What is the solution of the quadratic equation. Equation: 2x + 7x

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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Examine the table of equivalent ratios and complete this statement. For 5 servings, the ratio of cups of water to cups of juice

shepuryov [24]

Answer:

Step-by-step explanation: This is five-fold proportion

The first ratio gives solution namely

We will write general proportion

a:b= c:d= e:f = g:h= i:j = k

According to this the first ratio gives coefficient k

When we divide 24/2 =12 our coefficient k=12

In the second ratio we will multiply 3 with 12 and get 36.

In the third ratio we will multiplu 5.5 with 12 and get 66.

In the fourth we will divide 108 with 12 and get 9.

In the fifth we will multiply 15 with 12 and get 180.

Finally the ratio is 24:2=36:3=66:5.5=108:9=180:15

3 0

3 years ago

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Write a ratio that is equivalent to 3:5, other than 3:5 itself

natulia [17]

Answer:

9:15

Step-by-step explanation:

$\frac{3*3}{5*3}=\frac{9}{15}=9:15$

7 0

3 years ago

Help with algebra 2 I can’t figure out how to solve the problem .

defon

Answer: D

Step-by-step explanation:

Using the equation plot in the coordinates of the points to see if they fit the equation.

5x-3y < 30

A) 5(-3) -3(5) < 30

-15 -15 < 30

-30 < 30 This is true

B) 5(0) -3(0) < 30

0 - 0 < 30

0< 30 This is true

C) 5(-5) - 3(3) < 30

-25 - 9 < 30

-34 < 30 This is also true

D) 5(3) - 3(-5) < 30

15 + 15 < 30

30 < 30 This is not true because 30 is not greater that 30

3 0

3 years ago

Calculate the length of the altitude (h) of the rhombus

allochka39001 [22]

Answer:

h = 15

Step-by-step explanation:

Use Pythagorean Theorem to solve for h.

a² + b² = c²

8² + h² = 17²

64 + h² = 289

h² = 225

h = 15

7 0

3 years ago

What is the solution of the quadratic equation. Equation: 2x + 7x - 5= 10