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:
x1 y1 x2 y2
3 -1 -8 0
ΔY 1
ΔX -11
slope= - 1/11
B= - 8/11
Step-by-step explanation:
Answer:1,401.259
Step-by-step explanation:
The answer is A
To explain more on why it’s A
Because, Y, which is the shaded part on the graph
Is less than negative 2x, as you can see is above y
Answer:
Jennie earned $300
Step-by-step explanation:
We are already given the amount of time that she works and the rate. We just need to multiply the time by the corresponding rate. She worked 22 regular hours and gets $10 for each one. That means she earned $220 just from the regular hours.
Now we need to add the overtime hours. She worked 4 hours and made $20 for each one. In total, that's $80.
220+80=300
Jennie earned $300
