Answer:f in the chat
Step-by-step explanation:
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:
○ 4⁄6, -4⁄6
Step-by-step explanation:
Take the square root of both the denominator and numerator, and you will get the above two answers.
I am joyous to assist you anytime.
To solve for c, you need to get c onto one side of the equation, or make it c=__. So what I would do first is subtract a/b from both sides
a/b + c = d/c
-a/b
a/b - a/b + c = d/c - a/b
c = d/c-a/b
Answer: z = 3
Step-by-step explanation: To solve this equation for <em>z</em>, we can first combine our like terms on the left side of the equation. Since 12 and 7 both have <em>z</em> after their coefficient, we can subtract 12z - 7z to get 5z.
Now we have 5z - 2 = 13.
To solve from here, we add 2 to the left side of the equation in order to isolate 5z. If we add 2 to the left side, we must also add 2 to the right side. On the left side, the -2 and +2 cancel out. On the right, 13 + 2 simplifies to 15.
Now we have 5z = 15.
Solving from here, we divide both sides of the equation by 5 to get <em>z</em> alone. On the left side, the 5's cancel out and we are simply left with <em>z</em>. On the right side, 15 divided by 5 simplifies to 3 so we have z = 3.