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Recent problems solved by 'Abbey'

Abbey answered: 339 problems
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Money_Word_Problems/8916: what is a formuala. and a good explanation going through how you get from one step to another on.. " Cost and Money Problems "... Algebra 1... thank you
1 solutions

Answer 4874 by Abbey(339) About Me  on 2005-08-30 13:53:04 (Show Source):
You can put this solution on YOUR website!
Since we are tutors from all over the US, and there are hundreds of books called algebra I, there is no way any of us could give an answer to this question.
Perhaps you could try posting a problem, and we can give you an explanation for the solution and you can get what you need from it?


Average/8834: At noon, one ship sails north from Castaway Island at 15 knots and another ship sails east at 20 knots. (A knot is a nautical mph.) How far apart will the ships be at 2:00 p.m.?
1 solutions

Answer 4873 by Abbey(339) About Me  on 2005-08-30 13:50:23 (Show Source):
You can put this solution on YOUR website!
I'm confused i did not want help with this problem!!!


Complex_Numbers/8843: a five-digit perfect square in the form of 5abc6 has a thousands digit a, hundreds digit b, and tens digit c. if a< b< c, what is the sum of a+b+c?
1 solutions

Answer 4872 by Abbey(339) About Me  on 2005-08-30 13:46:35 (Show Source):
You can put this solution on YOUR website!
because this is a five digit square, we are squaring a 3 digit number that ends in 6 and is less than 250*250, but greater than 200*200
our choices then are
226^2=51076
236^2=55696
the only one that meets the criteria of a so the number is 55696
a+b+c = 20


Expressions-with-variables/8912: answer with work please.2/3x-5=5(x-3)
1 solutions

Answer 4871 by Abbey(339) About Me  on 2005-08-30 13:34:53 (Show Source):
You can put this solution on YOUR website!
%282%2F3%29x-5=5%28x-3%29
clear the parentheses:
2x%2F3-5=5x-15
add 5 to both sides:
2x%2F3++=5x-10
subtract 5x from both sides:
2x%2F3-5x=-10
convert 5x to a fraction
2x%2F3-15x%2F3=-10
combine x terms:
-13x%2F3=-10
multiply both sides by 3 to clear the denominator:
-13x=-30
divide both sides by -13
x=30%2F13


Miscellaneous_Word_Problems/8848: a fish was caught whos tail weighs 9 pounds. His head weighed as much as his tail and half his body,and his body weighs as much as his head and his tail. how much does the fish weigh

1 solutions

Answer 4870 by Abbey(339) About Me  on 2005-08-30 13:29:39 (Show Source):
You can put this solution on YOUR website!
let's break this apart into manageable pieces:
a fish was caught whos tail weighs 9 pounds.
Let the Tail (T) = 9 pounds
His head weighed as much as his tail and half his body,
Head (H) = T + 1/2 Body (B)
H=9+B/2
and his body weighs as much as his head and his tail.
B=H+T
B=H+9

how much does the fish weigh
since we know that the head =9+b/2, we can substitute into our second equation:
B=9+b/2+9
B=18+b/2
b-b/2=18
b/2=18
b=36
so the body weighs 36 pounds,
the head weighs 27 pounds
and the tail weighs 9 pounds
the fish (in total) weighed 72 pounds
That is certainly a whopper!


Exponents-negative-and-fractional/8879: If 4^(1/5) = x, then
a. x * x * x * x * x = 4
b. 1/(x * x * x * x * x) = 4
c. 4 * 4 * 4 * 4 * 4 = x
d. 1/(4 * 4 * 4 * 4 * 4) = x

1 solutions

Answer 4869 by Abbey(339) About Me  on 2005-08-30 13:19:23 (Show Source):


Linear-equations/8904: 2(p + 5) - (9 + p) = -3. I can not figure out how the book got the answer of -4. Could you please show all the steps invloved?
Thanks,
Brandy
1 solutions

Answer 4868 by Abbey(339) About Me  on 2005-08-30 13:17:47 (Show Source):
You can put this solution on YOUR website!
Since I don't know where you made your error, I can guess that either you forgot to distribute the negative sign in front of the (9+p)or you forgot to distribute the 2 to the (p+5), so:
using the distributive property we will clear the parentheses:
2(p + 5) - (9 + p) = -3
2p+10-9-p=-3
then combine like terms:
p+1=-3
subtract 1 from both sides:
p=-4


Mixture_Word_Problems/8906: use definitions or identites to find the exact value of the remaining 5 trig functions.
1. sin=(sqrt3)/4
2. cot=1/2
3. csc=5
4. sec = 5/3
5. cot=2
Thank you so much!!
1 solutions

