value we just got (y=2).
We can write: x+2*2=12
Now you move 2*2 (which is 4) to the other side: x=12-4
Now you get: x = 8
6 feet = 72 inches
1 inch = 2.54 centimeters
72 * 2.54 = 182.88 cm which equals
1.8288 meters
3(2)-18=-12
6-18 = -12
-12 = -12
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
The answer would be -5 1/4
