Find the area. 7 m 4 m 4 m square meters

Use complete sentences to describe why √-1 ≠ -√1

tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

$\displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }$

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

$\displaystyle \large{ {a}^{2} = a \times a = |b| }$

Where b is the result from a×a. Let's see an example.

Examples

$\displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}$

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

$\displaystyle \large{ {y}^{2} = - 1}$

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

$\displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }$

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

$\displaystyle \large{ \sqrt{ {x}^{2} } = |x| }$

Solving absolute value always gives the plus-minus. Therefore...

$\displaystyle \large{ y = \pm \sqrt{ - 1} }$

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

$\displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }$

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

5 0

3 years ago

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Combine like terms to find X 7x+=9x-3

blondinia [14]

Answer:x = -1.5

Step-by-step explanation:

Simplifying

7x + -9x = 3

Combine like terms: 7x + -9x = -2x

-2x = 3

Solving

-2x = 3

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '-2'.

x = -1.5

Simplifying

x = -1.5

4 0

2 years ago

A town population has been increased at a constant rate. in 2010 the population was 46,020. by 2012 the population had increased

baherus [9]

Answer:

1

Step-by-step explanation:

s he crossed toward the pharmacy at the corner he involuntarily turned his head because of a burst of light that had ricocheted from his temple, and saw, with that quick smile with which we greet a rainbow or a rose, a blindingly white parallelogram of sky being unloaded from the van—a dresser with mirrors across which, as across a cinema screen, passed a flawlessly clear reflection of boughs sliding and swaying not arboreally, but with a human vacillation, prod

themselves, Akakiy Akakievitch indulged in no kind of diversion.”

Yeah, I love sentences too. That’s why I created this online course in how to write a better sentence.

7 0

2 years ago

In a parking garage the number of suv's is 40% greater than the number of automobiles. there are 98 suv's. how many automobiles

chubhunter [2.5K]

A=automobile S=SUV
0.4A+A=98 (to change a percent to a decimal you move the decimal point two places to the right)
1.4A=98 (I combined like terms)
A=70 (divided each side by 1.4)

3 0

3 years ago

Sombody plssssssssss answer it (100) points

Bess [88]

Answer:

try doing the 3rd option

Step-by-step explanation:

we know x is the missing value

x+3=8

so what plus 3 equals 8?

Well 5 of course

So x= 5

5+3=8

6 0

2 years ago

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