I need step by step explanation for this!!

Explanation:

T = tens digit of original number

U = units digit of original number

"units digit" is the same as "ones digit"

The original number is in the form 10T+U. For example, let's say that T = 3 is the tens digit and U = 1 is the units digit. This means 10T+U = 10*3+1 = 31 is the original number. Though in this example, the digits don't add to 12.

To make the digits add to 12, we have the equation T+U = 12. This solves to U = 12-T which we'll use later.

The digits are reversed to get the new number 10U+T and this is 15 times the original tens digit, so

new number = 15*(original tens digit)

10U+T = 15T

from here we plug in U = 12-T which we found earlier. This effectively eliminates or gets rid of the U variable to leave us with T only

10U+T = 15T

10(12-T)+T = 15T replace U with 12-T

which we can now solve for T

10(12-T)+T = 15T

120-10T+T = 15T

-9T+120 = 15T

120 = 15T+9T ... adding 9T to both sides

120 = 24T

24T = 120

T = 120/24 divide both sides by 24

T = 5

The original tens digit is T = 5

The original units digit is U = 12-T = 12-5 = 7

So the original number is 10T+U = 10*5+7 = 57

Flipping the digits gets us 75 which is 15 times that of the original tens digit of 5. The original number has its digits add to 5+7 = 12. The answer has been confirmed.

Hey there!!

Basic formula :

√( x₂ - x₁ )² + (y₂ - y₁ )²

Coordinates :

R ( -1 , 3 ) ; S ( 3 , 3 ) ; T ( 5 , -1 ) ; U ( -2 , -1 )

Let us see the distance of the segment of RS

( x₂ = 3 , x₁ = -1 )  ( y₂ = 3 , x₁ = 3 )

√ ( 3 - ( -1 ) )² + ( 3 - 3 )²

√ ( 3 + 1 )² + ( 0 )²

√ ( 4 )² + 0

√ 16

= 4

First side = 4

Now, let us find the ST

( 3 , 3 ) ( 5 , - 1 )

( x₂ = 5 , x₁ = 3 ) ; ( y₂ = -1 , y₁ = 3 )

√ ( 5 - 3 )² + ( -1 - 3 )²

√ ( 2 )² + ( -4 )²

√ 4 + 16

√20

√4 × √5

the length of this side = 2√5 = 4.47

The length of TU :

( 5 , -1 ) ( -2 , -1 )

( x₂ = -2 , x₁ = 5 ) ; ( y₂ = -1 , y₁ = -1 )

√ ( -2 -5 )² + ( -1 + 1 )²

√ ( -7 )² + ( 0 )²

√ 49 = 7

The length of the third side = 7

The length of RU :

( -1 , 3 ) ( -2 , -1 )

( x₂ = -2  , x₁ = -1 ) ; ( y₂ = -1 , y₁ = 3 )

√ ( -2 + 1 )² + ( -1-4 )²

√ ( - 1 )² + ( -5 )²

√ 1 + 25

√26 = 5.09

The length of the fourth side = 5.09

Perimeter = 4 + 4.47 + 7 + 5.09

= 20.56

The perimeter = 20.56

Rounded off = 21 0r 20.6

Hope my answer helps!