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wolverine [178]
2 years ago
14

Hlp!

Mathematics
1 answer:
zzz [600]2 years ago
7 0

Answer:

Option B

x ≥ (-5)

Step-by-step explanation:

<h3><u>Given</u>;</h3>
  • -3(x + 4) ≥ x + 8

So,

-3(x + 4) ≥ x + 8

-3x – 12 ≥ x + 8

Add both sides 12 we get,

-3x – 12 + 12 ≥ x + 8 + 12

-3x ≥ x + 20

Similarly, subtract x from both sides we get,

-3x – x ≥ x – x + 20

-4x ≥ 20

Then, divide both sides by (-4) we get,

-4x/(-4) ≥ 20/(-4)

x ≥ -5

Thus, The answer is x ≥ (-5).

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Find the geometric sum 4 + 12 + 36 + . . . + 236,196.
Zolol [24]
The answer choices are sufficiently far apart that you can work this backward. The sum will be ...
  236,196*(1 + 1/3 + 1/9 + 1/27 + ...)
so a reasonable estimate can be given by an infinite series with a common ratio of 1/3. That sum is
  236,196*(1/(1 - 1/3)) = 236,196*(3/2)

Without doing any detailed calculation, you know the best answer choice is ...
  354,292


_____
There are log(236196/4)/log(3) + 1 = 11 terms* in the series, so the sum will be found to be 4(3^11 -1)/(3-1) = 2*(3^11-1) = 354,292.

Using the above approach (working backward from the last term), the sum will be 236,196*(1-(1/3)^11)/(1-(1/3)) = 236,196*1.49999153246 = 354,292

___
* If you just compute log(236196/4)/log(3) = 10 terms, then your sum comes out 118,096--a tempting choice. However, you must realize that the last term is larger than this, so this will not be the sum. (In fact, the sum is this value added to the last term.)
3 0
3 years ago
Mr.Brown has a gate that measures 65 ft by 72 ft. He needs to reinforce the gate by placing a strip of wood on the diagonal of t
Daniel [21]

Answer: 97ft

Step-by-step explanation:

Pythagore

Strip^2 = 65^2 + 72^2 = 9409

Strip = squareroot 9409 = 97 ft

7 0
3 years ago
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