Answer:
Step-by-step explanation:
Let the length of the rectangle be 'L'
And the width of the rectangle be 'W'
According to the statement:
Perimeter of a rectangle= 2(Length+Width)
You would have 4 left after dinner: (.875)(32)=28 so you have 28 completed before dinner and would have 4 left to do.
Answer:
3 ft.
Step-by-step explanation:
When you imagine the sentence, it is a right angled triangle. In this case, it's a Pythagoras Theorem. The formula for it is:
a²(opposite) + b²(adjacent) = c²(hypotenuse)
The building is the opposite, the distance between the foot of the ladder and the building is the adjacent, while the ladder is the hypotenuse.
We have the measurements except for the adjacent. So it will be:
c² - a² = b²
5² - 4² = b²
25 - 16 = b²
9 = b²
√9 = b
b = 3 ft
The answer is 3 ft.
Part A
Answer: The common ratio is -2
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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
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Part B
Answer:
The rule for the sequence is
a(n) = (-2)^(n-1)
where n starts at n = 1
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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)
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Part C
Answer: The next three terms are 16, -32, 64
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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)
The answer would be the Last option (D). This because it poses the proportion of 48 in (Amber's height) / 60 in (Lucy's height) and puts it equal to the proportion of x (what is Amber's height in the photo) / 3 (what is Lucy's height in the photo. Hope this helps :)
