In a two-digit number the units’ digit is 7 more than the tens’ digit. the number with digits reversed is three times as large as the sum of the original number and the two digits. find the number.

  18

Step-by-step explanation:

Let t and u represent the tens digit and the units digit, respectively. The problem statement lets us write equations relating these variables.

  u = t + 7 . . . . the units digit is 7 more than the tens digit

  10u +t = 3(10t +u +t +u) . . . . the number with digits reversed is 3 times ...

The second equation can be simplified to ...

  10u +t = 33t +6u . . . . eliminate parentheses

  4u = 32t . . . . . add -6u-t

  u = 8t . . . . . . . . divide by 4

Equating the two expressions for u, we have

  t +7 = 8t

  7 = 7t . . . . subtract t

  1 = t . . . . . divide by 7

  u = 8t = 8 . . . . find the value of u

  (t, u) = (1, 8)

The two-digit number is 18.

hi there!

question 1 answer: p/q can be terminating when q = 5^m * 2^n

question 2 answer: -1 and -1

question 3 answer: -4

question 4 answer: 5/12

hope this : )

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)