Answer:
12/1 times 1/8 = 1.5
Step-by-step explanation:
You multiply 12 by 1 to get 12, then divide 12 by 8 to get 1.5
You can solve this either just plain algebra or with the use of trigonometry.
In this case, we'll just use algebra.
So, if we let M be the the point that partitions the segment into a ratio of 3:2, we have this relation:
KM/ML = 3/2
KM = 1.5 ML
We also have this:
KL = KM + ML
Substituting KM,
KL = (3/2) ML + ML
KL = 2.5 ML
Using the distance formula and the given coordinates of the K and L, we get the length of KL
KL = sqrt ( (5-(-5)^2 + (1-(-4))^2 ) = 5 sqrt(5)
Since,
KL = 2.5 ML
Substituting KL,
ML = (1/2.5) KL = (1/2.5) 5 sqrt(5) = 2 sqrt(5)
Using again the distance formula from M to L and letting (x,y) as the coordinates of the point M
ML = 2 sqrt(5) = sqrt ( (5-x)^2 + (1-y)^2 ) [let this be equation 1]
In order to solve this, we need to find an expression of y in terms of x. We can use the equation of the line KL.
The slope m is:
m = (1-(-4))/(5-(-5) = 0.5
Using the general form of the linear equation:
y = mx +b
We substitue m and the coordinate of K or L. We'll just use K.
-5 = (0.5)(-4) + b
b = -1.5
So equation of the line is
y = 0.5x - 1.5 [let this be equation 2]
Substitute equation 2 to equation 1 and solving for x, we get 2 values of x,
x=1, x=9
Since 9 does not make sense (it does not lie on the line), we choose x=1.
Using the equation of the line, we get y which is -1.
So, we get the coordinates of point M which is (1,-1)
Answer:
Therefore his average speed for the entire trip is 8 mph.
Step-by-step explanation:
Given, In 50 minutes Luis traveled uphill to gift store at 6 mph.
6 mph means in 1 h= 60 minutes Luis can covered 6 mile.
In 1 minutes Luis can covered 
mile.
In 50 minutes Luis can covered 
mile
= 5 mile
Again when he come back at home, the speed was 12 mph.
12 mph means in 1 h= 60 minutes Luis can covered 12 mile.
Therefore he traveled 12 mile in 60 minutes
He traveled 1 mile in 
minutes.
He traveled 5 mile in 
minutes
= 25 minutes.
Total distance for the entire trip is =(5+5) mile=10 mile
Total time for the entire trip is = (50+25) minutes = 75 minutes
m/min
mph
= 8 mph
Therefore his average speed for the entire trip is 8 mph.
