Answer:
Slant height = 7.07 ft to nearest hundredth.
Step-by-step explanation:
The slant height = height of one of the triangular sides
Using Pythagoras:
S^2 = 1/2 * 10^2 + 10^2 = 50 ft.
S = √50 = 7.071
Answer:
12
Step-by-step explanation:
When n teams play each other once, the total number of games is n(n-1)/2. Since each team played every other one 3 times, the relationship between number of teams (n) and number of games is ...
3(n(n-1)/2) = 198
n(n-1) = 132 = 12·11 . . . . . . multiply by 2/3 and factor
n = 12 . . . . . . n = -11 is also an extraneous solution to this quadratic equation
12 teams participated in this championship.
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)
|2(-5) - 1| + 10
|-10-1| + 10
|-11| + 10
11 + 10
21 is your answer
Hope this helped!
