Complete Question
Let P (n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The parts of this exercise outline a strong induction proof that P (n) is true for n ≥ 18.
Show statements P (18), P (19), P (20), and P (21) are true, completing the basis step of the proof.
Answer:
P(18) is true
P(19) is true
P(20) is true
P(21) is true
Step-by-step explanation:
a. When n = 18
18 cents can be formed using two 7cents and one 4cents
i.e. 2 * 7 + 4 = 18
So, P(18) is true
b. When n = 19
19 cents can be formed using one 7cents and three 4cents
i.e. 1 * 7 + 3 * 4 = 19
So, P(19) is true
c. When n = 20
18 cents can be formed using five 4cents
i.e. 5 * 4 = 20
So, P(20) is true
d. When n = 21
18 cents can be formed using three 7cents
i.e. 3 * 7 = 21
So, P(21) is true
Answer:
Yes they do.
Step-by-step explanation:
You know this because if they show up to the store with the same amount of money and SPLIT the amount of money for the cookies, they will still have the exact same amount.
I'm not very good with word problems but if I am correct it is 660 minutes so about 11 hours?
Answer:
Polynomial expression that represents the area of blanket:
If 
: 
Step-by-step explanation:
The area of the rectangle can be calculated with the formula:
Being l the lenght of the rectangle and w the width of the rectangle.
In this case, the lenght and the width are represented with:
Substitute them into :
Then:
Use Distributive property (Remember the Product of powers property: 
):
Add like terms:
(Simplied form)
Evaluate :
The 2 small black lines through the sides of the triangle indicate that the 2 sides are the same length.
Because the 2 sides are the same the 2 bottom angles are also the same.
This means that 9x +3 = 84
Now we can solve for x:
9x +3 = 84
Subtract 3 from each side:
9x = 91
Divide both sides by 9:
x = 81 / 9
x = 9
