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Problem Packet for Class Practice 6.5-7.4 #1
Intermediate Algebra / MAT 135 Spring 2017 Master ( Master Templates)
Student Name/ID:
1. Divide.
2
8 x + 24 x + 22 ÷ 2 x + 3
Your answer should give the quotient and the remainder.
Quotient:
Remainder:
2. Divide.
3
2
8 x − 14 x + 20 x + 2 ÷ 4 x + 1
Your answer should give the quotient and the remainder.
Quotient:
Remainder:
3. Divide.
5 x 4 + 14 x 3 − 3 x 2 − 15 x + 10 ÷ − x 2 − 2 x + 1
Write your answer in the following form: Quotient
5 x 4 + 14 x 3 − 3 x 2 − 15 x + 10
2
−x − 2 x + 1
Problem Packet for Class Practice 6.5-7.4 #1
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= +
+
Remainder
.
2
−x − 2 x + 1
−x 2 − 2 x + 1
4
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2 UC Regents and ALEKS Corporation
4. Use synthetic division to find the quotient and remainder when
−7 x 4 − 11 x 3 + 8 x 2 + 10 x + 4 is
divided by x + 2 . Specifically, complete the synthetic division table below, and write your answer in the following
form: Quotient +
Remainder
−2 −7
x +2
−11
8
.
10
4
−7 x 4 − 11 x 3 + 8 x 2 + 10 x + 4
=
x +2
5. Use the remainder theorem to find
P 2
for
+
x +2
4
3
2
P x = −2 x + 3 x + 6 x − 5 .
Specifically, give the quotient and the remainder for the associated division and the value of P
2
.
6. Solve for v .
5 v −2
=
3
4
Simplify your answer as much as possible.
7. Solve for x .
4
8
=
x −4 x −5
Problem Packet for Class Practice 6.5-7.4 #1
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8. Solve for y .
2
3
− =1
5y
y
9. Solve for
w.
4
w
−3 =
w −4
w −4
10. Solve for x .
3
2
x − 9 x + 18
=
1
5
+
x −6 x −3
11. Solve for x .
−2
x
=
x +4 x +7
12. Solve for
u+
9
u
u.
=7 −
3
u
Problem Packet for Class Practice 6.5-7.4 #1
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13. Solve for y .
y +2 y +3
=
−1
y −2 y +4
14. Solve for
w.
6
12
w
+
= 2
w − 5 w − 3 w − 8 w + 15
15. Solve for
u.
3u
18
=− 2
u −3
u − 10 u + 21
16. A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing
159
129
pounds requires 212 milligrams of medicine. What is the amount of medicine required by a patient weighing
pounds?
17. Solve for
n 2.
w
w
+
=5
n1 n2
18. There are two machines that produce aluminum cans. The newer machine can produce
5400
cans in
180
270 minutes to produce that many cans. If the two machines work together,
how long will it take them to produce 5400 cans?
minutes. It takes the older machine
Problem Packet for Class Practice 6.5-7.4 #1
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60
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19. A company has two large computers. The slower computer can send all the company's email in
The faster computer can complete the same job in
will it take them to do the job?
20
60
minutes.
minutes. If both computers are working together, how long
Do not do any rounding.
5 kilometers against the current in the same amount of time it took him to swim 15 kilometers
with the current. The rate of the current was 2 kilometers per hour. How fast would Omar swim if there were no
20. Omar swam
current?
21. Simplify each expression.
Assume that the variables represent any real numbers.
w
26
=
____
6
=
____
z
22. Evaluate the following.
(a)
(b)
−
4
81 =
____
3
−64 =
____
23. Simplify.
4
1
16
Be sure to write your answer in lowest terms.
Problem Packet for Class Practice 6.5-7.4 #1
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24. Simplify.
5
32 w 35
Assume that the variable represents a positive real number.
25. Simplify each radical expression as much as possible.
Assume that the variables represent any real numbers.
(a)
(b)
5
6
5
x =
5 −z
____
6
=
____
26. Find the domain of the function.
f x = −x + 8
Write your answer using interval notation.
27. Find the domains of the functions f and
f x =
4
g x =
3
g.
x +7
2x +8
Write your answers using interval notation.
28. Simplify.
12 y
16
Assume that the variable
y represents a positive real number.
Problem Packet for Class Practice 6.5-7.4 #1
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29. Simplify.
63 w
15
Assume that the variable represents a positive real number.
30. Simplify.
54 t 7 u 10
Assume that all variables represent positive real numbers.
31. Write the following in simplified radical form.
4
243
32. Write the following in simplified radical form.
3
u
5
Assume that the variable represents a positive real number.
33. Write the following in simplified radical form.
4
16 w 10
Assume that the variable represents a positive real number.
34. Write the following expression in simplified radical form.
4
5 4
32 t u
Assume that all of the variables in the expression represent positive real numbers.
Problem Packet for Class Practice 6.5-7.4 #1
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35. Write the following as an exponential expression.
7
b
2
36. Evaluate.
1
4
256
=
____
=
____
1
3
27
37. Evaluate the following.
−16
(a)
−27
(b)
1
2
1
3
=
=
38. Simplify.
25
3
2
39. Simplify. Write your answers without exponents.
125
1
8
−
2
3
2
3
=
=
Problem Packet for Class Practice 6.5-7.4 #1
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40. Simplify.
