# Trish Goal

Most popular questions and responses by Trish Goal
1. ## Math

When Frederick was born, his grandparents gave hima a gift of \$2000, which was invested at a simple interest rate of 5% per year. How much money will Frederick have when he can collect the monet at the age of 18? ( Assume no money is added to the account

2. ## Algebra

The function f(x) satisfies f(sqrt(x+1))=1/x for all x>= -1, x does not = 0. Find f(2). Couldn't you just plug it in? sqrt(3) would be 1/sqrt 3? Thank you.

3. ## Algebra

Let a and b be real numbers, where a

4. ## Algebra

When Frederick was born, his grandparents gave hime a gift of \$2000, which was invested at an interest rate of 5% per year, compounded yearly. How much money will Frederick have when he collects the money at the age of 18? gGive your answer to the nearest

5. ## Algebra

Find the greatest integer value of b for which the expression 9x^2+4x^2+11x+7/x^2+bx+8 has a domain for all real numbers? Thank you!

6. ## Algebra

Let p(x)=2x^3-113 and let q be the inverse of p. Find q(137). Please explain in steps. I posted this already but I did not list my steps. The first step would be to find the inverse of 2x^3-113 which would be: y=(x+113/2)^1/3. and then would I just plut in

7. ## Algebra

The polynomial f(x) has degree 3. If f(-1)=15, f(0)=0, f(1)=-5, f(2)=12, then what are the x-intercepts of the graph of f?

8. ## Math/Algebra

The graphs of y=3-x^2+x^3 and y=1+x^2+x^3 intersect in multiple points. Find the maximum difference between the y-coordinates of these intersection points.

9. ## Algebra

Find the greatest integer value of b for which the expression 9x^3+4x^2+11x+7/x^2+bx+8 has a domain for all real numbers. Thank you!

10. ## Algebra

I already posted this question, I just wanted to clarify my answer. Problem: When Frederick was born, his grandparents gave hime a gift of \$2000, which was invested at an interest rate of 5% per year, compounded yearly. How much money will Frederick have

11. ## Algebra

Find all positive integer values of c such that the equation x^2-7x+c=0 only has roots that are real and rational.

12. ## Algebra

Define #N by the formula #N=.5(N)+1. Calculate #(#(#50)). Thank you!

13. ## algebra

Suppose a function f(x) has a domain of (-inf,inf) and range [-11,3]. If we define a new function g(x) by g(x)=f(6x) +1, then what is the range of g(x)? Express your answer in interval notation. Thank you!

14. ## Math

Sue can either borrow 10,000 dollars for 5 years with a simple interest of 7% annually or an interest which compounds annually for 6%. How much more money, rounded to the nearest dollar, would she have to pay back for the more expensive interest

15. ## algebra

Compute the domain of the real-valued function f(x)=sqrt(1-sqrt(2-x)). Thank you

16. ## Algebra

Find all complex numbers z such that z^2=2i. Write your solutions in form, separated by commas. So, "1+2i, 3-i" is an acceptable answer format, but "2i+1; -i+3" is not. Thank you!

17. ## Math

1. Find all values of p such that 2(x+4)(x-2p) has a minimum value of -18. I know that y is the minimum value,I know x is -4. But, I am not sure how to find p. 2.The temperature of a point (x,y) in the plane is given by the expression x^2+ y^2 - 4x +

I already posted this question,and Henrey answered it. I just wanted to clarify a few things to make sure I am on the right track Problem: Joanie takes a \$6,000 loan to pay for her car. The annual interest reate on the loan is 12%. She makes no payments

19. ## Algebra

Part a: Let f(x)=x^4-3x^2+2 and g(x)=2x^4-6x^2+2x-1. Let a be a constant. What is the largest possible degree of f(x)+a*g(x)? Part b: Let x^4-3x^2+2 and g(x)=2x^4-6x^2+2x-1. Let b be a constant. What is the smallest possible degree of the polynomial f(x) +

20. ## Algebra

Find all points (x,y) that are 13 units away from the point (2,7) and that lie on the line x-2y=10.

21. ## algebra

Let x#y=x^2/y for all x and y such that y cannot equal 0. Find all values of a such that a#3=9. Thank you.

22. ## algebra

The function f(x) satisfies f(sqrt(x+1))=1/x for all x>= -1, x does not = 0. Find f(2)Thank you!

23. ## Algebra

Kimberly borrows 1000 dollars from Lucy,who charged interest of 5% per month ( which compounds monthly). What is the least integer number of months after which Kimberly will owe more than twice as much as she borrowed.

24. ## Algebra

Kimberly borrows 1000 dollars from Lucy,who charged interest of 5% per month ( which compounds monthly). What is the least integer number of months after which Kimberly will owe more than twice as much as she borrowed?

