30)

31)
a simple case for that would just be, using an equation with an imaginary value, let's do so

when you get a "solution" or zero with an "i" or an imaginary value, is just a way to say, there's really no solution, the function never touches the x-axis
Answer:
15
Step-by-step explanation:
multiply both sides by 15
45x=675
Divide both sides by 45
x=15
Let the weight of the full Volume of nails in the box be W.
Let the weight of the box be B.
2/3 W + B = 130 ........i From the first statement.
3/8 W + B = 74 ......ii From the second statement.
Equation (i) Minus (ii)
2/3 W - 3/8 W + B - B = 130 - 74
(16W - 9W) / 24 = 56
7W / 24 = 56.
W = 56 * 24 / 7
W = 192 Pounds.
Substituting V = 64 in equation (i)
2/3 W + B = 130
2/3 * 192 + B = 130
2 * 64 + B = 130
128 + B = 130
B = 130 -128 = 2.
Therefore, weight of box, B = 2 pounds.
Answer:
<em>Proof below</em>
Step-by-step explanation:
Let's assume a is a type 1 integer. By definition, it means we can find an integer n such that
a=3n+1
We need to prove
is a type 1 integer
Expanding

If
is a type 1 integer, then we should be able to find an integer m such as

Equating

solving for m

Since we know n is an integer, then the expression of m gives an integer also. Having found the required integer m, the assumption is proven