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2 years ago

Solve this system of equations using elimination with multiplication

Mathematics

1 answer:

romanna [79]2 years ago

5 0

Answer:

Step-by-step explanation:

3x - 4y = -11

x - 2y = -5

Compare the coefficients of the variables.

The coefficients of the x terms, 3 and 1, are multiples of each other.

The coefficients of the y terms, -4 and -2, are also multiples of each other.

That makes it easy to eliminate either variable.

I'll eliminate the y variables. Multiply the second equation by -2, then add it to the first equation:

₋-2x + 4y = 10

3x - 4y = -11

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

x + 0y = -1 , so x = -1.

Substitute -1 for x in either equation and solve for y:

3(-1) - 4y = -11

y = 2

(x,y) = (-1, 2)

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It took a car 4 days to travel 4717 miles. What was this car’s average speed, in miles per hour? (Round to the nearest per hour)

KiRa [710]

Answer:

51 MPH

Step-by-step explanation:

4 days is 96 hours, all you have to do is 4717/90

which is 51.41111 (with the 1 repeating) rounded to the nearest MPH (Nearest whole number) is 51

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2 years ago

An airline claims that 90% of the time, its planes are on schedule. If three flights are selected at random, what is the probabi

serg [7]

1. Check the tree diagram in the picture attached.

2. The blue segment represents "on time"
The red segment represents "not on time"

3. blue - blue - red represents the case 1st on time, 2nd on time, 3rd not on time.

the combined probability is 90/100*90/100*10/100=9/10*9/10*1/10=99/1000=0.099

4. Remark with a tree diagram we can tell anything asked about the probability of an experiment.

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3 years ago

What are the values of the plots on the number lines?

Elina [12.6K]

Answer:

14. - 15

Step-by-step explanation:

The first one is located at 14. The second one is located at - 15

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2 years ago

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

Read 2 more answers

Solve the following equation using the distributive property

Elanso [62]

Answer:

the awnser is either a or c

Step-by-step explanation:

i hope my awnser helps

7 0

2 years ago