Answer:
x ≈ 3.9
Step-by-step explanation:
Call the segment shared by the two triangle "y". The Pythagorean theorem tells you ...
sum of squares of sides = square of hypotenuse
y² +6² = 10²
x² +7² = y²
Substituting for y² using the second equation, we get ...
x² +7² +6² = 10²
x² = 10² -7² -6² = 100 -49 -36 = 15
Taking the square root, we find ...
x = √15 ≈ 3.9
Answer:
x = 13y + 0.625
Step-by-step explanation:
4(2x - 3y) = y + 5
8x - 12y = y + 5
8x = y + 5 + 12y
8x = 5 + 13y
8x ÷ 8 = 5 + 13y ÷ 8
x = 5 + 13y ÷ 8
x= 13y + 5 ÷8
x = 13y + 0.625
ANSWER
EXPLANATION
The given rational function is
We need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of
which is
When we rationalize we obtain:
The denominator is now a difference of two squares:
We apply this property to get
This simplifies to
Or
<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>
