The coefficients are -7, 8, -3, 1, and -9
<span>Dawn was at 6 am.
Variables
a = distance from a to passing point
b = distance from b to passing point
c = speed of hiker 1
d = speed of hiker 2
x = number of hours prior to noon when dawn is
The first hiker travels for x hours to cover distance a, and the 2nd hiker then takes 9 hours to cover that same distance. This can be expressed as
a = cx = 9d
cx = 9d
x = 9d/c
The second hiker travels for x hours to cover distance b, and the 1st hiker then takes 4 hours to cover than same distance. Expressed as
b = dx = 4c
dx = 4c
x = 4c/d
We now have two expressions for x, set them equal to each other.
9d/c = 4c/d
Multiply both sides by d
9d^2/c = 4c
Divide both sides by c
9d^2/c^2 = 4
Interesting... Both sides are exact squares. Take the square root of both sides
3d/c = 2
d/c = 2/3
We now know the ratio of the speeds of the two hikers. Let's see what X is now.
x = 9d/c = 9*2/3 = 18/3 = 6
x = 4c/d = 4*3/2 = 12/2 = 6
Both expressions for x, claim x to be 6 hours. And 6 hours prior to noon is 6am.
We don't know the actual speeds of the two hikers, nor how far they actually walked. But we do know their relative speeds. And that's enough to figure out when dawn was.</span>
The known facts
- the sum of Natalie's age and Fred's age is 36
- the sum of Fred's age times four and Natalie's age is 72
Now, let's set up the equations where N is Natalie's age and F is Fred's age.
N + F = 36 ---- equation 1
N + 4F = 72 ---- equation 2
equation 2 minus equation 1 ---> 3F = 36 ---> F = 12, thus N = 24
Thus Fred is 12 years old, and Natalie is 24 years old.
Answer:
answer is in explanation
Step-by-step explanation:
Answer:
For not exact divisions: Writing the results as Quotient + Remainder over the Divisor.
For exact division: just the quotient.
Step-by-step explanation:
Hi there,
In both algorithms, for long and synthetic divisions we must write the result as an expression following that order:

When the Division leaves no Remainder, i.e. an exact, the Remainder is equal to zero, so

Check below for the algorithms for each division and the way of writing their expressions (results).