Step-by-step explanation:
the introduction of a fraction tells us that we are dealing with multiplications, and therefore a geometric sequence (where every new term is created by multiplying the previous term by a constant factor, the ratio r).
I think your teacher made a mistake, or you made one when typing the question in here.
there is no factor r that creates
15×r = 9
and
9×r = 5/27
it would mean that
15 × r² = 5/27
r² = 5/27 / 15 = 5/27 × 1/15 = 5/405 = 1/81
r = 1/9
but 15 × 1/9 = 5 × 1/3 = 5/3 is NOT 9
and 9 × 1/9 = 9/9 = 1 is NOT 5/27
so, this can't be right.
on the other hand
15 × r = 9
r = 9/15 = 3/5
and then
9 × 3/5 = 27/5
so, either the sequence should have been
15, 5/3, 5/27
or (and I suspect this to be true)
15, 9, 27/5
under that assumption we have
s1 = 15
r = 3/5
sn = sn-1 × r = s1 × r^(n-1) = 15 × (3/5)^(n-1)
s10 = 15 × (3/5)⁹ = 15 × 19683/1953125 =
= 3 × 19683/390625 = 59049/390625 =
= 0.15116544 ≈ 0.151
Answer:
x = -1.5625
Step-by-step explanation:
Solve for x:
-8 x - 12.5 = 0
Add 12.5` to both sides:
(12.5 - 12.5) - 8 x = 12.5
12.5 - 12.5 = 0:
-8 x = 12.5
Divide both sides of -8 x = 12.5 by -8:
(-8 x)/(-8) = 12.5/(-8)
(-8)/(-8) = 1:
x = 12.5/(-8)
12.5/(-8) = -1.5625:
Answer: x = -1.5625
Answer:
7/6 cups
Step-by-step explanation:
Given the following information :
Mug is 2/7 full
Amount of water in the mug = 1/3 cup
Assume the full capacity of the mug = m
Then the current capacity of water in mug = (2/7) of m = (2/7)m
Current capacity of water in mug is equivalent to 1/3 cup of water
Hence,
(2/7)m = 1/3
2m/7 = 1/3
Cross multiply
(2m * 3) = 7 * 1
6m = 7
m = 7/6
m = 1 1/6 cups
3(2x+8)=8x+46
6x+24=8x+46
-2x+24=46
-2x=22
x=-11
3(2(-11)+8)=8(-11)+46
3(-22+8)=-88+46
3(-14)=-42
-42=-42
Hope I didn't mess up for your sake
