What is the intersection of the lines y=4x+1 and y= -2x + 4

The intersection is point is (1/2 , 3)

Step-by-step explanation:

y = 4x + 1

y = -2x + 4

Next, move the x's to the side of the y's and change the positive to negative and vice versa.

y - 4x = 1

y + 2x = 4

Then, multiply the top or bottom equation by -1

-y + 4x = -1

y + 2x = 4

Or

y - 4x = 1

-y - 2x = -4

Then, subtract the y or add them to erase the y's

4x =  -1

2x = 4

Or

-4x = 1

-2x = -4

Next, add or subtract the x's and what they equal

6x   = 3

Or

-6x = -3

Then, find x

3/6x = 1/2

Or

-3/-6x = 1/2

x = 1/2

Finally, substitute 1/2 into one of the 2 equation

y= 2+1

y = 3

Or

y = -1 +4

y = 3

and get the point of (1/2 , 3)

Thanks for the Question

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl