Sixty is twenty less than twice a number "x" . find "x"

Final question for my homework

zubka84 [21]

20% = 0.20

- - 0.20 = 0.80

28*0.80 = 22.40

22.40-2 = 20.40

it cost $20.40

6 0

3 years ago

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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.

5 0

2 years ago

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The number of gift baskets Nikki can make varies directly with the amount of time she spends making the baskets . She can make 1

scoundrel [369]

Answer:

40

Step-by-step explanation:

The number of gift baskets Nikki can make varies directly with the amount of time she spends making the baskets .

Let n be the number of baskets and let t be the mount of time it takes to make the basket. This means that:

n α t

=> n = kt

where k = constant of proportionality

She can make 4 baskets in every 1/2 hour.

This means that:

4 = k * 1/2

=> k = 4 * 2 = 8 baskets per hour

The time is now 5 hours (t = 5). Therefore:

n = 8 * 5 = 40 baskets

She can make 40 baskets in 5 hours.

8 0

3 years ago

Suppose you are constructing a scale model solar system using a scale ratio of 1 to 10 billion. In your scale model what will be

Shkiper50 [21]

Answer:

Step-by-step explanation:

First convert km to meters

143000 km = 143,000,000m = 1.43*10^8 m

Now convert 10 billion to scientific notation1 00

10 billion = 1 * 10^10

What this means is that 1 * 10^10 meters in outer space = 1 meter for the scale model.

Now show what the ratio is for

1.43*10^8

======== Divide by the denominator

1 * 10^10

1.43 * 10^(8 - 10)

1.43 * 10 ^ - 2 meters

Answer: 0.0143m or B

6 0

2 years ago

Judah deposited $450 into an account that earns simple interest, and after 4 years, the interest in the account was 90$. What wa

guapka [62]

Answer:

$22.50 I think I'm not 100% sure, Im sorry

Step-by-step explanation:

90/4 is 22.5 a year

4 0

2 years ago