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Recent problems solved by 'stanbon'
stanbon answered: 57135 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>NextPolynomials-and-rational-expressions/108609: Besides 0, what is the other factor of 14y - y^2 = 0
1 solutions
Answer 79192 by stanbon(57203)   on 2007-11-07 15:40:54 (Show Source):
You can put this solution on YOUR website!Besides 0, what is the other factor of 14y - y^2 = 0
------------
Comment: 0 is not a factor; it is a zero or root of the equation.
--------------------
14y - y^2 = 0
y(14-y)=0
The factors are y and 14-y
y = 0 or 14-y=0
y = 0 or y = 14
The zeroes are 0 and 14
=====================
Cheers,
Stan H.
|
expressions/108610: Multiply.
(4xy3) ( 2x2y )( 5xy2)
1 solutions
Answer 79190 by stanbon(57203) on 2007-11-07 15:37:59 (Show Source):
You can put this solution on YOUR website!Multiply.
(4xy^3) ( 2x^2y )( 5xy^2)
Multiply the coefficients to get: 40
Multiply the x-factors to get: x^4
Multiply the y-factors to get: y^6
-----------------
Answer: 40x^4y^6
=====================
Cheers,
Stan H.
|
Coordinate-system/108611: Find the slope of the line with the equation 4x+6y=11
Answers to pick from are 4, -2/3, 2/3, 11/6
My answer was 4, but I do not know if I am correct, my workbook does not explain how to do it very well!!
1 solutions
Answer 79189 by stanbon(57203) on 2007-11-07 15:35:35 (Show Source):
You can put this solution on YOUR website!Find the slope of the line with the equation 4x+6y=11
Answers to pick from are 4, -2/3, 2/3, 11/6
My answer was 4,
-------------------------
Solve the equation for "y":
6y = -4x+11
y = (-2/3)x+(11/6)
----------
The slope is -2/3
================
Cheers,
Stan H.
|
Coordinate-system/108606: Find the y-intercept of the line with the equation 2x-6y=15
The answers for me to pick from are -5/2, 15/2, -15/2, 15
I came up with the answer -5/2, here is my work...
15=2x-6y
15 divided by -6 = -5/2
Answer -5/2
Am I correct?
1 solutions
Answer 79188 by stanbon(57203) on 2007-11-07 15:33:32 (Show Source):
You can put this solution on YOUR website!Find the y-intercept of the line with the equation 2x-6y=15
----------
Here are two ways to work the problem:
1st: To find the y-intercept let x=0:
You get -6y = 15; y = -5/2
-------------------
2nd: Put the equation in slope-intercept form:
6y = 2x-15
Divide both sides by 6 to get:
y = (1/3)x-(5/2)
y-intercept is -5/2
===============
Cheers,
Stan H.
|
Quadratic_Equations/108595: The following matrix is obtained from the augmented matrix of a system of equations.
1 0 3 20
0 1 2 -2
0 0 1 4
What is the solution to the system is?
1 solutions
Answer 79181 by stanbon(57203) on 2007-11-07 15:15:14 (Show Source):
You can put this solution on YOUR website!1 0 3 20
0 1 2 -2
0 0 1 4
What is the solution to the system is?
----------------
Assuming the variables are a, b, c,
The 3rd line implies that c = 4
If c=4 the 2nd line implies b+2c=-2; b+8=-2; b=-10
If c=4 and b=-10 the 1st line implies a + 3c = 20; a+12=20; a=8
==================
Cheers,
Stan H.
|
Graphs/108601: How would I answer these problems I am really stuck. Any help would be greatly appreciated. Thank you.
Suppose the graph of y = x^2 is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?
a)  (Cannot copy and paste this graph)for this parablola
Answer: g(x) = (x + 1)^2 – 3 (vertical shift down 3 units) Y = X^2 - 3
Is this right???
b)  x , y, axis U shape goes right over 4 on the x axis
Answer: g(x) = (x – 4)^2 (horizontal shift right 4 units) Is this right???
3) Consider the following graph of y = f(x).
a) If h(x) = f(x) + 2, what would the new coordinates of P be after the shift? Give answer in (x, y) form.
Answer:
b) If , what would the new coordinates of P be after the reflection? Give answer in (x, y) form.
Answer:
4) Consider the function: f(x)= x^2+ 4x + 1
a) Find h, the x-coordinate of the vertex of this parabola.
