A straight line is 180 degrees. As a result, 180-35=x, or x=145
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)
9514 1404 393
Answer:
14.9 cm
Step-by-step explanation:
To find c using the Law of Sines, you must know angle C. That is found from ...
C = 180° -A -B = 180° -150° -12° = 18°
Then the law of sines tells you ...
c/sin(C) = b/sin(B)
c = b·sin(C)/sin(B) = (10 cm)·sin(18°)/sin(12°)
c ≈ 14.9 cm
The answer should be n= 1500
Answer:
(-1)(11)(3)(5)
Step-by-step explanation:
First off: -165 separates into the factors (-1) and (165). Next, we divide 165 by 15, obtaining 15(11).
So far, we have (-1)(11)(15).
15 is still factorable. We get:
(-1)(11)(3)(5), which is the desired prime factorization of -165.
