Math 121, Quiz 1, September 24, 2004
Name: Hints and Answers
Instructions. Do all problems, and show all of your work. Calculators are not allowed.
1. (2 pts) Solve the equation 5(t−3) = 2t+ 12.
Answer. 5(t−3) = 2t+ 12 implies 5t−15 = 2t+ 12 implies 3t= 27 implies t= 9.
2. (2 pts) Solve the equation 9|x+ 4| − 5 = 31.
Answer. The equation implies 9|x+ 4|= 36. Therefore, |x+ 4|= 4 and so x+ 4 = 4 or
x+ 4 = −4. Therefore, x= 0 or x=−8.
3. (2 pts) A messenger ran at 8 miles per hour from his residence to the King’s palace, he
walked back at 3 miles per hour. The total trip took him 11 hours. How far is it from the
messenger’s residence to the King’s palace?
Answer. Let tbe time it took the messenger to run to the King’s palace, and let dbe the
distance one direction. Then d= 8t(running there) and d= 3(11−t) walking back. Therefore,
8t= 3(11 −t) and so 11t= 3(11) which implies t= 3 hours. Therefore, the distance from the
residence to the King’s palace is 3(8) = 24 miles.
4. (2 pts) Solve the equation A=1
2h(b1+b2) for b2.
Answer. A=1
2h(b1+b2) implies b1+b2=2A
himplies b2=2A
h−b1implies b2=2A−b1h
h.
5. (2 pts) Write the complex number 3−2i
4+5iin standard form.
Answer. Multiply numerator and denominator by complex conjugate and simplify:
(3 −2i)(4 −5i)
(4 + 5i)(4 −5i)=12 −23i+ 10i2
41 =2−23i
41 =2
41 −23
41i.