Download 117_work - JustAnswer

1. Factor completely. 16v 2  25  (4v  5)(4v  5) (Type N if binomial is not factorable)
2. Simplify.
5

1
1
  (Type a fraction or an integer. Type N if the root is not a real
1024
4
number)
3. Find a polynomial for the perimeter and for the area.
a) The perimeter is 4a+14
a+7
(Simplify do not factor)
a
b) The area is a 2  7a (Simplify do not factor)
4. s 2  10s  25  (s  5)( s  5) (Type N if trinomial is not factorable)
5. ADD. (3x 2  6 xy  y 2 )  (7 x 2  6 xy  y 2 )  ( x 2  xy  6 y 2 )  3x 2  11xy  6 y 2
6. Rewrite the following expression with positive exponents. (5 xy) 3 / 7 
1
(5 xy) 3 / 7
__________________
7. Use the foil method to find the product. (3x 8  3)( x 9  2)  3x17  3x 9  6 x 8  6
8. Find the variation constant and an equation of variation where y varies directly as x and
y= 16 when x=8. The variation constant is K=2
The equation of variation is y=2x
9. Solve. 5 x  29  x  3 The solution is x= 4 (Use comma to separate answers. Type N
if solution is not a real number.)
10. Solve. a 2  a  20  0 The solution is a= -5, 4 (Use comma to separate answers as
needed. Type N if there is no solution.)
11. Simplify by factoring. Assume that all expressions under radicals represent nonnegative
numbers. 18a 2 b  3a 2b (Type answer, using radicals as needed)
12. If the sides of a square are lengthened by 6cm the area becomes 144cm 2 . Find the
length of a side of the original square. The length of the original side is 6 cm.
13. Multiply and simplify by factoring. Assume that all expressions under radicals
represent nonnegative numbers.
form)
3
y 7 3 81y 8  3y 5 3 2 (Simplify. Type in a radical
14. Use rational exponents to simplify.
5
x10  x 2 (Simplify your answer)
15. If a basketball player has a vertical leap of about 30 inches, what is his hang time?
Use hang-time function v  48t 2 His hang-time is 0.8 seconds. (Simplify. Type an
integer or a decimal. Round to the nearest tenth.)
4d
16d 2
3d  6
(Type an exponential notation


2
d 2
3d  12d  12 4d
with positive exponents.)
16. Multiply and simplify.
17. Identify the degree of each item of the polynomial and the degree of the polynomial.
 6 x 3  7 x 2  8 x  5 The of the first term is 3 the second 2 the third 1 the fourth 0
The degree of the polynomial is 3
18. Subtract and simplify if possible.
2  w 5w  4 4 w  2


(Simplify your answer)
w5 5w
w5
p3  7 p
The
p 2  49
numbers for which the rational expression is undefined are -7, 7 (Use comma to
separate answers)
19. Find all numbers for which the rational expression is undefined.
7
1
1 
1

20. Multiply.  r   r    r 2  r 
(Simplify your answer.)
10
10
2 
5

21. TV sets. What does it mean to refer to a 20 inch or a 25 inch TV set? Such units refer
to the diagonal of the screen. A 35 inch TV set also has a width of 28 inches. What is
the height of a 35 inch TV set?
21 Inches.
22. Find the vertex, line of symmetry and the maximum and the minimum value of f (x)
1
Graph the function. f ( x)  ( x  9) 2  8 The vertex is (-9, 8) Type an ordered pair)
2
The line of symmetry is x  -9 What is the maximum/minimum value of f (x) ? 8 is
the value f (9)  8 a minimum? Graph.
23. Simplify by removing factors of 1.
s6
s 2  36
The simplified form is
.
2
s6
( s  6)
24. a) Solve 4 x 2  12 The solutions are x= 3and  3 (Type an exact answer, using
radicals as needed. Rationalize all denominators. Express all complex numbers in
terms of i. Use comma to separate answers as needed.)
b) Find the x intercepts of f ( x)  4 x 2  12 .What are the x-intercepts?
( 3 ,0)and ( 3 ,0) (Type an ordered pair. Type an exact answer, using radicals as
needed. Rationalize all denominators. Express all complex numbers in terms of i. Use
comma to separate answers as needed. Type N if there are no x-intercepts.)
25. Use the quadratic formula to solve the equation. x 2  3x  4 The solution is
3 i 7
3 i 7

and 
2
2
2
2
(Simplify answer. Type an exact answer, using radicals as needed. Rationalize all
denominators. Express all complex numbers in terms of i. Use integers of fractions
for any numbers in the expression. Use comma to separate answers as needed.)
3r
r
r 2  9r
26. Add and simplify if possible. 2
(Simplify answer)


r  36 r  6 r 2  36
27. Add. (2s 4  3s 3  4s 2  12s  7)  (55  10s 3  3s 2  4s  3)  (5s 4  s 2  4s  4)
I think the 5^5 should have been s^5… that’s how I’ll solve it.
The answer is s 5  3s 4  7 s 3  8s 2  4s  8
(Simplify your answer.)
28. Find the greatest common factor for the group of terms.  66a 4 ,11a 5 . The greatest
common factor is 11a 4
29. Solve. x 2  14 x  4  0 The solution is x   7  53and  7  53 (Simplify your
answer. Use a comma to separate answers. Type exact answer, using radicals as
needed. Type N if there is no solution.)
30. Evaluate the polynomial for x  3 .
(Simplify you answer.)
2 x 2  5 x  4 When x  3, 2 x 2  5 x  4  37
31. Find the following. Assume that variables can represent any real number.
(a  5) 2  |a+5|
32. Solve b 2  3b  28  0 The solution is b  -4, 7 (use comma to separate answers.
Type N if no solution.)
33. Multiply (5 3  15 2 )( 4 3  12 2 )  -300 (Simplify answer. Type an exact
answer, using radicals as needed.)
34. Factor completely. 112b 2  392bf  343 f 2  7(4b+7f)(4b+7f)
35. Perform the indicated operations and simplify.
y  8 y  1 y  27