25. ## Algebra

I already posted this question and Reiny answered it, I just wanted to clarify my answer Problem: If f(x) is a polynomial of degree 4, and g(x) is a polynomial of degree 2, then what is the degree of polynomial f(x)-g(x)? Reiny: so f(x) has to contain an

26. ## Algebra

What are the coordinates of the points where f(x)=x^3-x^2+x+1 and g(x)=x^3+x^2+x-1 intersect?

27. ## Algebra

Let p(x)=2x^3-113 and let q be the inverse of p. Find q(137). Please explain in steps. Thank you.

28. ## Algebra

My calculator is broken. The "+" key works correctly,but whenever I try to compute a-b, the calculator performs b-a instead. What answer does mny calculator compute for the expression ((7-10)+3)-5? Thank you!

29. ## Algebr

The values of a function f(x) are given in the table below: x=1, f(x)=3 x=2, f(x)=13 x=3. f(x)=8 x=5,f(x)=1 x=8,f(x)=0 x=13, f(x)=5 If f^-1 exists, what is f^-1((f^-1(5)+f^-1(13))/ f^-1(1))? I am not quite sure how to do this.

30. ## Algebra

Suppose that f(x)=4x+5. What is f^-1(f^-(9))? I am pretty sure we can plug in 9 for f(x) which gives us the value of 1. But then we have one more f^-1 but the inverse of 1 is -1. So would the answer be one?

31. ## Algebra

Let f(x)=x^2-2x. Find all real numbers x such that f(x)=f(f(x)). Thank you.

32. ## Algebra

The inverse of f(x)=2x-1/x+5 may be writeen in the form f^-1(x)=ax+b/cx+d where a,b,c, and d are real numbers. Find a/c. Thank you!

33. ## Algebra

Define #N by the formula #N=.5(N)+1. Calculate #(#(#50)).

34. ## Algebra

If P(x)=4+2sqrt(x+2) and G(x)=4-3X, then what is the largest constant such that P(G(a)) is defined? Thank you!

35. ## Algebra

Let f(x)-3x-7/x+1. Find the range of f. Give your answer as an interval. Please enter your response in interval notation. I figured out the domain, ( -inf,-1) and (-1, inf) .

36. ## Algebra

Let f(x)-3x-7/x+1. Fidnd the range of f. Give your answer as an interval. Please enter your response in interval notation. I figured out the range, ( -inf,-1) and (-1, inf) Thank you.

37. ## Basic Computer Science

This was the assignment: If the first parameter is less than the second parameter add the two and print the result 10 times. THIS PROGRAM IS IN JAVA. I did everything but I can't figure out how to print the result as a loop 10 times. public static void

38. ## Algebra

When the product (3x+2y+1)(x+4y+5) is expanded, what is the sum of the coefficients of the terms which contain a nonzero power of y? I got 3x^2+14xy+16x+8y^2+14y+5 would the answer be 36?

39. ## Algebra

I already posted this question,Steve answered it. I just wanted to clarify my answer. Problem:Find h(x) with terms in order of decreasing degree, if 9x^3-3x+1+h(x)=3x^2-5x+3. Steve: h(x) = (3x^2-5x+3)-(9x^3-3x+1) so, just subtract tghe coefficients of like

40. ## Algebra

Assume that f(3)=4. Name a point that must be on the graph of y=f(x)+4

41. ## Algebra

What are the coordinates of the points where the graphs of f(x)=x^3-x^2+x+1 and g(x)=x^3+x^2+x-1 intersect? Give your answer as a list of points separated by semicolons. (So "(1,-3); (2,3); (5,-7)" is a valid answer format.)

42. ## Algebra

Let f(x)=px+q, where p and q are real numbers. Find p+q if f(f(f(x)))=8x+21. Thank you. I got this p^3 +p^2q + pq + q = 29 Would you try to solve that? if yes, then how?

43. ## Algebra

The function f(x,y) accepts an ordered pair as input and gives another ordered pair as output. It is defined according to the following rules: If x>4, f(x,y)=(x-4,y). If x4, f(x,y)=(x,y-4). Otherwise, f(x,y)=(x+5,y+6). A robot starts by moving to the point

44. ## Algebra

Find all complex numbers such that z^2=2i. Thank you!

45. ## algebra

Let A(t)3-2t^2+4^t. Find A(2)-A(1)Thank you!

46. ## Algebra

How many real numbers are not in the domain of the function f(x)=(1/x-64)+(1/x^2-64)+(1/x^3-64)? Thank you!

47. ## algebra

How many real numbers are not in the domain of the function f(x)=(1/x-64)+(1/x^2-64)+(1/x^3-64)?

