Find the equation of a line passing through the point (2,3), and perpendicular to the line with equation 3y-6x=4? The answer in the book is 2y- x-8=0 and I don't know how I am always getting this wrong. My working out has been rearranging the first equation and finding that the gradient is -2.

Having a -2 gradient means, m1 (in this case, -2) x m2 = -1, thus m2 must be 1/2.

Then doing, y-3= 1/2(x-2)

thus giving me 2(y-3)=1(x-2)

2y - 6 = x -2

rearranging to give me: 2y = x + 4

I understand if rearranged to other form it would be, 2y -x -4 = 0 but I don't know how it is -8?

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

see below

step-by-step explanation:

x+2> 6

subtract 2 from each side

x+2-2 > 6-2

x > 4

there is an open circle at 4 since is it is greater than and the line goes to the right