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xenn [34]
3 years ago
11

When working with inequalities what do you do when its x squared > 16 and vice versa does the sign flip.

Mathematics
2 answers:
S_A_V [24]3 years ago
6 0

Answer:

x4

\{x\in \mathbb{R}|  \:\left(-\infty \:,\:-4\right)\cup \left(4,\:\infty \:\right)    \}

Step-by-step explanation:

x^2>16

x\sqrt{16}

x4

The interval notation will be:

\{x\in \mathbb{R}|  \:\left(-\infty \:,\:-4\right)\cup \left(4,\:\infty \:\right)    \}

The contrary,

x^2

is -4

guajiro [1.7K]3 years ago
6 0

No it doesn't flip. You split into two possible cases with two separate inequalities.

x^2 > 16

| x | > 4

And since now you are working with an absolute value, you split into 2 possible cases.

if x >= 0: then x > 4

if x < 0: then -x > 4

x < -4

FOR THE FIRST:

x ∈ (4, + ∞)

FOR THE SECOND:

x ∈ (-∞, -4)

Their UNITY is: x ∈ (-∞, -4) U (4, +∞)

And that's how you go about solving these. Hope I helped! :)

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The number 66 is increased to 72. What is the percentage by which the number was increased, to the nearest tenth of a percent?
Lunna [17]

Answer:

The increase is 9.1%

Step-by-step explanation:

<u>Step 1:  Make an equation </u>

66 * x = 72

66x = 72

<u>Step 2:  Divide both sides by 66 </u>

66x / 66 = 72 / 66

x = 1.09090

<u>Step 3:  Find the increased </u>

1 - 1.09090

0.091 * 100

9.1%

Answer:  The increase is 9.1%

6 0
3 years ago
Explain why a graph that fails the vertical-line test does not represent a function. Be sure to use the definition of function i
777dan777 [17]

Answer:

The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.

Step-by-step explanation:

The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.

I attached an Image you can visualize it clearly

P.S I ain't that good at drawing though :P

3 0
3 years ago
A country's population in 1995 was 164 million. in 2001 it was 169 million. estimate the population in 2015 using the exponentia
Vaselesa [24]
1995.          164 million
2001.          169 million
t = 2001 - 1995 = 6
169 =164 *  p^{6}
 p^{6} = \frac{169}{164}= 1.0304878 \\  p =  \sqrt[6]{1.0304878}
p = 1.00502
t 1 = 2015 - 2001 = 14
f ( t1 ) = 169 * 1.00502^{14}
f (t1) = 169 * 1.0762 = 181.27
Answer: a country´s population in 2015 will be 181 million.
4 0
3 years ago
How do I graph the solution
notsponge [240]
Make the circle closed and the > needs to be underlined

8 0
3 years ago
The graph of a system of equations will intersect at more than one point?
Bess [88]
I believe the answer is sometimes
6 0
3 years ago
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