Answer:
183.20
Step-by-step explanation:
9.95x16=159.20
159.20+24=183.20
The slope of the ramp would be 5/9
Answer:
He told me that he was a nice fellow
I told him that he looked sad and tired
She told me that I was a clever person
She told them that they could pass their exams if they worked hard
Sabnam said that she had gone to the hospital the previous day
Shilpa said that she had been extremely nervous the previous week
Husaain said that they had gone to bed early the previous night
Rahul said that he had not taken a taxi home the previous night
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:
x>10
Step-by-step explanation:
What this is saying is the variable "x" is any number.
To then make it an inequality im using the greater than symbol (not to be confused with greater than or equal to symbol)
So this means if x= "any number" and has a greater than symbol.
"any number" is greater than 10.
