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```1. Graph and clearly shade the polygonal set that satisfies the following system of linear inequalities.
=
3y
=4 4
−
2y
4x
x+
6
6
2
−6
−4
−2
−2
2
4
6
−4
−6
2. Find the corner point of the above polygonal set.
4 20
,
11 11
3. Find the equation of the line perpendicular to 5x − 2y = 0 and passing through the
point (−4, 1).
3
2
y=− x−
5
5
4. The endpoints of a line segment are (3, −2) and (a, 5). The slope of the line segment
5
is − . Find the value of a.
3
9
a=−
5
5. A company is in the business of producing and selling gambots. The total cost to
produce 20 gambots is \$167, and the total cost to produce 80 gambots is \$188. Find
a linear function, C(q), that gives the total cost to produce q gambots.
C(q) =
7
q + 160
20
6. Solve the following equations.
For some of them, you may find the quadratic for√
2
−b ± b − 4ac
mula handy: x =
. If the solution is imaginary or there is no solu2a
here (though you might want to if you have time).
a)
4
2
−5 =
2−x
3
x=
22
17
b) x2 + 8x = 20
x = −10, 8
c) 2(x − 2)2 + 4 = 13
√
x =2±
d) 2(x2 − 3x) = 5 − x2
e) 8
p
(2t − 1)3 = 16
3
√
2 6
x = 1±
3
√
3
4
1
t= +
2
2
7. Simplify the following as much as possible.
√
√ √
√
a) 3(3 18 − 5 12) − 2 6
√
7 6 − 30
r
72A4 B7
3
b)
27A−3 B11
r
2A2 3 A
B
3B
8. Find the roots of f (x) = 2x3 − x2 − 9x + 6 if (x − 2) is a factor.
√
−3 ± 33
x = 2,
4
9. Solve the following equation by completing the square: 2x2 − 6x − 3.
√
15
3
x= ±
2
2
10. A toy rocket is shot in the air so that its height above the ground in feet after t
seconds is given by h(t) = −16t2 + 256t.
a) When does the rocket attain its maximum height above the ground, and what
is this maximum height?
t = 8sec, height is 1024 feet.
b) When does the rocket hit the ground?
t = 16
c) Draw a sketch of the graph of h(t) for t ≥ 0, showing clearly the points that
correspond to parts a and b. Scale your axes.
(8, 1024)
1100
1000
900
800
700
600
500
400
300
200
100
−2
b
2
4
6
8
10
12
14
16
18
11. I have 24 coins, dimas and quarters only. If their total value is \$3.60, how many of
each type of coin do I have? To get any credit, you must set up two equations with
two unknowns and solve the resulting system of equations algebraically.
8 quarters and 16 dimes
EXTRA CREDIT Consider the functions f (x) = x2 − 7x and g(x) = −4x2 + 10. There are
three values of x for which f (x) = g(x). One of them is x = 2. Find the other two. You
must find these algebraically, not by guessing and checking. (Hint: The fact that x = 2 is
a olution should be used at some point in finding the other two.)
x = −5, −1
```
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