(a) In triangle ABC, the line BD is perpendicular to AC. AD= (x + 6) cm, DC = (x + 2) cm and the height BD=(x + 1) cm. The area of triangle ABC is 40 cm? i) Show that x2 + 5x - 36= 0. ii) Solve the equation x2 + 5x – 36 = 0. iii) Calculate the length of BC.

The swimming pool is open when the high temperature is higher than 20∘c. lainey tried to swim on monday and thursday (which was 3 days later). the pool was open on monday, but it was closed on thursday. the high temperature was 30∘c on monday, but decreased at a constant rate in the next 3 days. write an inequality to determine the rate of temperature decrease in degrees celsius per day, d, from monday to thursday.

Celeste wants to have her hair cut and permed and also go to lunch. she knows she will need $50. the perm cost twice as much as her haircut and she needs $5 for lunch. how much does the perm cost?

I'm at a bookstore with $\$35$ in my pocket and a $20\%$-off coupon. what is the cost of the most expensive book i can buy with my money and the coupon? (assume that there are books of every possible price in the bookstore. it's a large bookstore! )