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SVEN [57.7K]
3 years ago
5

Consider the function f (x) = StartLayout Enlarged left-brace first row negative StartFraction x + 5 Over x + 3 EndFraction, x l

ess-than negative 2 second row x cubed + 6, x greater-than-or-equal-to negative 2 EndLayout.
Which statement describes whether the function is continuous at x = –2?

The function is continuous at x = –2 because f(–2) exists.
The function is continuous at x = –2 because Limit as x approaches negative 2 plus f(x) = f(–2).
The function is not continuous at x = –2 because Limit as x approaches negative 2 f(x) ≠ f(–2).
The function is not continuous at x = –2 because Limit as x approaches negative 2 f(x) does not exist.

Mathematics
1 answer:
zalisa [80]3 years ago
8 0

Answer:

D

Step-by-step explanation:

Edge

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Which is the simplified form of the expression ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript nega
AlekseyPX

Answer:

The option "StartFraction 1 Over 3 Superscript 8" is correct

That is \frac{1}{3^8} is correct answer

Therefore [(2^{-2})(3^4)]^{-3}\times [(2^{-3})(3^2)]^2=\frac{1}{3^8}

Step-by-step explanation:

Given expression is ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript negative 3 Baseline times ((2 Superscript negative 3 Baseline) (3 squared)) squared

The given expression can be written as

[(2^{-2})(3^4)]^{-3}\times [(2^{-3})(3^2)]^2

To find the simplified form of the given expression :

[(2^{-2})(3^4)]^{-3}\times [(2^{-3})(3^2)]^2

=(2^{-2})^{-3}(3^4)^{-3}\times (2^{-3})^2(3^2)^2 ( using the property (ab)^m=a^m.b^m )

=(2^6)(3^{-12})\times (2^{-6})(3^4) ( using the property (a^m)^n=a^{mn}

=(2^6)(2^{-6})(3^{-12})(3^4) ( combining the like powers )

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=2^03^{-8}

=\frac{1}{3^8} ( using the property a^{-m}=\frac{1}{a^m} )

Therefore [(2^{-2})(3^4)]^{-3}\times [(2^{-3})(3^2)]^2=\frac{1}{3^8}

Therefore option "StartFraction 1 Over 3 Superscript 8" is correct

That is \frac{1}{3^8} is correct answer

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3 years ago
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Step-by-step explanation:

Use the Pythagorean theorem:

3^2+5^2 = c^2

34 = c^2

sqrt34 = c

5.83 = c

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