Answer 4867 by Abbey(339) About Me  on 2005-08-30 13:13:56 (Show Source):
You can put this solution on YOUR website!
In order to solve these trig problems, you should remember:
sin^2X+cos^2X=1
and remember that
tan=sin/cos
cot=cos/sin
sec=1/cos
csc=1/sin
1. sin=(sqrt3)/4 then:
cos=(sqrt13)/4
tan=(sqrt3/sqrt13)
csc=4/(sqrt3)
sec=4/(sqrt13)
cot=(sqrt13)/(sqrt3)
2. cot=1/2 then:
sin=2/(sqrt5)
cos=1/(sqrt5)
tan=2
csc=(sqrt5)/2
sec=sqrt5
cot=1/2
3. csc=5 then:
sin=1/5
cos=(2sqrt6)/5
tan=1/(2sqrt6)
sec=5/(2sqrt6)
cot=(2sqrt6)
4. sec=5/3 then:
sin=4/5
cos=3/5
tan=4/3
csc=5/4
cot=3/4
5. cot=2 then:
sin=1/(sqrt5)
cos=2/(sqrt5)
tan=1/2
csc=sqrt5
sec=(sqrt5)/2


Equations/8908: I have done this before, however I am not coming up with the correct way to solve the problem. Ax+By=c solve for y?
1 solutions

Answer 4866 by Abbey(339) About Me  on 2005-08-30 13:08:50 (Show Source):
You can put this solution on YOUR website!
Ax+By=c
subtract Ax from both sides of the equation:
By=c-Ax
divide both sides by b
y=(c-Ax)/b


Square-cubic-other-roots/8909: Simplify square root of (x^2+4).
thanks, Kyle
1 solutions

Answer 4865 by Abbey(339) About Me  on 2005-08-30 13:07:47 (Show Source):
You can put this solution on YOUR website!
this is in its simplest form (no two numbers mutliplied together will give you x^2 + 4)


Equations/8910: I am working hard to get to the point where I could solve word problems in Algebra. Problem: The second angle of a triangular parking lot is four times as large as the first angle. The third angle is 45 degrees less than the sum of the other two angles. How long are the angles?
1 solutions

Answer 4864 by Abbey(339) About Me  on 2005-08-30 13:06:44 (Show Source):
You can put this solution on YOUR website!
let the first angle = x
let the second angle =4x
let the third angle = x+4x-45
so when these are added together, they will total 180 degrees:
x+4x+x+4x-45=180
add 45 to both sides and combine like terms:
10x=225
x=22.5 degrees
so if the first angle =22.5 degrees, the second angle must = 90 degrees and the final angle equals 90+22.5-45 = 67.5 degrees.


Graphs/6357: Find x and y-intercepts for the equation. Then graph the eguation.
15y-3x=-9
1 solutions

Answer 3412 by Abbey(339) About Me  on 2005-08-01 10:36:09 (Show Source):
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First put this into y=mx+b format:
add 3x to both sides:
15y=3x-9
divide by 15:
y=(3/15)x-(9/15)
reduce fractions:
y=(1/5)x-(3/5)
your y intercept occurs when x=0:
y=-3/5, so the y-intercept is (0,-3/5)
the x intercept will be when y=0
0=(1/5)x-(3/5)
add 3/5 to both sides:
3/5=1/5x
multiply both sides by 5:
3=x, so the x intercept occurs at (3,0)


Numeric_Fractions/6181: I just need to know if I am right or not. My question is Reduce the fraction
-20t^5 u^2 v^3
--------------
48t^7 u^4 v
I think the answer is
-5v^2
---------
12t^2 u^2
1 solutions

Answer 3317 by Abbey(339) About Me  on 2005-07-30 09:36:41 (Show Source):
You can put this solution on YOUR website!
you are correct


Mixture_Word_Problems/6186: without using a calculator find the value of the following
1. logbase8 8 = is it 1?
2. logbase3(1/9) = -2??
3. logbase1/3 9= 27???
4. logbase5 cuberoot25 = I have no idea
5. logbasesqrt3 9 = ??
6. lne^3= ??
Can someone help me with these i thought i understood but i'm really stuck.
thank you so much.
1 solutions

