Step-by-step explanation:
a2 = a1×r
a3 = a1×r²
a1×r + a1×r² = 6×a4 = 6×a1×r³
1.
r + r² = 6r³
6r³ - r² - r = 0
r×(6r² - r - 1) = 0
the first solution is obvious : r = 0.
but this is no useful ratio for a geometric sequence.
the other 2 solutions are in
6r² - r - 1 = 0
the general solutions for a quadratic equation are
(-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 6
b = -1
c = -1
so,
(1 ± sqrt(1 - 4×6×-1))/12
r = (1 ± sqrt(25))/12
r = (1 ± 5)/12
r1 = (1+5)/12 = 6/12 = 1/2
r2 = (1-5)/12 = -4/12 = -1/3
2.
we can ignore r2 (negative) and just focus on r1 (1/2).
the second term is 8. that means
a2 = 8 = a1×r = a1×1/2
a1 = 2×a2 = 16
so, we have
a1 = 16
a2 = 8
a3 = a2×1/2 = 8×1/2 = 4
a4 = a3×1/2 = 4×1/2 = 2
a5 = a4×1/2 = 2×1/2 = 1
a6 = a5×1/2 = 1×1/2 = 1/2
a7 = a6×1/2 = 1/2 × 1/2 = 1/4
Answer:
1. 300 and 330
2. the red car has better mileage
3. well I did 300 divided by 12 and got 25. then I did 330 divided by 15 and got 22 so the red has better mileage
If the whole angle (ABC) is equal to 133, we can add angles ABD and DBC to find x.
10x+13=133
Subtract 13 from both sides to get
10x=120
Divide both sides by 10 to get that x=12
We can now plug the value of x into ABD to find its measure.
7(12)+4
Simplifies to 84+4, which is 88
So angle ABD is equal to 88 degrees.
:)
Answer:
Thus, n = 4 is the solution.
Step-by-step explanation:
1. perform the indicated multiplication, obtaining 3n + 24 = 36
2. Subtract 24 from both sides: 3n = 12
3. Solve this result for n: n = 12/3. Thus, n = 4 is the solution.
Answer:
A!
Step-by-step explanation:
10 cubic feets volume is equivalent to 25.85 inches.
