1) If the sides of a square are lengthened by 5cm, the area becomes 81cm^2. Find the length of a side of the original square.
2) Use rational exponents to write x^1/8*y^1/3*z^1/6 as a single radical expression.
3) Divide (35b^3+18b^2+27b+35)/(5b+4)
4) Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in the standard form, ax^2+bx+c=0. Solution: 8, only solution.
5) Jack usually mows his lawn in 7 hours. Marilyn can mow the same yard in 4 hours. How much time would it take for them to mow the lawn together?
6) If a pro basketball player has a vertical leap of about 20 inches, what is his hang time? Use the hangtime function V =48 T^2 His hang time is how many seconds?
7) Subtract the polynomials. (-5v^2+5v+4)-(9v^2+4)
8) Express using a positive exponent p^-6=
9) Solve. 10x^4-19x^2+6=0 The solution is x= (simplify your answer. Type an exact answer, using radicals as needed. Rationalize all denominators. Use a comma to separate as needed. Type N if there is no solution.
10) Use the FOIL method to find the product. (7x^4-5)(x^7-9)
The solution is comprised of detailed explanations of various algebra problems: long division of polynomial, simplifying rational exponent, working together word problem, etc.