48. ## Algebra

How many real numbers are not in the domain of the function f(x)=(1/x-64)+(1/x^2-64)+(1/x^3-64)? Thank you!

49. ## algebra

Find the smallest integer x where the expression srt(x-2)/x^2+x-6 is defined. I factored the denominator (x+3)(x-2) and the smallest value is 2 so the whole expression would have a value of 0. But, that is not the right answer. Thank you!

50. ## Algebra

What is the minimum possible value for y=x^2+12x+5? I am not sure where to even start. Thank you!

51. ## Algebra 2

What is the minimum possible value for y=x^2+12x+5? I am not sure where to start.

52. ## Math

Find all values of p such that 2(x+4)(x-2p) has a minimum value of -18? I know x=-4 but I do not know that helps us. Please explain in steps! The temperature of a point (x,y) in the plane is given by the expression x^2-y^2-4x+2y. What is the temperature of

53. ## Computer Science

I posted this question before. The assignment was: write a Java method if the first parameter is less than the second parameter add the two and print the result ten times. How do I write the result 10 times as a loop? This is what I've got but I have a ton

54. ## Basic Computer Science

Write a method in Java that takes two parameters. If the first parameter is equal to the second parameter multiply both and print the result. Thanks.

55. ## Algebra

Find the leading coefficeint in the polynomial -3(x^4-x^3+x)+7(x^4+2)-4(2x^4+2x^2+1) after it is simplified. I got this -3x^4+3x^2-3x+7x^4+14-8x^4-8x^2-4 and I simplified it to -4x^4-5x^2+10 so what would the leading coeffiecient be -4?

56. ## Algebra

What is the coefficient of x^3 when 24x^4+6x^3+4x^2-7x-5 is multiplied by 6x^3+3x^2+3x+4 and the like terms are combined? I got 144x^7+108x^6+90x^5+114x^4+24x^3 so the answer would be 24. But I am not sure if I am right.

57. ## Algebra

Suppose that f is a polynomial such that (x^2-1)*f(x)=5x^6-x^5+3x^4+x^3-25x^2+38x-17. What is the degree of?

58. ## Algebra

Consider the polynomials: F(x)= 4x^3 + 3x^2 + 2x +1 G(x)= 3 - 4x + 5x^2 - 6x^3 Find c such that the polynomial f(x)+cg(x) has degree 2.

59. ## Algebra

What are the coordinates of the points where f(x) =x^3-x^2+x+1 And g(x)=x^3+x^2+x-1 intersect?

60. ## Algebra

Assume that f(3)=4. Name a point that must be on the graph of y=1/2f(x/2).

61. ## Algebra/Math

The graphs of a function f(x)=3x+b and its inverse function f^-1(x) intersect at the point (-3,a). Given that b and a are both integers, what is the value of a?

62. ## Algebra

The function f(x,y) accepts an ordered pair as input and gives another ordered pair as output. It is defined according to the following rules: If x>4, f(x,y)=(x-4,y). If x4, f(x,y)=(x,y-4). Otherwise, f(x,y)=(x+5,y+6). A robot starts by moving to the point

63. ## Algebra

Given the functions f(x)=x+5/3 and g(x)=1/f^-1(x)+1, find the value of g(3). The first step would first be to find the inverse of x+1, the denominator of the fraction. I think the inverse would be 1-x. And now we have 1/1-x so we can just plu in 3. Right?

64. ## Algebra

If h(y)=1+y/2-y, then what is the value of h^-1(5)? Express your answer in simpilest form. The first step would be to find the inverse of the 1+y/2-y which would be 2y-xy I think, and then would we plug in 5 for x or y?

65. ## Algebra

The values of a function f(x) are given in the table: x=1, f(x)=3 x=2. f(x)=1 x=3. f(x)=5 x=4, f(x)=4 x=5, f(x)=2 If f^-1 exists, then what is f^-1(f^-1(f^-1(1)))? I am not quite sure what this question is asking. I know it is asking to find the inverse 3

66. ## Algebra

Given the function f(x)=3x^3+2, find the value of x so that f^-1(x)=4. Thank you. I tried to solve for the inverse by susbsituting y in for x so: x=3y^3+2 and then I subtracted 2 so x-2=3y^3 and I am stuck here, do I just cube root the whole thing? If so,

67. ## Algebra

Let f(x)=1/ax+b where and b are non zero constants. Find all solutions to f^-1(x)=0. Express your answer in terms of a and/or b. Thank you.

68. ## Algebra

Define f(x)=3x-8. If f^-1 is the inverse of f, find the value (s) of x for which f(x)=f^-1(x). Thank you!

