The lines represented by the equations y=\frac{4}{5}x+8y= 5 4 ​ x+8 and 20y+25x=18020y+25x=180 are

Given:

The equations of lines are

To find:

The relation between two of lines.

Solution:

The slope intercept form of a line is

Where, m is slope and b is y-intercept.

We have,

       ...(i)

         ...(ii)

Equation (i) can be written as

            ...(iii)

On comparing (i) with slope intercept form, we get

On comparing (iii) with slope intercept form, we get

Now,

The product of slopes of both lines is -1. We know that the product of slopes of two perpendicular lines is -1.

Therefore, the given lines are perpendicular.

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b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.