y  9 y  9 y 2  81
10
y9
36. Find the following.
12
( 2)12  2 (Simplify. Type N if solution is not a real number. )
37. For the following equation, state the value of the discriminant and then describe the
nature of the solutions.  2 x 2  10 x  18  0 What is the value of the discriminant?
244
Which of the below statements is correct?
c) There are two real solutions.
38. Multiply. (r  p)(r 2  rp  p 2 )  r 3  p 3 (Simplify)
39. Factor completely. 25b 2  4  20b  (5b-2)(5b-2) (Type N if the solution is not
factorable)
40. Factor. 56  15a  a 2  (a-8)(a-7) (Type N if trinomial is not factorable)
41. Factor out the GCF. 2 x 4  6 x 3  8 x 2 The factorization is 2 x 2 ( x 2  3x  4) (Type
answer in factored form)
42. Express using a positive exponent. c 7 
1
(Simplify. Type a positive exponent.)
c7
43. Use rational exponents to write x1 / 5  y 1 / 6  21 / 2 as a single radical expression. Choose
the correct expression b)30 x 6 y 5 z 15
44. Divide and simplify.
1
b9
 5 (Type an exponential notation with positive
14
b
b
exponents.)
45. Find the vertex, the line of symmetry, the maximum or minimum value of the
quadratic function, and graph the function. f(x)  -2x 2  2x  3 The x-coordinate
7
of the vertex is ½ Type a simplified fraction) The y-coordinate of the vertex is
2
(Type a simplified fraction) The equation of the line of symmetry is x  ½ (Type a
7
simplified fraction) What is the maximum/minimum value of f (x) ?
(Type a
2
1 7
simplified fraction) The value f    is ? a maximum Graph.
2 2
46. Multiply and simplify. Assume variables represent nonzero real numbers.
y15  y 0  (Simplify your answer. Type an exponential notation with positive
exponents.)
y 15
47. Simplify by taking roots of the numerator and the denominator. Assume that all
729 x 8
expressions under radicals represent positive numbers.
 (Type exact
y3
answer, using radicals as needed. Type N if the root is not a real number.)
I think you have a typo here, I think it should be a cube root, not a square root.
9x 2 3 2
x
y
48. Simplify by removing factors of 1.
n 1
7n 2  7n
The simplified form is
2
5n  7
35n  49n
5x  5 x  1
25x

The answer is
(Simplify answer. Use
77
55 x
7
fractions or an integer for any numbers in the expression).
49. Divide and simplify
50. Rationalize the denominator. Assume that all expressions under radicals represent
r  s r  2 rs  s
positive numbers.
(Simplify answer. Type an exact answer,

rs
r s
using radicals as needed.)
51. Write a quadratic equation in the variable x having the given numbers as solutions.
Type the equation in a standard form ax 2  bx  c  0 Solution: 6, only solution. The
equation is x 2  12 x  36  0
52. Factor the trinomial. c 3  2c 2  48c The answer is c(c-8)(c+6) (Type N if trinomial
is not factorable)
53. In a right triangle, find the length of the side not given. b  2, c  13 The length of
the third side is 3 (Simplify answer. Type an exact answer, using radicals as
needed.)
a
13
2
54. Jack usually mows his lawn in 7 hours. Marilyn can mow the same yard in 3 hours.
How much time would it take for them to mow the lawn together? They could mow
1
the lawn in 2
hours if they worked together. (Simplify answer. Use proper
10
fraction mixed numbers or an integer).
55. Multiply. (5 x  3)(5 x 2  2 x  9) The answer is 25 x 3  25 x 2  51x  27 (Simplify)
56. Subtract. Simplify by collecting like radical terms if possible. 4 32  3 2 = 13 2
(Simplify answer. Type an exact answer, using radicals as needed.)
57. Rewrite the rational exponent.
5
20  201 / 5 (Simplify)
58. Solve for x. 4x(x - 1) - 5(x)  3 x=____ (Simplify. Use comma to separate answers.
Type N if no solution.)
Are you sure you typed this correctly?
9/8+sqrt(129)/8
9/8-sqrt(129)/8
3 7 1
  The solution is 12 (Simplify. Type an integer or a fraction. Type
w w 3
N if no solution.)
59. Solve.
60. Solve. 10 x 4  29 x 2  10  0 The solution is x=____ (Simplify answer. Type an
exact answer, using radicals as needed. Rationalize all denominators. Type N if there
is no solution. Use comma to separate answers as needed.)
10
10 10
10
,
,
,
2
2
5
5
61. Find the x-intercepts for the graph of the equation y  x 2  2 x  3 The x-intercepts
are (-3, 0), (1, 0) (Type an ordered pair. Use a comma to separate answers.)
62. Solve. ( x  9)( x  10)( x  5)  0 The solution is -9 < x < -5 or x > 10 (Use at least
one inequality or compound inequality to express answer For answers with more than
one inequality, separate with comma or the word “or”. Type R if the answer is all real
numbers. Type N for no solution.)
63. Subtract the polynomials. (8c 2  4c  3)  (7c 2  3)   15c 2  4c (Simplify)
64. Convert to decimal notation. 8.84  10 7 
decimal.)
88400000
(Simplify. Type an integer or a
65. Divide. (30b 3  8b 2  34b  30)  (5b  3) Choose the correct answer a)
6
6b 2  2b  8 
5b  3
66. Multiply. (3z ) 2 (4 z 6 ) 2  144z 14