69. ## Algebra

The inverse of f(x)=2x-1/x+5 may be writeen in the form f^-1(x)=ax+b/cx+d where a,b,c, and d are real numbers. Find a/c. Thank you!

70. ## algebra

Consider the f(x)=srt(x+1/x-1) and g(x)= sqrt(x+1)/sqrt(x-1). Explain why f and g are not the same function. Thank you!

71. ## algebra

Let f be a function such that f(x+y)=x+f(y) for any two real numbers x and y. If f(0)=2, then what is f(2012)? Thank you!

72. ## Algebra

what is the domain of the function u(x)=1/sqrt(x)? Thank you!

73. ## Algebra

What is the range of the function f(x)=1/1-x? Express your answer in interval notation. Thank you!

74. ## Algebra

What is the smallest integer value of c such that the function f(x)=x^2+1/x^2-x+c has a domain of all real numbers? Thank you!

75. ## algebra

What is the range of the function r(x)-1/(1-x)^2? Express your answer in interval notation. Thank you!

76. ## Algebra

Let f be a function such that f(x+y)=x+f(y) for any two real numbers x and y. If f(0)=2, then what is f(2012)? Thank you!

77. ## Algebra

There are three real numbers x that are not in the domain of f(x)=1/ 1+ (1+1/x). What is the sum of those three numbers. 0 is one of them,I don't know the other ones.Thank you!

78. ## Computer Science

This was the assignment: If the first parameter is less than the second parameter add the two and print the result 10 times. THIS PROGRAM IS IN JAVA. I did everything but I can't figure out how to print the result as a loop 10 times. public static void

79. ## Algebra

Solve for x, when (2^(x+1))^3*4^x=8192

80. ## Algebra

Is 2000(1+0.05)^18=4183.24?

81. ## Algebra

Solve for x, when (2^(x+1)^3)*4^x=8192.

82. ## Algebra

Given that 2^x+2^x+2^x+2^x=512, what is the value of x? I think it simpliflies to 2^4x=512. and 2^9=512 but to get 9 you have to mulitply something to 4, but its 2.25 is that right?

83. ## Algebra

Solve for x: (1/25)^x+2=125^-x

84. ## Algebra: Steve

I already asked this question,I just wanted to clarify the answer. Problem: The polynomial f(x) has degree 3. If f(-1)=15, f(0)=0, f(1)=-5, f(2)=12, then what are the x-intercepts of the graph of f? Steve: clearly, f(0) = 0 so, f(x) = ax^3+bx^2+cx =

85. ## Algebra

There is a polynomial which, when multiplied by x^2+2x+3, gives 2x^5+3x^4+8x^3+8x^2+18x+9. What is the polynomial?

86. ## Algebra

Find t if the expansion of the product of x^3-4x^2+2x-5 and x^2+tx-7 has no x^2 term.

87. ## Algebra

Suppose f is a polynomial such that f(0)=47, f(1)=32,f(2)=-13, and f(3)=16. what is the sum of the coefficients of f?

88. ## Algebra

Let f(x)=4x^7+x^5+3x^2-2x+c. For what value of c is f(-1)=0?

89. ## Algebra

Find h(x) with terms in order of decreasing degree, if 9x^3-3x+1+h(x)=3x^2-5x+3.

90. ## Algebra

If p(x)=x^4-3x+2, then find the coefficient of the x^3 term in the polynomial (p(x))^3.

91. ## Algebra

If f(x) is a polynomial of degree 4, and g(x) is a polynomial of degree 2, then what is the degree of polynomial f(x)-g(x)?

92. ## Algebra

Let f,g, and h be polynomials such that h(x)=f(x)*g(x). If the constant term of f(x) is -4 and the constant term of h(x) is 3, what is g(0)?

93. ## Algebra

Let a and b be real numbers, where a

94. ## Algebra

Let a and b be real numbers, where a

95. ## Algebra

What are the coordinates of the points where f(x)=x^3-x^2+x+1 and g(x)=x^3+x^2+x-1 intersect?

96. ## Math

How many square units are in the area of the triangle whose vertices are the x and y intercepts of the cuure y=(x-3)^2(x+2)?

97. ## Algebra

Given that f(x) is a function such that f(1)=2, f(4)=3, f(7)=4, and f^-1(x) is the inverse of f(x), what is f^-1(f^-1(3))? I am really getting confused with the two F^-1. Please help. Thank you.

98. ## Algebra

If f(x)=x^5-1/3, find f^-1(-31/96). I think the first step would be to find the inverse of -31/96, but I am not sure how to find that :). Then I could make x^5-1/3= the inverse of -31/96.

99. ## Algebra

Let f(x)=px+q, where p and q are real numbers. Find p+q if f(f(f(x)))=8x+21. Thank you.