The location of point j is (-5,4). the location of point m is (10,-1). find the location of points k and l. point k is 2/5 of the way from j to m and point l is 4/5 of the way from j to m

The location of point K is (1 , 2)

The location of point L is (7 , 0)

Step-by-step explanation:

* Lets revise how to find the location of a point between two points

- If point (x , y) is between two points (x1 , y1) , (x2 , y2) at a ratio

 m1 from (x1 , y1) and m2 from (x2 , y2)

∴ x = [x1(m2) + x2(m1)]/(m1 + m2)

∴ y = [y1(m2) + y2(m1)]/(m1 + m2)

* Now lets solve the problem

- Point J is (-5 , 4) and point M is (10 , -1)

∵ Point K is 2/5 of JM

∴ m1 = 2 ⇒ ratio from K to J

∴ m2 = 5 - 2 = 3 ⇒ ratio from K to M

∴ x = [(-5)(3) + (10)(2)]/(2 + 3) = [-15 + 20]/5 = 5/5 = 1

∴ y = [(4)(3) + (-1)(2)]/(2 + 3) = [12 + -2]/5 = 10/5 = 2

* The location of point K is (1 , 2)

∵ Point L is 4/5 of JM

∴ m1 = 4 ⇒ ratio from K to J

∴ m2 = 5 - 4 = 1 ⇒ ratio from K to M

∴ x = [(-5)(1) + (10)(4)]/(2 + 3) = [-5 + 40]/5 = 35/5 = 7

∴ y = [(4)(1) + (-1)(4)]/(2 + 3) = [4 + -4]/5 = 0/5 = 0

* The location of point L is (7 , 0)

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)