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Oksana_A [137]
3 years ago
8

If the fifth and eighth terms of an arithmetic sequence are minus 9 and minus 21, respectively, what are the first four terms of

the sequence?
Mathematics
1 answer:
Reil [10]3 years ago
4 0
One way to do this problem is to determine the common difference.  If the 5th and 8th terms are -9 and -21, we can do this by subtracting -9 from -21:

-21-(-9) = -12.  The 5th and 8th terms are not consecutive, so we have to think in terms of (8-5), or 3, times the common difference to get from -9 to -21.

Note that -12 divided by 3 is -4.  Thus, the common difference is -4.

Check:  -9 - 4 = -13; -13 - 4 = -17; -17 - 4 = -21 (which is correct).

We know that the 5th term is -9.  To find the 4th term, work backwards:  subtract (-4) from -9, which produces -9+4=-5.

The fourth term is -5.  Subtracting -4 from this (which is the same as adding 4 to this -5) produces the third term; it is -1.  Can you now find the 2nd and 1st terms using the same approach?

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Answer = 55,25 inches

Solution -

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⇒ x = y + 30

Then four square pieces of side 6 are cut from each corner,

so the new length and width are

x-12 , y-12

Then the volume of the new box created will be

(x-12)(y-12)6

in the question the volume of the given figure is given to be 3354

so (x-12)(y-12)6 = 3354

putting the value of x in the the above equation

⇒ (y+30 - 12)(x-12) = 3354/6 = 559

⇒ (y+18)(y-12) = 559

⇒ y² + 6y - 775 = 0

⇒ y² + 31y - 25y -775 = 0

⇒ (y+31)(y-25) = 0

⇒ y = -31, 25

as length can not be -ve , so y = 25

then x = 25+30 = 55

Hence the dimensions of the metal piece are 55, 25 inches

3 0
3 years ago
Find the value of x number on top is 6 and other is 9
faltersainse [42]

Answer:

x = - 12, 3

Step-by-step explanation:

By tangent secant theorem:

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5 0
2 years ago
Help! Best Answer = Brainiest!
r-ruslan [8.4K]

Answer:

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Step-by-step explanation:

4 0
3 years ago
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maria [59]

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ikadub [295]

Answer:

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2 years ago
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