Answer 3316 by Abbey(339) About Me  on 2005-07-30 09:31:50 (Show Source):
You can put this solution on YOUR website!
1. logbase8 8 = is it 1? This is correct.
2. logbase3(1/9) = -2?? This is correct
The first two problems seemed to be no problem for you, you simply put them into the same form and solved, so we can rewrite the following problems in the same form to see the answers as well:
3. logbase1/3 9= 27??? rewrite 9 as (1/3)^-2 so the problem is now:
log+%281%2F3%29%5E%281%2F3%29%5E-2=+-2
4. logbase5 cuberoot25 = rewrite cube root of 25 as 5%5E%282%2F3%29 so the problem now reads:
log%285%29%5E5%5E%282%2F3%29=2%2F3
5. logbasesqrt3 9 = rewrite 9 as sqrt%283%29%5E4
log+%28sqrt%283%29%29%5E%28sqrt%283%29%5E4%29=4
6. lne^3= = rewrite this as 3*lne (the lne=1) so, 3*1=3


Quadratic_Equations/6194: Hello
I need to solve the following problem:
A company uses the function: C(x) = 2x2 – 40x + 250 to model the cost of producing x units. How many units must be made to minimize the cost?
Thanks much
Mhunter
1 solutions

Answer 3315 by Abbey(339) About Me  on 2005-07-30 09:21:47 (Show Source):
You can put this solution on YOUR website!
C%28x%29+=+2x%5E2+%96+40x+%2B+250+
if the cost is minimized, then it will equal zero:
0+=+2x%5E2+%96+40x+%2B+250+
divide both sides by 2:
0=x%5E2-20x%2B125
factor:
%28x%2B5%29%28x-25%29
x=-5 or 25
since we are talking about producing an item, we cannot produce negative items, so we can discard the -5 answer.
costs will be minimized if 25 units or more are produced.


Age_Word_Problems/6190: if A is 3 yrs older than B and B is twice of the age of C..the total sum of ages are 30 then what is the age of B?
1 solutions

Answer 3314 by Abbey(339) About Me  on 2005-07-30 09:17:19 (Show Source):
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A is 3 years older than B:
A=3+B
B is twice the age of C:
B=2C
so A compared to C is
A=3+2C
the sum of their ages is 30:
(3+2C)+(2C)+C=30
3+2C+2C+C=30
3+5C=30
subtract 3 from both sides:
5C=27
divide both sides by 5
C=27/5 or 5 and 2/5 years
so B is
2(27/5) =54/5 = 10 and 4/5 years
and A is 13 and 4/5 years
check:
10 and 4/5 + 13 and 4/5 + 5 and 2/5 = 30, so it is correct


Geometry_Word_Problems/6206: what is the volume + surface area of a cylinder

1 solutions

Answer 3313 by Abbey(339) About Me  on 2005-07-30 09:08:55 (Show Source):
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if you think about slicing a cylinder lengthwise and unpeeling it, it would look like a rectangle, right? (roll up a piece of 8.5x11 paper and it makes a cylinder)
so the formula for the surface area will be length * width. the trick here is to remember that the length will be the height of the cylinder, and the width will be the circumference of the cylinder:
circumference = 2pi*radius
so the area = 2pi*radius*height
the volume is the area of opening to the cylinder * height
pi%2Ar%5E2%2Ah
so the volume + surface area =
pi%2Ar%5E2%2Ah%2B%282pi%2Ar%29


Numeric_Fractions/6201: I am not sure if I am doing this question right, Can someone help me? My question is multiply,
3xyz^2 2y
------ by -----
6y^4 xz^4
I think the answer is
x^2
---------
3y^2 z^2
Am I right?
1 solutions

Answer 3312 by Abbey(339) About Me  on 2005-07-30 09:00:45 (Show Source):
You can put this solution on YOUR website!
because everything is being multiplied (and not added or subtracted) you can take every cancellation opportunity:
%283xy%5E2%2A2y%29%2F%286Y%5E4xz%5E4%29
so the (3*2) in the numerator cancels with the 6 in the denominator:
%28xy%5E2%2Ay%29%2F%28y%5E4xz%5E4%29
then the x in the numerator cancels with the x in the denominator:
%28y%5E2%2Ay%29%2F%28y%5E4z%5E4%29
then the (y^2*y) in the numerator will cancel with three of the Y's in the denominator:
1%2F%28yz%5E4%29


Numeric_Fractions/6200: I am not sure if I am doing this question right or not. Reduce the fraction.
-20t^5 u^2 v^3
--------------
48t^7 u^4 v
I think the answer is
-5v^2
-----------
12t^2 u^2
Am I right?