Answer:
Show your work here:
b) Substitute the two whole number values immediately to the left and right of h into the function to find the corresponding y. Fill in the following table. Make sure your x-values are in increasing order in your table.
Answer:
x y
h =__
c) Use MS Excel to graph the function by plotting the points found in the table in part b.
Answer:
5) Find the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote.
a)f(x)= 2x+3/x+2
Answer:
Horizontal:
Vertical:
b)g(x)= 5x/x^2+1
Answer:
Horizontal:
Vertical:
c)
Answer:
Horizontal:
Vertical:
d)
Answer:
Horizontal:
Vertical:
1 solutions
Answer 79179 by stanbon(57203) on 2007-11-07 15:09:28 (Show Source):
You can put this solution on YOUR website!How would I answer these problems I am really stuck. Any help would be greatly appreciated. Thank you.
Suppose the graph of y = x^2 is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?
a)g(x) = (x + 1)^2 – 3
The (x+1) moves each point of y=x^2 one to the left
The -3 moves the result of the 1st move down three.
 graph(400,300,-10,10,-10,10,(x+1)^2-3
------------------------------
Answer: b) x , y, axis U shape goes right over 4 on the x axis
Answer: g(x) = (x – 4)^2 (horizontal shift right 4 units) Is this right???
Yes, that is correct.
-----------------------------------
3) Consider the following graph of y = f(x).
a) If h(x) = f(x) + 2, what would the new coordinates of P be after the shift? Give answer in (x, y) form.
Answer: (x, f(x)+2)
------------------------
b) If , what would the new coordinates of P be after the reflection? Give answer in (x, y) form.
Answer: That depends on what line you reflect in:
If you reflect in the y-axis the answer is (-x,h(x))
If you reflect in the x-axis the anser is (x,-h(x))
---------------------------------
4) Consider the function: f(x)= x^2+ 4x + 1
a) Find h, the x-coordinate of the vertex of this parabola.
Answer: (-2,-3)
Show your work here:
Complete the square on the x-terms:
x^2+4x +? = f(x)-1+?
x^2+4x+4 = f(x)+3
(x+2)^2 = f(x)+3
-----------------------------
b) Substitute the two whole number values immediately to the left and right of h into the function to find the corresponding y. Fill in the following table. Make sure your x-values are in increasing order in your table.
Answer:
f(x)= x^2+ 4x + 1
x y
If x = -4, y = 16-16+1 = 1
If x = -3, y = 9-12+1 = -2
If x = -1, y = 1-4+1 = -2
If x = 0, y = 0+0+1 = 1
h =__
=====================
c) Use MS Excel to graph the function by plotting the points found in the table in part b.
Answer:
I'll leave that to you.
------------------------------
5) Find the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote.
a)f(x)= 2x+3/x+2
Answer:
Horizontal:y = 2x/x = 2
Vertical: x = -2
------------------
b)g(x)= 5x/x^2+1
Answer:
Horizontal: y = 0x^2/x^2 = 0
Vertical: none since x^2+1 cannot be zero
---------------------
c)
Answer:
Horizontal:
Vertical:
d)
Answer:
Horizontal:
Vertical:
=======================
Cheers,
Stan H.
|
real-numbers/108598: Can you help me solve this equation for real solutions?
x^3-6x+3=0
1 solutions
Answer 79173 by stanbon(57203) on 2007-11-07 14:51:35 (Show Source):
You can put this solution on YOUR website!solve this equation for real solutions?
x^3-6x+3=0
-------------
I graphed it with a TI-83 and found zeroes at
x = -2.553191... , x = 0.5239764..., x = 2.1451027...
===============
Cheers,
Stan H.
|
Mixture_Word_Problems/108543: This question is from textbook Algebra 1
Nature's Best wants to combine nuts they sell for $3.60 a pound with dried fruit they sell for $2.40 a pound to create a trail mix. How much of each snack should they use to make 10 pounds of trail mix that would sell for $3.30 a pound?
We know the answer is 7.5 pounds of nuts and 2.5 pounds of dried fruit but we cannot come up with the algebraic equation to solve it. Thanks!
1 solutions
Answer 79162 by stanbon(57203) on 2007-11-07 13:41:03 (Show Source):
You can put this solution on YOUR website!Nature's Best wants to combine nuts they sell for $3.60 a pound with dried fruit they sell for $2.40 a pound to create a trail mix. How much of each snack should they use to make 10 pounds of trail mix that would sell for $3.30 a pound?
