MATH 107 Algebra Quiz Problems

Hi,

I need step by stepsolutions to all 10 questions in the attached file.

Thanks

Name: ____________________
Date: _____________________
MATH 107
Quiz 4
1) Find all real solutions for x2 = 1.65(3 − x)2 and use a
calculator to approximate your answers, rounded to two
decimal places.
2) Find all complex solutions for x =
3
√7 − x
.
3) Carl’s friend Jason participates in the Highland Games. In
one event, the hammer throw, the height h in feet of the
hammer above the ground t seconds after Jason lets it go is
modeled by h(t) =− 8t2 + 24.16t + 10 . What is the hammer’s
maximum height? What is the hammer’s total time in the air?
Round your answers to two decimal places.
4) The height h in feet of a model rocket above the ground t
seconds after lift-off is given by
h(t) =− 15t2 + 300t f or 0 ≤ t ≤ 20.
When is the rocket at least 350 feet off the ground? Round
your answer to two decimal places..
5) Find the real zeros of the given polynomial and their
corresponding multiplicities. Use this information along with
a sign chart to provide a rough sketch of the graph of the
polynomial. Compare your answer with the result from a
graphing calculator. Also, state the domain and range.
f (x) = x2 (x − 1)(x + 1)(x + 2)3
6) Find the domain of f (x) =
16 − 4×2
x2 −4
. Identify any vertical
asymptotes of the graph of f(x). Identify any holes in the
graph. Find the horizontal asymptote, if it exists. Find the
slant asymptote, if it exists. Graph the function using a
graphing calculator.
7) Find all real solutions. Be sure to check for extraneous
solutions.
3y−1
y 2 +1
=1
8) Solve the rational inequality. Express your answer using
3
2×2 + x
interval notation. x x+2 −x−2
≥0
9) A faucet can fill a sink in 7 minutes while a drain will empty
the same sink in 10 minutes. If the faucet is turned on and
the drain is left open, how long will it take to fill the sink?
10) Working together, Daniel and Donnie can clean the llama
pen in 50 minutes. On his own, Daniel can clean the pen in
90 minutes. How long does it take Donnie to clean the llama
pen on his own?