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Gelneren [198K]
3 years ago
6

Rewrite f(x) = -(x + 3)2 - 1 from vertex form to standard form. (2 points)

Mathematics
1 answer:
Mandarinka [93]3 years ago
6 0

Answer:

f(x) = -x^2 - 6x - 10

Step-by-step explanation:

Please write the original equation as  f(x) = -(x + 3)2 - 1, as "(x + 3)2 is meaningless.  We want:

f(x) = -(x + 3)^2 - 1, where " ^ " denotes exponentiation.

Expanding this, we get:

f(x) = -(x^2 + 6x + 9) - 1, or

f(x) = -x^2 - 6x - 9 - 1, or:

f(x) = -x^2 - 6x - 10          This matches the first answer choice.

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Water is added or drained from a tank each day. The first day, 910 of a gallon is added to the empty tank. The second day, 710 o
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Answer:

The quantity of water in the tank after 15 days is 1610.0 gallons OR 1.61 × 10³ gallons.

Step-by-step explanation:

The amount of water in the tank after 15 days is given by the series

910+(−710)+810+(−610)+⋯+310+(−110)+210

From the series, we can observe that, if water is added for a particular day then water will be drained the following day.

Also, for a day when water is to be added, the quantity to be added will be 100 gallon lesser than the quantity that was last added. Likewise, for a day when water is to be drained, the quantity to be drained will be 100 gallons lesser than the quantity that was last drained.

Hence, we can complete the series thus:

910+(−710)+810+(−610)+710(-510)+610(-410)+510(-310)+410(-210)+310+(−110)+210

To evaluate this, we  get

910-710+810-610+710-510+610-410+510-310+410-210+310-110+210

= 1610.0 gallons

Hence, the quantity of water in the tank after 15 days is 1610 gallons OR 1.61 × 10³ gallons.

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