Mark each of the following statements as true or false (inappropriate notation should fall under "false").
a. 14 = 25 mod 11
b. 14 ≡ 25 (mod 11)
c. 14 = 3 mod 11
d. 14 ≡ 3 (mod 11)
e. 3 = 14 mod 11
f. 3 ≡ 14 (mod 11)
g. 3 ≡ 14 mod 11
h. 3 = 14 (mod 11)

a.False

b.True

c.False

d.True

e.True

f.True

g.False

h.False

Step-by-step explanation:

a.The quotient of 25/11 =2, 25-2*11=3 not 14

b.25/11 and 14/11 have the same remainder which is 3

c.The quotient of 3/11 =0, 3-0*11=3 not 14

d.14/11 and 3/11 have the same remainder which is 3

e.The quotient of 14/11 is 1, 14-1*11=3

f.14/11 and 3/11 have the same remainder which is 3

g.Incorrect expression

I. Incorrect expression

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17   {equation 1}

xy = -24         {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6   or     y = (-17-1)/6

y = -16/6           or     y = -18/6

y = -2 2/3         or   y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation: