An integer may be a multiple of 3.
An integer may be 1 greater than a multiple of 3.
An integer may be 2 greater than a multiple of 3.
It is redundant to say an integer is 3 greater than a multiple of 3 (that's just a multiple of 3, we've got it covered). Same for 4, 5, 6, 7...
Let's consider a number which is a multiple of 3. Clearly, we can write 3+3+3+3+... until we reach the number. It can be written as only 3's.
Let's consider a number which is 2 greater than a multiple of 3. If we subtract 5 from that number, it'll be a multiple of 3. That means we can write the number as 5+3+3+3+3+... Of course, the number must be at least 8.
Let's consider a number which is 1 greater than a multiple of 3. If we subtract 5 from that number, it'll be 2 greater than a multiple of 3. If we subtract another 5, it'll be a multiple of 3. That means we can write the number as 5+5+3+3+3+3+... Of course, the number must be at least 13.
That's it. We considered all the numbers. We forgot 9, 10, 11, and 12, but these are easy peasy.
Beautiful question.
Answer:
White = 1.67 gallons
Blue = 0.33 gallons
Step-by-step explanation:
White : blue = 3 : 1
Total ratio = 3 + 1
= 4
Gallons = 2
White = 3 /4 × 2
= 6 /4
= 3/2 gallons
Blue = 1 / 4 × 2
= 2/4
= 1/2
If he later decide to dilute the color to a ratio of 5:1
Total ratio = 5 + 1
= 6
Total gallons = 2
White = 5 / 6 × 2
= 10/6
= 5/3 gallons
Or
= 1.67 gallons
Blue = 1 / 6 × 2
= 2 / 6
= 1/3 gallons
Or
= 0.33 gallons
Answer:
x² + (y + 8)² = 81
Step-by-step explanation:
Centre (h,k) = (0,-8)
radius (r) = 9
(x - h)² + (y - k)² = r²
(x - 0)² + (y + 8)² = 9²
x² + (y + 8)² = 81
