3.Sum of digits of a two digit number is 14. When 18 is added to the original number, then the new number is obtained by exchanging the digits of the original number. Express the statements in equation.

let the numbers be xy

general form of the number =10x+y

sum of digits of a number =14

x+y=14………[1]

if 18 is added to the number, then digits are interchanged

10x+y+18=10y +x

9x-9y=-18

X-y=-2………[2]

the linear equations are 1) x+y=14

2) X-y=-2

adding [1],[2]

2x=12

x=6

x+y=14

y=14-x

y=14-6

y=8

there fore the number =10*6+8

=68

check:-

1)6+8=14

2)68+18=86

I hope this helped!

Step-by-step explanation:

8

step-by-step explanation:

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)