3
1
5
u
3
·u
Assume that the variable represents a positive real number.
41. Simplify.
v
1
8
3
v
4
Write your answer using only a positive exponent.
Assume that the variable represents a positive real number.
42. Simplify the expression.
y
−
1
2
y
1
3
1
y
4
Write your answer using only positive exponents.
Assume that all variables are positive real numbers.
43. Simplify.
u
9
7
5
6
Write your answer without parentheses.
Assume that the variable represents a positive real number.
Problem Packet for Class Practice 6.5-7.4 #1
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44. Simplify the expression.
c
−2
·a
1
5
4
5
Write your answer without using negative exponents.
Assume that all variables are positive real numbers.
45. Simplify.
45 w + 20 w
Assume that the variable represents a positive real number.
46. Simplify.
3
45 w + 3 w
80 w
Assume that the variable represents a positive real number.
47. Simplify as much as possible.
5
8y
63 x + x
2
7x y
2
Assume that all variables represent positive real numbers.
48. Simplify.
−
3
375 x 4 + 3
3
81 x 4
Assume that the variable represents a positive real number.
49. Simplify.
45 × 2 20
Problem Packet for Class Practice 6.5-7.4 #1
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50. Simplify.
2v9w
8v2w2
Assume that all variables represent positive real numbers.
51. Simplify.
5
4 5
8u ·
12 u
3
Assume that the variable represents a positive real number.
52. Multiply and simplify.
x− 2
x +5 2
x+ 2 =
2
=
53. Write in simplified radical form with at most one radical.
6
y·
4
y
3
Assume that the variable represents a positive real number.
54. Rationalize the denominator and simplify.
9
5
Problem Packet for Class Practice 6.5-7.4 #1
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55. Rationalize the denominator and simplify.
3
15
56. Rationalize the denominator and simplify.
9
3 3 +2
57. Rationalize the denominator and simplify.
11 + 2
11 − 2
58. Rationalize the denominator and simplify.
−7
2 v +1
Assume that the variable represents a positive real number.
59. Rationalize the denominator and simplify.
5
3
2
Problem Packet for Class Practice 6.5-7.4 #1
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60. Rationalize the denominator and simplify.
3
3
25 u
2 x 11
Assume that all variables represent positive numbers.
Problem Packet for Class Practice 6.5-7.4 #1
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Problem Packet for Class Practice 6.5-7.4 #1 Answers for class
MAT 135 Spring 2017 Master
1.
Quotient:
4x +6
Remainder: 4
2.
Quotient:
2x2 −4x +6
Remainder:
−4
3.
5 x 4 + 14 x 3 − 3 x 2 − 15 x + 10
−x 2 − 2 x + 1
= −5 x 2 − 4 x + 6 +
4.
−2 −7
−7
−11
14
3
x +4
−x 2 − 2 x + 1
8
−6
2
10
−4
6
4
−12
−8
−7 x 4 − 11 x 3 + 8 x 2 + 10 x + 4
−8
= −7 x 3 + 3 x 2 + 2 x + 6 +
.
x +2
x +2
5.
Quotient = −2 x
3
2
−x +4x +8
Remainder =11
P 2 =11
6. v
=
26
3
7. x = 3
13
Problem Packet for Class Practice 6.5-7.4 #1
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13
5
8. y = −
9. No solution
10. No solution
11. x = −8 ,
12. u = 4 ,
−1
3
13. y = −1 ,
−6
14. w = −6
15. u = 1 , 6
16. 172 milligrams
17. n 2 =
n1w
5n1 −w
18. 108 minutes
19. 15 minutes
20. Rate he swam with no current: 4 kilometers/hour
21.
w
= w 13
26
3
z
6
= z
−
4
81 = −3
3
−64 = −4
22.
(a)
(b)
23.
1
2
7
Problem Packet for Class Practice 6.5-7.4 #1
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24. 2 w
7
25.
(a)
(b)
5
5
x =x
6
26.
6
5 −z
= 5 −z
− ∞, 8
27.
Domain of f:
−7 , ∞
Domain of g :
− ∞, ∞
28. 2 y
8
3
7
7w
29. 3 w
30. 3 t
3 5
31. 3
4
32. u
3
3
33. 2 w
u
2
2 4
34. 2 t u
35. b
6t
u
4
w
2
2t
2
7
36.
1
256
27
4
1
3
=4
=3
Problem Packet for Class Practice 6.5-7.4 #1
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37.
1
−16
(a)
2
= −4
1
−27
(b)
3
= −3
38. 125
39.
125
2
3
−
=
1
25
=
1
4
2
1
8
3
14
15
40. u
1
41.
5
8
v
1
42.
5
12
y
15
14
43. u
4
44.
a
2
c
45. 5
25
5
5w
46. 15 w
2
5w
Problem Packet for Class Practice 6.5-7.4 #1
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2
y
3
3x
47. 25 x
48. 4 x
7x
49. 60
50. 4 v
5
w
5
51. 2 u
vw
3u2
52.
x− 2
x +5 2
53.
12
y
9 5
5
55.
5
5
27
2
= x + 10
3 − 18
23
57.
13 + 2 22
9
58.
−14 v + 7
4v −1
59.
5
3
60.
2 x + 50
11
54.
56.
x + 2 =x −2
3
2
4
100 u x
2x4
Problem Packet for Class Practice 6.5-7.4 #1
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