8. In A, because those trees are in the deciduous.
9. All of these forests contains life and lot and lots of trees.
Hope this helps!
Answer:
300 paper clips in one box
300 multiply to 10 box =3,000 paper clips
Part A
Answer: The common ratio is -2
-----------------------------------
Explanation:
To get the common ratio r, we divide any term by the previous one
One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2
Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time
Side Note: each term is multiplied by -2 to get the next term
============================================================
Part B
Answer:
The rule for the sequence is
a(n) = (-2)^(n-1)
where n starts at n = 1
-----------------------------------
Explanation:
Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio
The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)
============================================================
Part C
Answer: The next three terms are 16, -32, 64
-----------------------------------
Explanation:
We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms
-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64
showing that the next three terms are 16, -32, and 64
An alternative is to use the formula found in part B
Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier
Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier
Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier
while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
Answer:
≈ 39.7ft
Step-by-step explanation:
The Pythagorean theorem:
(a and b are the two shorter legs and c is the largest leg, which is also the opposite side of the right angle)
First, the value of a and c is given. So, we can go ahead and plug those value in and then solve for b.
To find b, we have to get it by itself. So we subtract 2025 from both sides then square root both sides. Resulting in:
≈ 39.7ft
64*2 is 128
1/2 of a cup of chocolate powder is 64g
laura added 4/6 of a cup
laura went over by 1/3 of a cup
