1. Find all numbers for which the rational expression is undefined. t^3-6t/t^2-9
The numbers for which the rational expression is undefined are -3,3
2. Multiply. (c+1/4)(c+1/2)= c2+ 3/4 c + 1/8
(Simplify your answer)
3. Divide. (20b^3+12b^2+28b+40) ÷(4b+4)
Answer: 5b2-2b+9 + 4/(4b+4)
4. a. Solve 2x^2=6
What are the solutions? -3,3
(Give an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i.
b. What are the x-intercepts?
(-3,0),(3,0)
(Give an ordered pair. Give an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i
6. Jack usually mows his lawn in 6 hours. Marilyn can mow the same yard in 4 hours. How much time would it take for them to mow the lawn together?
2 2/5 (mixed number)
(Simplify your answer. Give an integer, proper fraction, or mixed number)
7. Multiply and simplify. Assume variables represent nonzero real numbers. b^17·b^0=
b17
(Simplify your answer. Give exponential notation with positive exponents)
8. Solve. 15x^4-19x^2+6=0
The solution is x= -6 /3,6/3,-15/5,15/5
(Simplify your answer. Give an exact answer, using radicals as needed. Rationalize all denominators)
10. Subtract. Simplify by collecting like radical terms if possible. 4√8 - 6√2=
2√2
(Simplify your answer. Give an exact answer using radicals as needed)
11. Rewrite the following expression with positive exponents. (2xy)^-3/5
1/(2xy)^3/5
12. Multiply and simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. 3√y^4 3√81y^5=
3y3 3√3 (the last term is cubic root of 3)
(Simplify your answer. Give in radical form)
13. If a pro basketball player has a vertical leap of about 25 inches, what is his hang time? Use the hang-time function V=48T^2
His hang time is 0.7
(Simplify your answer. Give an integer or a decimal. Round to the nearest tenth)
14. Multiply. (9x+9)(2x^2+2x+7)
The answer is 18x^3+36x^2+81x+63
(Simplify your answer)
15. Solve. √3x+24 = x+2
The solution is x= 4
(Simplify your answer.)
16. Solve. s^2-5s-50=0
The solution is s= -5, 10
17. Use the quadratic formula to solve the equation. x^2-x=-9
The solution set is (1+√35 i)/2, (1-√35 i)/2
(Simplify your answer. Give an exact answer, using radicals as needed. Express complex numbers in terms of i. Use integers or fractions for any numbers in the expression.)
18. Find the variation constant and an equation of variation where y varies directly as x and y = 30 when x = 6
The variation constant is k = 5
The equation of variation is y = 5x
19. Perform the indicated operations and simplify. z-7/z-9 - z+1/z+9 + z-45/z^2-81=
11/(z+9)
20. Multiply and simplify. 4y^2/2y^2-8y+8=
Checkthisone
(Give exponential notation with positive exponents)
21. Identify the degree of each term of the polynomial and the degree of the polynomial. -3x^3+6x^2+6x+3
The degree of the first term is 3
The degree of the second term is 2
The degree of the third term is 1
The degree of the fourth term is 0
The degree of the polynomial is 3
22. Multiply. (2√3 -6√7)(3√3 +9√7)= -360
(Simplify your answer. Give an exact answer, using radicals as needed)
23. Multiply. (-3z)^2(2z^7)^2= 36x16
24. Use the FOIL method to find the product. (3x^2-6)(x^3-5)= 3x^5-6x^3-15x^2+30
25. Factor completely. 144c^2+648ct+729t^2= 9(4c+9t)(4c+9t)
26. Factor completely. 5x^8-40x^7+20x^6
The complete factorization is 5x^6(x^2-8x+4)
(Give your answer in factored form)
27. Add. (5x^2-6xy+y^2) + (-8x^2-7xy-y^2) + (x^2+xy-2y^2)
The answer is -2x^2-12xy-2y^2
28. If the sides of a square are lengthened by 8 cm, the area becomes 256 cm^2. Find the length of a side of the original square.
