The answer: The 3 (three) consecutive odd integers are: -3, -1, 1.
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Explanation:
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To represent 3 (three consecutive odd integers):
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Let "x" be the first odd integer.
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Let "(x+2)" be next consecutive odd integer.
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Let "(x+4") be the third odd integer.
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The sum of these three consecutive odd integers:
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x + (x + 2) + (x + 4) = x + x + 2 + x + 4 = 3x + 6 ;
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Six ("6") times the sum of these 3 (three) consecutive odd integers =
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6*(3x+6) = 6(3x + 6) = -18 (as given in the problem).
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Given: 6(3x + 6) = -18 ; We can divide EACH SIDE of the equation by "6", to cancel the "6" on the left-hand side into a "1";
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{6(3x + 6) } / 6 = -18 / 6 ; to get:
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3x + 6 = -3 ; Now, we can subtract "6" from EACH SIDE of the equation:
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3x + 6 - 6 = -3 - 6 ; to get:
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3x = -9 ; Now, we can divide EACH SIDE of the equation by "3"; to isolate "x" on one side of the question; and solve for "x" ;
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3x / 3 = -9 / 3 ; x = - 3 ;
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Remember, from above:
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Let "x" be the first odd integer. We know that "x = -3".
Is this an odd integer? Yes!
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Let "(x+2)" be next consecutive odd integer. So (x+2) = (-3+2) = -1.
Is this an odd integer? Yes! Is this "{-1}" the next consecutive odd integer with respect to "{-3}"? Yes!
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Let "(x+4") be the third odd integer. So (x+4) = (-3+4) = 1.
Is this an odd integer? Yes! Is this "{1"} the next consecutive odd integer with respect to "{-1}"? Yes!
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So, our 3 (three) consecutive odd integers are: -3, -1, 1.
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To check our work: Is 6 times the sum of our 3 consecutive odd integers, equal to "(-18)" ?
The sum of our 3 consecutive odd integers = -3 + (-1) + 1 = -3 - 1 + 1 = -3.
6 * -3 = ? -18? Yes!
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Answer: Area= 459.73cm^2
Step-by-step explanation: Circumference of a circle is 2πr
76=2×3.14×r
r= 76÷(6×3.14)
r=12.10
Area of a circle= πr^2
Area= 3.14×(12.10)^2
Area= 456.73cm^2
Answer:
The approximate monthly rate of growth is 1.24%
Step-by-step explanation:
we have the future value formula
we have
----> annual interest rate
so
Find the approximate monthly rate of growth
Remember that
so
Divide the number of periods t by 12
Applying power rules property
Convert to percentage
therefore
The approximate monthly rate of growth is 1.24%
This is NOT an arithmetic sequence because there is no common difference. It is a geometric sequence because there is a common ratio. Meaning that each term is a constant ratio or multiple of the previous term. The recursive rule for this geometric sequence is:
a(n)=3*a(n-1), a(1)=3
83 boxes are required to carry 800 books.
According to the question:
One Box can hold weight = 30 pounds
We know that , 1 pound= 0.45 kg
hence, 30 pounds = 30 x 0.45 = 13.5kg
hence, one box can carry 13.5 kg of weight.
Now,
Weight of 1 book = 1.4 kg
So, Total Weight of 800 books= 1.4 x 800 kg
And , No. of boxes required to carry 800 books = (1.4 x 800)/13.5 = 82.96
or approximately 83 boxes
Hence, 83 boxes are required to carry 800 books.
Learn more about Unitary Method at :
brainly.com/question/19423643
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