Perpendicular lines. solve the problem with clear steps.

Original line: y=1/2x-9

Perpendicular lines have opposite slopes from the original lines. Since the original slope is 1/2, the perpendicular slope will be -2/1 or -2. The numbers switch places and switches from positive to negative.

New line: y=-2x+b

To solve for the y-intercept (b), plug the given coordinates (3,2) into the x and y spots in the equation:

2=-2(3)+b

Now, solve for b.

2=-6+b

Add 6 to both sides.

8=b

The y intercept is 8.

Now, your perpendicular line equation is:

y=-2x+8

I hope this helps :)

32/80  

91/140

the last one 54 doesn't go into 45. 54/100 ?

step-by-step explanation:

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81