The distance between the lines: 4x+3y-11 and 8x+6y=15 is​

The distance between the lines: 4x+3y-11 and 8x+6y=15 is​

Step-by-step explanation:

You have two parallel and different lines. The form of the implicit equations is:

A*x + B*y + C= 0

A'*x + B'*y + C'=0

Since the two lines are parallel, the coefficients of their general equations must satisfy that the slopes are equal.

Therefore, the equations can be transformed so that the coefficients A and B are equal, multiplying or dividing one of them by a constant.

So, the distance between two lines can be expressed as follows:

In this case, you have:

Then, you have:

Replacing in the definition of distance:

Solving:

The distance between the lines: 4x+3y-11 and 8x+6y=15 is​

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

b

step-by-step explanation: