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2 years ago

What value of n makes the equation true?

Mathematics

1 answer:

Anastasy [175]2 years ago

5 0

Answer:

Step-by-step explanation:

$(4^{3} /4)^{3} = 4^{n} \\(4^{2})^{3} = 4^{n} \\4^{6} = 4^{n} \\n=6$

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Algebra help please

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3 years ago

How many times does 16 go in 41

charle [14.2K]

41/16
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3 years ago

Activity 1 Calculate the following: 1. 68% of 418,

il63 [147K]

Answer:

284.24

Step-by-step explanation:

by multiplying 0.68 to 418 we get 68% of 418

7 0

2 years ago

Read 2 more answers

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

2 years ago

Read 2 more answers

.The endpoints of AB are A(1,4) and B(6,-1).

Brums [2.3K]

Answer:

5√2

Step-by-step explanation:

Finding distance :-

d = √{ ( 1 -6)² + (4+1)²}
d = √{ -5² + 5² }
d = √{ 25 + 25}
d = √50
d = 5√2

4 0

2 years ago

What value of n makes the equation true?​

What value of n makes the equation true?