--------------
Let amt. of nuts be "x" lbs ; value is 3.60x dollars
-------------
Amt of fruit is "10-x" lbs ; value is 2.4(10-x) = 24-2.4x dollars
----------------------
Amt of mix is 10 lbs ; value is 3.3*10= 33 dollars
------------------------
EQUATION:
value + value = 33 dollars
3.6x + 24-2.4x = 33
1.2x = 9
x = 7.5 lbs (amt of nuts in the mix)
10-x = 2.5 lbs (amt of fruit in the mix)
=================
Cheers,
Stan H>
|
Equations/108561: Use the LCD to determine which fraction is greater
26. 2/5,3/10
Any help with this equation would be greatly appreciated:)
1 solutions
Answer 79161 by stanbon(57203) on 2007-11-07 13:34:32 (Show Source):
You can put this solution on YOUR website!Use the LCD to determine which fraction is greater
26. 2/5,3/10
LCD of the two fractions is 10
2/5 = 4/10
3/10 = 3/10
----------------
2/5 is greater than 3/10
=============
Cheers,
Stan H.
|
Equations/108559: Find the Least Common Multiple of the numbers or monomials.
25.12ab^2,22a^b
Any help with this equation would be greatly appreciated:)
1 solutions
Answer 79158 by stanbon(57203) on 2007-11-07 13:31:05 (Show Source):
You can put this solution on YOUR website!Find the Least Common Multiple of the numbers or monomials.
25. 12ab^2,22ab
LCM of the coefficients: 2^2*3*11 = 132
LCM of the a's: a
LCM of the b's: b^2
--------------
LCM of the two monomials: 132ab^2
================
Cheers,
Stan H.
|
Graphs/108558: Find the slope of the line perpendicular to x=3y
1 solutions
Answer 79156 by stanbon(57203) on 2007-11-07 13:26:53 (Show Source):
You can put this solution on YOUR website!Find the slope of the line perpendicular to x=3y
-----------
Rule: lines are perdicular if the product of their slopes is -1
--------------
Given line can be written as y = (1/3)x so
the given line has a slope of (1/3).
------------
Let "m" be the slope of the perpendicular line:
EQUATION:
(1/3)m = -1
m = -3
-----------
The slope of the line perpendicular to x = 3y is -3
==============
Cheers,
Stan H.
|
Equations/108557: Find the Least Common Multiple of the numbers or monomials.
24. 5x^3y,15xy
Any help with this equation would be greatly appreciated:)
1 solutions
Answer 79155 by stanbon(57203) on 2007-11-07 13:23:17 (Show Source):
You can put this solution on YOUR website!Find the Least Common Multiple of the numbers or monomials.
24. 5x^3y,15xy
LCM of the coefficients: 15
LCM of the x's : x^3
LCM of the y's : y
------------
LCM of the two monomials: 15x^3y
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Cheers,
Stan H.
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Equations/108555: Find the Least Common Multiple of the numbers or monomials.
23.8,18
Any help with this equation would be greatly appreciated:)
1 solutions
Answer 79154 by stanbon(57203) on 2007-11-07 13:21:17 (Show Source):
You can put this solution on YOUR website!Find the Least Common Multiple of the numbers or monomials.
23. 8,18
8 = 2^3
18 = 2*3^2
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LCM contains each factor to its highest power
--------------
LCM = 2^3*3^2 = 8*9 = 72
==============
Cheers,
Stan H.
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Equations/108553: Find the Great Common Factor of the numbers or monomials.
12.9ab^2,108ab^3
Any help with this equation would be greatly appreciated:)
1 solutions
Answer 79153 by stanbon(57203) on 2007-11-07 13:18:11 (Show Source):
You can put this solution on YOUR website!Find the Great Common Factor of the numbers or monomials.
12. 9ab^2,108ab^3
-----------
GCF of the coefficients: 9
GCF of the a's: a
GCF of the b's: b^2
--------------
GCF of both monomials: 9ab^2
=============
Cheers,
Stan H.
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Travel_Word_Problems/108549: Check you please check my answer.
5)Suppose that the function P=13+45lnx represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2000.
Carry all calculations to six decimals on each intermediate step when necessary.
a)Use this model to approximate the percentage of spam in the year 2003.