The length of a side of the original square is 8
29. Express using a positive exponent. d^-3= 1/d^3
(Simplify your answer. Give a positive exponent)
30. Solve. 1/v=6/v-1/2
The solution is v=10
(Simplify your answer. Give an integer or a fraction)
31. Factor. b^2+18b+81= (b+9)(b+9)
(Factor completely)
32. Factor completely. 9m^2+16-24m= (3m-4)(3m-4)
33. Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. √a - √b/ √a + √b=
(a+b-2√ab)/(a-b)
(Simplify your answer. Give an exact answer, using radicals as needed)
34. Divide and simplify. v^6/v^18=
1/v^12
(Give exponential notation with positive exponents)
35. Factor. 40-13r+r^2= (r-5)(r-8)
36. Find the x- intercepts for the graph of the equation y=x^2+2x-8
The x- intercepts are (-4,0),(2,0)
(Give an ordered pair)
37. 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+1
The x-coordinate of the vertex is 1/2
(Give a simplified fraction)
The y-coordinate of the vertex is 3/2
(Give a simplified fraction)
The equation of the line of symmetry is x= 1/2
(Give a simplified fraction)
The maximum/minimum of f(x) is 3/2
(Give a simplified fraction)
The value f(1/2)=3/2 is maximum
38. Subtract. Simplify, if possible. 4-v/v-7 - 2v-7/7-v=
(Simplify your answer) (v-3)/(v-7)
39. Solve. x^2+2x-4=0
The solution is x= -1-5,-1+5
(Simplify your answer. Give an exact answer, using radicals as needed)
40. Multiply. (a+d)(a^2-ad+d^2)= a^3+d^3
(Simplify your answer)
41. Simplify. 5√- 1/1024= -1/5
(Simplify your answer. Give a fraction or an integer)
42. Evaluate the polynomial for x=1. 3x^2-4x+2
When x=1, 3x^2-4x+2= 1
(Simplify your answer)
43. Factor the trinomial. r^3-7r^2-18r
The answer is r(r-9)(r+2)
(Factor completely)
44. Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. √32a^2b= 4a√2b
(Give an exact answer, using radicals as needed)
45. Simplify by removing factors of 1. p^2-25/(p+5)^2
The simplified form is (p-5)/(p+5)
46. Subtract the polynomials. (-13s^2+6s+4) - (6s^2+4)=
(Simplify your answer) -19s^2+6s
47. Convert to decimal notation. 8.69 x 10^7= 86,900,000
(Simplify your answer. Gave an integer or a decimal)
48. Add. (2v^4-2v^3+4v^2+13v-8) + (v^5+8v^3+4v^2-4v+4) + (-5v^4+v^2-5v-4)
The answer is v^5-3v^4+6v^3+9v^2+4v-8
(Simplify your answer)
49. For the following equation, state the value of the discriminant and then describe the nature of the solutions. 17x^2+4x-7=0
What is the value of the discriminant 492
Which one of the statements below is correct?
A. The equation has two real solutions correct
B. The equation has two imaginary solutions
C. The equation has one real solution
50. Simplify by removing factors of 1. 9p^2+9p/45p^2+81p
The simplified form is (p+1)/(5p+9)
51. Solve for x. 4x(x-2)-5x(x-1)=2
x= -2, -1
(Simplify your answer)
52. Write a quadratic equation in the variable x having the given numbers as solutions. Give the equation in standard form, ax^2+bx+c=0
Solution: 4, only solution
The equation is x^2-8x+16
53. Use rational exponents to write x^1/6·y^1/7·z^1/4 as a single radical expression.
84(x^14y^12z^21)
54. Simplify by taking roots of the numerator and the denominator. Assume that all expressions under radicals represent positive numbers. 3√8x^8/y^3=
(2x^2)(3x^2)/y
(Give an exact answer, using radicals as needed)
55. Solve. v^2+2v-48=0
v= -8,6
(Give an integer or a simplified fraction)
56. Divide and simplify. 5w-15/77 ÷ w-3/14w
The answer is 10w/11
(Simplify your answer. Use integers or fractions for any numbers in the expression)
57. Television sets. What does it mean to refer to a 20-in TV set or a 25-in TV set? Such units refer to the diagonal of the screen. A 30-in TV set also has a width of 24 inches. What is its height?
What is the height of a 30-in TV 18
58. Find the following. 20√(-4)^20=
(Simplify your answer) 4
59. Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function. f(x)=1/5(x+2)^2+5
The vertex is (-2,5)
(Give an ordered pair)
The line of symmetry is x= -2
What is the maximum/minimum value of f(x) 5
Is the value, f(-2)=5, a minimum or maximum
minimum
60. In a right triangle, find the length of the side not given. b=1, c=√17
The length of the third side is 4
(Simplify your answer. Give an exact answer using radicals as needed)
61. Rewrite with a rational exponent. 5√19=
(Simplify your answer) 51/19
62. Factor completely. 36v^2-121= (6v-11)(6v+11)
63. Find the greatest common factor for the group of terms. -66a^2, 11a^5
The greatest common factor is 11a^2
64. Add. Simplifyifpossible. 6u/u^2-36 + u/u-6=
(Simplify your answer) (u^2+12u)/(u^2-36)
65. Find the following. Assume that variables can represent any real number. √(a+5)^2=
66. Solve. (x+6)(x-15)(x+3) > 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is {x|-6<x<-3 or x>15}
(Use at least one inequality or compound inequality to express your answer. For answers with more than one inequality, separate the inequalities with a comma or the word "or")
B. The solution is all real numbers
C. There is no solution