Howard must decide if he will purchase discount points for his mortgage. Two discount points which cost 2% of the mortgage amount will result in a 0.5% decrease in the interest rate. The terms of the mortgage are shown below. Howard's Mortgage $423,000 30 year fixed 5% annual rate 0 discount points M = $2,270.76 4.5% annual rate 2 discount points M = $2,143.28 Howard plans to stay in his house for about five years. Should Howard purchase the two discount points? Explain your reasoning.

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15

step-by-step explanation:

let pq = qr = rs = x, and xz = y and zu = z.

if the horizontal lines are parallel, then corresponding segments are in proportion:

substitute:

therefore 3 = y = z.

xu = y + z → xu = 3 + 3 = 6

130 degrees. i have no other way to explain