You can use a pencil and either long or short division, or
you can punch them into your calculator.
You can forget about them being "rational numbers".
That fact doesn't have any effect on how you divide them.
All the numbers you've ever worked with until this year have
been rational numbers, but nobody ever gave them that name
before.
If a number is written down in front of you, on paper or on the
screen, then it's a rational number.
The answer is B
The answer is B
Answer:
1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18 and 23 cents cant be made with 5-cents and 7-cent postage.
Step-by-step explanation:
You can make any multiple of 5 with those stamps. Also, you can make any number x with stamps proven that that number is big enough. If you start with a number that is a multiple of 5, then you can increase that number by 2 each time you replace a 5 with a 7 (in each example, we are starting in a postage of value 5j made by 5-cent stamps):
- If x = 5j + 1, for an integer j, (j ≥ 4), then you can replace 4 five cent stamps with 3 7 cent stamps, to obtain x.
- If x = 5j + 2, you can replace 1 five cent stamp with one seven cent stamp to obtain x (j≥1)
- If x = 5j+3, you can replace 5 five cent stamps with 4 seven cent stamps to obtain x (j ≥5).
- If z = 5j+4, you can replace 2 five-cent stamps with 2 seven-cent stamos to obtain x (j≥2)
Note therefore, that if j is at least 5, then we can obtain a postage with value x. This means that any postage of value at least 25 can be made witg five-cent of seven-cent stamps. Lets see for smaller values
- 1, 2, 3 and 4 cent postage are impossible to make
- 5 cent package is possible, so is 7
- 6,7, 8 and 9 are impossible to make (any package with at least 2 stamp has a value at least 10)
- 10 is possible (5+5)
- 11 is not possible (5+5 = 10, 5+7 = 12)
- 12 is possible (5+7)
- 13 is impossible (5+7 = 12, but 7+7 = 14. Also any combination of 3 stamps has a value at least 15)
- 14 is possible (7+7)
- 15 is possible (5+5+5)
- 16 is not possible (5+5+5 = 15, 5+5+7 = 17)
- 17 = 5+5+7 is possible
- 18 is not possible (5+7+7 = 19, and any postage with 4 stamps has a value of 20 or higher)
- 19 = 5+7+7 is possible
- 20 = 5+5+5+5 is possible
- 21 = 7+7+7 is possible
- 22 = 5+5+5+7 is possible
- 23 is not possible (you cant reach 23 with 3 stamps, and you will get a value at least 25 with 5. If you use 4 stamps, you can obtain only even values)
- 24 = 5+5+7+7 is possible
So we conclude that the amounts of postage that are impossible to make are: 1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18 and 23 cents.
These equations that are neither parallel nor perpendicular.