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:
2x<20 (divide both sides by 2, same as you would if an = were between them)
x<10 or B
Complete Question:
Lenny asked 125 randomly chosen seventh grade students at his school to name their favorite beverage there are 1500 seventh grade students in the school predict the number of seventh grade students in his schoolwhose favorite food is pizza. 58 of the 125 students likes pizza.
Answer:
n = 696
Step-by-step explanation:
Sample size = 125
number of students out of the 125 that like Pizza = 58
Probability that a student will like pizza, P = 58/125
P = 0.464
Since there are 1500 seventh grade students in the school, based on the probability that a student likes pizza = 0.464, number of seventh grade students in the school that like pizza will be:
n = 100 * P
n = 1500 * 0.464
n = 696
Answer:
liner
Step-by-step explanation:
they look like a line on a graph
