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3 years ago

1. 3x+y=52x-y=102. 2x+2y=3X-4y=-1

Mathematics

2 answers:

schepotkina [342]3 years ago

3 0

1. X=5 and Y=-15

2. X=1 and Y=0.5

PtichkaEL [24]3 years ago

3 0

1. Since y in first equation is positive and y in second equation is negative, the easiest was to solve this system is:
3x+y+2x-y=5+10
5x=15
x=3

Now use the x to find y:
3*3+y=5
9+y=5
y=5-9
y=-4

2. You can either multiply the first equation by 2 so that we get the same numbers in front of the y but with different signs or simply express one of the variables and write it in second one.
First way:
2x+2y=3 /*2(multyplying by 2)

4x+4y=6 (that's our first equation)
x-4y=-1 (that's our second equation)

now we just add the equations:
4x+4y+x-4y=6+(-1)
5x=6-1
5x=5
x=1

now we find y:
1-4y=-1
-4y=-1-1
y=-2/-4
y=1/2

Second way:
We express x from the second equation and get:
x=-1+4y
now we change x in the first equation with our new x:
2*(-1+4y)+2y=3
-2+8y+2y=3
10y=5
y=1/2

x=-1+4*(1/2)
x=-1+2
x=1

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The distance is 676,800 kilometers, which in scientific notation has a value of 6.748*10⁵ kilometers.

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A space shuttle travels at a speed of 28,200 kilometers per hour. Given that in 1 day there are 24 hours, it is possible to apply the following rule of three: if in 1 hour the space shuttle travels 28,200 kilometers, in 24 hours how much distance will the space shuttle travel?

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Scientific notation is a quick way to represent a number using powers of base ten. This notation is used to be able to express very large or very small numbers very easily.

The numbers are written as a product:

a*10ⁿ

where:

a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.
n is a whole number, which is called an exponent or an order of magnitude. Represents the number of times the comma is shifted. It is always a whole number, positive if it is shifted to the left, negative if it is shifted to the right.

To write the number 676,800 in scientific notation, perform the following steps:

The decimal point is moved to the left as many spaces until it reaches the right of the first digit. This number is then written, which will be the coefficient a in the expression of the previous product. In this case a=6.76800= 6.748

The base 10 is written with the exponent equal to the number of spaces that the comma moves. This is a positive number because the comma is shifted to the left. In this case n= 5

Then, <u><em>the distance is 676,800 kilometers, which in scientific notation has a value of 6.748*10⁵ kilometers.</em></u>

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3 years ago