1. Demonstrate the validity of the following identities by means of truth tables: (5 pts each) a. DeMorgan’s theorm for three variables: (x+y+z)’ = x’y’z’ And (xyz)’ = x’+y’+z’ b. The distributive law: x+yz = (x+y)(x+z)

All the three statements presented are indeed valid and satisfy the De Morgan's theorem.

Step-by-step explanation:

The truth tables are presented in the attached images.

a) The statement (X + Y + Z)' = (X'Y'Z') has its proof in the first image attached.

b) The statement (XYZ)' = (X' + Y' + Z') has its proof in the second image attached.

c) The statement (X + YZ) = (X + Y)(X + Z) has its proof in the third image attached.

the answer is 31.27mph

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.