Find the value of d for which the graph of x-4y=9 will be perpendicular to the graph of dx-12y=14

Start by getting the equation x-4y=9 into y=mx+b form by isolating the y.

*Subtract x from both sides*

-4y=-x+9

*Divide both sides by -4*

y=1/4x-9/4

Do the same thing with the other equation dx-12y=14.

*Subtract dx from both sides*

-12y=-dx+14

*Divide both sides by -12*

y=d/12x-7/6

Graphs are perpendicular when their slopes are negative reciprocals.  The negative reciprocal of 1/4 is -4.  Therefore, d/12 must equal -4:

d/12=-4

*Multiply both sides by 12*

d=-48

Hope this helps!!

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19

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.