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practice problems
D. Benjamin Antieau
3 July 2008
Solve the following equations.
- (2x + 7)(x − 10) = 0.
- 3x(x − 5) = 0.
- x^2 − 2 x − 15 = 0.
- 25x^2 − 40 x + 16 = 0.
- 9n^2 + 30n + 25 = 0.
- − 2 t^3 = 108t − 30 t^2.
- 2z(z + 6) = 2z^2 + 12z − 8.
- 3c^2 − 8 c + 2 = c(3c − 8).
- x 182 + x 2 + 1 = 0.
- y^3 + 4y^2 = 9y + 36.
- 2x^3 = 50x.
- m^2 (3m − 2) = m.
While buzzing innocent hikers on top of Angel’s Landing in Zion National Park, a 1500-foot peak in the middle of the canyon, a helicopter pilot drops his sunglasses. The height h(t) of the sunglasses after t seconds is given by h(t) = − 16 t^2 + 1500.
When will the sunglasses hit the ground?
Find the domain of the following rational functions.
- f (x) = (^73) −xx.
- R(x) = (^) x (^3) +3+2x (^2) −x 2 x.
- C(x) = (^) xx 2 +3− 4.
Simplify the following.
- 43 xx−−^86.
- x x^22 −−^26 xx−+9^3.
- (^2) x (^32) −x 32 x− 2 x+2−^3 x− 3.
- (^16) q (^38) −q^216 q 2.
- 8 x 43 x−−^276.
- x^24 − 9 ÷ x x^22 −−^6 xx−+9 6.
- (^) aa 2 −+^5 abb ÷ (^15) b 2 b−−a^32 a.
- 94 xx+9+8 · (^32) xx 2 +4− 3.
Add or subtract the following expressions.
- x 2 −x^5 − x 2 +5x.
- (^2) x+10^3 + (^3) x+15^8.
- (^) a 2 ab−b 2 + (^) a+bb.
- (^) a (^2) +2^2 a+1 + (^) a (^23) − 1.
- (^3) x (^29) −x+2 2 x− 8 − (^3) x (^2) +^7 x− 4.