P=13+ln((2003) ), P=13+in(3.76394022+148), P=13(342.11), P=447.43
Thank You
1 solutions
Answer 79151 by stanbon(57203) on 2007-11-07 13:13:03 (Show Source):
You can put this solution on YOUR website!P=13+45lnx represents the percentage of inbound e-mail in the U.S. that is considered spam, where x is the number of years after 2000.
P(2003) = 13 + 45 ln(2003-2000)
P(2003) = 13 + 45 ln(3)
P(2003) = 13 + 45*1.098612289...
P(2003) = 62.43755299... or 62.4%
=============
Cheers,
Stan H.
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Equations/108548: Find the Greatest Common Factor of the numbers or monomials.
11. 23x^2,6x
Any help with this equation would be greatly appreciated:)
1 solutions
Answer 79150 by stanbon(57203) on 2007-11-07 13:08:08 (Show Source):
You can put this solution on YOUR website!23x^2,6x
---------
Look at the coefficients: the GCF is the number 1
Look at the x-factors: the GCF is x
-----------------
GCF = x
----------------
Cheers,
Stan H.
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Quadratic_Equations/108519: The question ask is to "solve by factoring" the problem listed below. The answer given is -1, -12.
x^2-13x=-12
x^2-13x+12 = -12+12
x^2-13x+12 = 0
I'm stuck past this point!
1 solutions
Answer 79142 by stanbon(57203) on 2007-11-07 09:21:51 (Show Source):
You can put this solution on YOUR website!The question ask is to "solve by factoring" the problem listed below. The answer given is -1, -12.
x^2-13x=-12
x^2-13x+12 = -12+12
x^2-13x+12 = 0
(x-12)(x-1)= 0
x = 12 or x = 1
============
Cheers,
Stan H.
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percentage/108513: I have a percentage problem ....A school bus holds 57 students and is only 40% full. How many students are on the bus? I have the answer at 22.8, It got returned to me marked wrong because it is an unreasonable answer? I cannot figure out why it is unreasonable when it is the correct answer? Can someone please help me with this?
Thank you very much,
Bonnie Cook
1 solutions
Answer 79140 by stanbon(57203) on 2007-11-07 09:01:02 (Show Source):
You can put this solution on YOUR website!The mathematical answer may be 22.8
but the "realistic" answer must be
a whole number.
I think your answer should be 22;
no one is 0.8 of a person.
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/108481: a stereo manufacture makes 3 types of streos: standard y1, quality y2 and deluxe y3. his profit margin from each is 15, 20 and 24 repectively. the standard model requires 3 hours for wiring and 1 hour for encasing. the quality model requires 1 hour for wiring and 5 hours for encasing. the deluxe model requires 3 hours for wiring and 2 hours for encasing. if 120 hours are available for wiring an 60 hours for encasing , express the output mix that will maximize profits as equations and inequalities
1 solutions
Answer 79139 by stanbon(57203) on 2007-11-07 08:04:02 (Show Source):
You can put this solution on YOUR website!a stereo manufacture makes 3 types of streos:
standard y1, quality y2 and deluxe y3.
--------------
his profit margin from each is 15, 20 and 24 repectively.
the standard model requires 3 hours for wiring and 1 hour for encasing.
the quality model requires 1 hour for wiring and 5 hours for encasing.
the deluxe model requires 3 hours for wiring and 2 hours for encasing.
if 120 hours are available for wiring and 60 hours for encasing ,
express the output mix that will maximize profits as equations and inequalities
--------------
Wiring Eq: 3y1 + y2 + 3y3 <= 120
Encase Eq: y1 + 5y2+ 2y3 <= 60
Profit Eq: Profit = 15y1 +20y2 +24y3
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Comment: You would need a 3rd equation to solve for y1,y2,y3
The profit equation is the object function and can only be
used to find the max or the min of profit.
------------
Cheers,
Stan H.
============
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Linear_Equations_And_Systems_Word_Problems/108312: Corporation Wally Mart allows each of its traveling employees
an amount of money per day for a hotel room and food expenses.
One employee travels for 4 days and 4 nights and is allotted $480 while another
employee travels for 3 days and 2 nights and is allotted $270.
a) Give the system of equations for solving this situation.
b) Find the amount allowed for a hotel room and daily food expenses
1 solutions
Answer 79138 by stanbon(57203) on 2007-11-07 07:56:03 (Show Source):
You can put this solution on YOUR website!One employee travels for 4 days and 4 nights and is allotted $480
That's 4 rooms and 12 meals
-------------------------------
while another employee travels for 3 days and 2 nights and is allotted $270.