1 solutions

Answer 3311 by Abbey(339) About Me  on 2005-07-30 08:50:12 (Show Source):
You can put this solution on YOUR website!
you are absolutely right


Radicals/6207: Simplify the radicals....
radical sign 40 + radical sign 10 + radical sign 2/5
1 solutions

Answer 3310 by Abbey(339) About Me  on 2005-07-30 08:48:21 (Show Source):
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sqrt%2840%29%2Bsqrt%2810%29%2Bsqrt%282%29%2F5
First get rid of the denominator by multiplying everything by 5:
5%2Asqrt%2840%29%2B5%2Asqrt%2810%29%2Bsqrt%282%29
The key to simplifying radicals is to factor what is inside the radical
5%2Asqrt%282%2A2%2A2%2A5%29%2B5%2Asqrt%282%2A5%29%2Bsqrt%282%29
then pull out groups of numbers according to the index on the radical - if there is no index, it is by twos. In this case, we can only pull out a set of two "2"'s from the first radical sign. When you pull out the group represent it in front of the radical by one of it's members
example:
sqrt%283%2A3%2A3%29=3%2Asqrt%283%29
so your problem becomes:
5%2A2%2Asqrt%282%2A5%29%2B5%2Asqrt%282%2A5%29%2Bsqrt%282%29
then add anything that has the same radical:
10%2Asqrt%2810%29%2B5%2Asqrt%2810%29%2Bsqrt%282%29
15%2Asqrt%2810%29%2Bsqrt%282%29




Radicals/6208: My question says to simplify the radical
(radical sign 6 - radical sign 5)(radical sign 6 + radical sign 5)
Thank you
1 solutions

Answer 3309 by Abbey(339) About Me  on 2005-07-30 08:38:01 (Show Source):
You can put this solution on YOUR website!
%28sqrt%286%29-sqrt%285%29%29%2A%28sqrt%286%29%2Bsqrt%285%29%29
Use the FOIL method:
%286%2Bsqrt%2830%29-sqrt%2830%29-5%29
=1


Quadratic_Equations/6216: a retailer spent $48 to purchase a number of special mugs. two of them were broken in the store, but by selling each of the remaining mugs for $3 above the original cost per mug, she made a total profit of $22.
construct an equation that will allow us to solve for the # of mugs, denoted by N, that were originally purchased.(QUADRATIC EQUATIONS)
a)if the price for n mugs is $48, how can we express the cost per mug?
b)we are told that the retailer, in order to make a specific profit, sells the remaining mugs for $3 over the original cost per mug. using this imformation, and your answer to step (a), how can we express the selling price per mug?
c)since to of the mugs were broken in the store, how can we represent the # of mugs that are available for sale?
d)use your answers from step (b) and (c) to construct an expression for the amount of money made on the sale of the remaining mugs.
e)the profit on the mugs can be found by subtracting the cost of the mugs from the amount of money made on the sale of the mugs. write an equation that states this relationship between the money made, the cost, and the profit.
PLEASE HELP!!!!!!!!!!!!!!!!!!!!
1 solutions

Answer 3308 by Abbey(339) About Me  on 2005-07-30 08:31:52 (Show Source):
You can put this solution on YOUR website!
Let n = the number of mugs purchased by the retailer
Let n-2 = the number of mugs available for sale (the retailer broke two)
Let (48/n) - the cost of each mug purchased by the retailer ($48 spent divided by the number of mugs)
If she sold each mug for a 3 profit
(3+(48/n)) is the sale price of each mug
(n-2)(3+(48/n)) = the total sales (the number of mugs sold*the price)
the total sales = cost + $22 profit
(n-2)(3+(48/n))=48+$22





expressions/6132: x^2 + 2x - 15 = 0
1 solutions

Answer 3273 by Abbey(339) About Me  on 2005-07-28 20:39:30 (Show Source):


Polynomials-and-rational-expressions/6138: Please show me how to solve: (x/y)^3 / (x/2y)^3
(x/y) is a fraction and (x/2y) is a fraction
Thank you!!!!!!!!!!!
1 solutions

Answer 3272 by Abbey(339) About Me  on 2005-07-28 20:27:36 (Show Source):
You can put this solution on YOUR website!
first clear your parentheses, by raising everything to the power indicated:
%28x%2Fy%29%5E3+%2F+%28x%2F2y%29%5E3
%28x%5E3%2Fy%5E3%29%2F%28x%5E3%2F8y%5E3%29
with complex fractions, you just flip the bottom turn and multiply:
%28x%5E3%2Fy%5E3%29%2A%288y%5E3%2Fx%5E3%29
8x%5E3y%5E3%2Fx%5E3y%5E3
the x^3 and y^3 terms reduce to 1, so the answer is 8


