a : b : c = 12 : 10 : 15. To explain, if b is defined as two-fifths of c, denoting this relationship as b =

, it follows that 2c = 5b. Substituting yields c =

. Similarly, with 4a = 3c, we can express a as

. By manipulating these fractions, we find a : c =

:

, simplifying to 4:5. For b and c, from prior relationships, b:c =

:

simplifies to 2:3. Noticing that if b equals 15, we derive a : c = 12 : 15 and b : c = 10 : 15, which leads us to the simplified ratio of a : b : c = 12 : 10 : 15.
When faced with a pile of pennies, if I need to determine whether the count is even or odd without actual counting, I understand that even numbers are divisible by 2, while odd numbers are not. I would arrange the pennies into two rows and form pairs of 2. If there's an additional penny left after pairing, this signifies an odd total; conversely, if all can be paired off, then the number is even.
I have provided the graphs for the functions f(x) (depicted in blue) and g(x) (depicted in red) in the attached PDF file.
The questions to address are:
1) Determine u(1) and
2) Determine v(1)
Solutions:
1) u(x) = f(x) g(x) => u(1) = f(1) * g(1)
Based on the graphs, when f(1) equals 1 and g(1) equals 2, then the product f(1)*g(1) gives us 1*2 = 2
Answer: 22) v(x) = f(x) / g(x) => v(1) = f(1) / g(1) = 1 / 2 = 0.5
Answer: 0.5
Given: The angle < CEB is divided by EF.
< CEF = 7x +31.
< FEB = 10x -3.
We will find the values of x and the measures of < FEB, < CEF, and < CEB.
Solution: The angle < CEB is divided into two angles < FEB and < CEF.
Therefore, < FEB is equal to < CEF.
By substituting the values of < FEB and < CEF, we obtain:
10x -3 = 7x +31
By adding 3 to both sides, we have:
10x -3 +3 = 7x +31 +3.
Thus, 10x = 7x + 34
After subtracting 7x from both sides, we conclude:
10x -7x = 0 + 34.
This simplifies to 3x = 34.
Dividing both sides by 3 yields:
x = 11.33.
Substituting x=11.33 into < CEF = 7x +31 gives us:
< CEF = 7(11.33) +31 = 79.33 +31 = 110.33.
< FEB = < CEF = 110.33 (approximately)
< CEB = < FEB + < CEF = 110.33 +110.33 = 220.66 (approximately)