The sum of the digits of a two-digit number is 13. the units digit is one more than twice the tens digit. find the number,

the sum of the digits of a three-digit number is 6. the hundreds digit is twice the units digit, and the tens digit equals to the sum of the other two. find the number.

1)49

2)231

Step-by-step explanation:

1)

4+9=13

4*2=8

8+1=9

2)

2+3+1=6

2+1=3

1*2=2

#1. 49 #2. 231

Step-by-step explanation:

#1. 4 x 2 + 1 =

8 + 1 =

9

add 40 + 9 = 49

#2. x + 2x + (x + 2x) = 6

6x = 6  

x = 1  

2x = 2

x + 2x = 3  

(2 x 100) + (3 x 10) + 1 or 231.

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(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240