Numeric_Fractions/6139: I am having a hard time with Algebraic Fractions. My question is Reduce the fraction 6x/12x to lowest terms? Is the answer 1/2x??? Please let me know.
1 solutions

Answer 3271 by Abbey(339) About Me  on 2005-07-28 20:21:34 (Show Source):
You can put this solution on YOUR website!
you are very close, but the x/x reduces to just 1, so 6x/12x will reduce to just 1/2


Linear-equations/6144: what are the coordinates of the point where each line crosses the y-axis?
y=3x+4
1 solutions

Answer 3270 by Abbey(339) About Me  on 2005-07-28 20:20:25 (Show Source):
You can put this solution on YOUR website!
substitute 0 for x in your equation:
y=3(0) + 4
y=4
so the point is (0,4)


Mixture_Word_Problems/6143: Abby these are the last 2 i'm stuck on. Can you help?
Express the sum or difference of the log. express powers as factors
1. log5(cuberootx^2+1)All under the radical /(x^2-1)^2
2. log x^3sqrt(x+1)/(x-2)^2
Thank you so much! You are a great help!
1 solutions

Answer 3269 by Abbey(339) About Me  on 2005-07-28 20:19:13 (Show Source):
You can put this solution on YOUR website!
okay, if the (x^2-1) is part of the logarithm, but not under the radical, then:
log5%28x%5E2%2B1%29%5E%281%2F3%29-log5%28x%5E2-1%29%5E2
%281%2F3%29%2Alog5%28x%5E2%2B1%29-2%2Alog5%28x%5E2-1%29
2. log x^3sqrt(x+1)/(x-2)^2
log%28%28x%5E3%2Asqrt%28x%2B1%29%29%2F%28x-2%29%5E2%29
log%28%28x%29%29%5E3%2Blog%28%28x%2B1%29%29%5E%281%2F2%29-log%28%28x-2%29%29%5E2
3%2Alog%28%28x%29%29%2B%281%2F2%29%2Alog%28%28x%2B1%29%29-2%2Alog%28%28x-2%29%29



Mixture_Word_Problems/6140: Abby let me try again..
log5 {cuberoot x^2+1} all under the radical divided by (x^2-1)
Thank you. Caroline

1 solutions

Answer 3268 by Abbey(339) About Me  on 2005-07-28 20:10:13 (Show Source):
You can put this solution on YOUR website!
okay, if the (x^2-1) is part of the logarithm, but not under the radical, then:
log5%28x%5E2%2B1%29%5E%281%2F3%29-log5%28x%5E2-1%29
%281%2F3%29%2Alog5%28x%5E2%2B1%29-log5%28x%5E2-1%29
by the way, someone else just posted this same problem with the divisor as %28x%5E2-1%29%5E2


Numeric_Fractions/6141: I am having a hard time with Algebraic Fractions. My question is Simplify the fraction-(2x/-xy)completely? Is the answer -2/xy??? Please let me know?
1 solutions

Answer 3267 by Abbey(339) About Me  on 2005-07-28 20:05:00 (Show Source):
You can put this solution on YOUR website!
If you simplify x/x you get 1 (any number divided by itself is 1)
so -2x/-xy:
the negatives cancel and the x's reduce to (1)
the answer is 2/y


Mixture_Word_Problems/6142: Abby can you help me with these 3 problems?
express as a single logarithm
1. log3u^2 - log3v
2. log2(1/x)+log2(1/x^2)
3. log (x^2+2x-3/x^2-4)-log(x^2+7x+6/x+2)
1 solutions

Answer 3266 by Abbey(339) About Me  on 2005-07-28 20:02:27 (Show Source):
You can put this solution on YOUR website!
the difference of logs with the same base can be expressed as a fraction:
1. log3%28u%5E2%2Fv%29
The sum of logs with the same base can be expressed as multiplication:
2. log2%281%2Fx%5E3%29
This is a complex fraction, so you have to flip and multiply:
3. log%28%28%28x%5E2%2B2x-3%29%28x%2B2%29%29%2F%28%28x%5E2-4%29%28x%5E2%2B7x%2B6%29%29%29%29


Equations/6113: I am trying to find the value of x in the following equation:
(x-y)/x=.3
Thanks for any help you can give.
Kathy
1 solutions

Answer 3262 by Abbey(339) About Me  on 2005-07-28 14:31:56 (Show Source):
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first separate the (x-y)/x to get:
x%2Fx-y%2Fx=.3
then multiply through by x to get rid of the denominator:
x-y=.3x
subtract x from both sides:
-y=-.7x
then divide both sides by -.7:
y%2F.7=x