A certain state charges a 12% tax rate on incomes up to $25,000 and 16% on income beyond that. If Rachel makes $33,000 per year, how much income tax will she pay?

$4,280

Step-by-step explanation:

If the state charges 12% on incomes up to $25,000, that means you pay that rate on the first $25,000 you make, regardless of your total income. 0.12⋅25,000=3,000, so that's how much Rachel would pay on her *first* $25,000. Now she also has to pay the higher rate of 16% on any income beyond that level. Her total income is $33,000 so subtracting $25,000 will give us her income beyond that level: $33,000−$25,000=$8,000. At the higher rate, she would pay 0.16⋅$8,000=$1,280 on that income. Her total income tax would be 3,000+1,280=$4,280 .

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2