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3 years ago

Please assist me with this problem

Mathematics

2 answers:

timurjin [86]3 years ago

7 0

Answer:

y = sqrt(5)

x = sqrt(10)

Step-by-step explanation:

y = sqrt(5)

Opposite angles are equal

x is the hypotenuse

x² = 5 + 5

x² = 10

x = sqrt(10)

Verizon [17]3 years ago

3 0

<h3>Answers:</h3><h3>x = sqrt(10)</h3><h3>y = sqrt(5)</h3>

============================================

Explanation:

Naturally I start with x as that letter precedes y in the alphabet; however, it's easier to start with y because it is a leg of this triangle. We will then use the value of y to find x later.

For any 45-45-90 triangle, the two legs are the same length. So that's why we're able to quickly see that y = sqrt(5)

To get the hypotenuse, we multiply the leg length by sqrt(2). This trick only works for 45-45-90 triangles.

hypotenuse = leg*sqrt(2)

x = sqrt(5)*sqrt(2)

x = sqrt(5*2)

x = sqrt(10)

The rule I used is sqrt(a)*sqrt(b) = sqrt(a*b)

----------------

An alternate path is to use the pythagorean theorem to find x

a^2+b^2 = c^2

(sqrt(5))^2 + (sqrt(5))^2 = x^2

5 + 5 = x^2

10 = x^2

x^2 = 10

x = sqrt(10)

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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.

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2 years ago

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(1) 1 - 6

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3 years ago

What is greater 5/8 or 60%

luda_lava [24]

Answer: 5/8 :)

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What does a equal -5(6a+21)=-15

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Step 1 : Simplify both sides
-5(6a+21)=-15
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Please assist me with this problem​

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