That's 2 rooms and 9 meals
------------------------------
a) Give the system of equations for solving this situation.
1st Equation: 4r+12m = 480
2nd Equation: 2r+9m = 270
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b) Find the amount allowed for a hotel room and daily food expenses
1st Eq: r + 3m = 120
r = 120-3m
Substitute into 2nd Eq to solve for m:
2(120-3m)+9m = 270
240-6m+9m = 270
3m = 30
m = 10 ($10 for each meal)
---------
Substitute into r = 120-3m to solve for r:
r = 120-3*10
r = $90 ($90 allowed for a room)
============
Cheers,
Stan H.
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Polynomials-and-rational-expressions/108484: Which of the ordered pairs
(–12, 3), (3, 0), (–12, –3), (–22, 5)
are solutions for the equation x + 5y = 3?
1 solutions
Answer 79136 by stanbon(57203) on 2007-11-07 07:45:46 (Show Source):
You can put this solution on YOUR website!Which of the ordered pairs
(–12, 3), (3, 0), (–12, –3), (–22, 5)
are solutions for the equation x + 5y = 3?
------------
All are solutions except (-12,-3)
==============
Cheers,
Stan H.
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Equations/108498: What is the value of x in 5x-2x+9=6? Could you show me the solution?
1 solutions
Answer 79134 by stanbon(57203) on 2007-11-07 07:40:41 (Show Source):
You can put this solution on YOUR website!What is the value of x in 5x-2x+9=6
Combine "like" terms on the left side to get:
3x+9 = 6
Divide both sides by 3 to get:
x + 3 = 2
Subtract 3 from both sides to get:
x = -1
=========
Cheers,
Stan H.
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Probability-and-statistics/108467: Hi, can you help me with this question as i've been figuring out for long and still could not get the answer:
In the coming school holiday,the probability for Dave to visit his brother in Ireland is 3/5 and the probability of him going on island vacation is 2/3. Calculate the probability that Dave
a) will not visit his brother nor on an island vacation
b) will only do one activity.
Pls help me, i'm doing my o levels next week thanks
1 solutions
Answer 79132 by stanbon(57203) on 2007-11-07 07:38:38 (Show Source):
You can put this solution on YOUR website!In the coming school holiday,the probability for Dave to visit his brother in Ireland (A)is 3/5
and the probability of him going on island vacation (B) is 2/3.
Calculate the probability that Dave
------------
a) will not visit his brother nor on an island vacation
P(A' and B') = P(A')*P(B') = (2/5)*(1/3) = 2/15
-------------------
b) will only do one activity.
P(A and B) = P(A)*P(B) = (3/5)(2/3)= 2/5
P(A' and B') = 2/15 (from part a above)
Therefore: P(A or B exclusively) = 1-[2/5 + 2/15] = 1-(40/75)= 1-8/15= 7/15
===============
Cheers,
Stan H.
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Polygons/108468: how mant dimesions does a basketball have? why?
1 solutions
Answer 79131 by stanbon(57203) on 2007-11-07 07:28:26 (Show Source):
You can put this solution on YOUR website!It has a diameter which is one dimension. (length)
It has a surface area which is two dimensions.(length and width)
It has a volume which is three dimensions.(length width height)
==========
Cheers,
Stan H.
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Probability-and-statistics/108469: I am doing permutation problems using the formula nPr = n!/(n-r)!. The problem I am having difficulty with is nP3 = 24. I can get it this far:
n(n-1)(n-2)...2x1 / (n-3)(n-4)...2x1 = 24
n(n-1)(n-2) = 24 Then I'm not sure how to finish. Please help.
1 solutions
Answer 79130 by stanbon(57203) on 2007-11-07 07:24:51 (Show Source):
You can put this solution on YOUR website!nP3 = 24
n!/(n-3)! = 24
n(n-1)(n-2)=24
n(n^2-3n+2)=24
n^3-3n^2+2n-24=0
I graphed this and found n=4 is a solution.
============
Checking:
4P3 = 4!/(4-3)! = 4!/1! = 4! = 24
OK
============
Cheers,
Stan H.
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Trigonometry-basics/108499: a rectangle has a length twice its width. A square with the same area has a side 2 units longer than the width of the rectangle. Find the dimensions of the rectangle.
1 solutions
Answer 79129 by stanbon(57203) on 2007-11-07 07:17:40 (Show Source):
You can put this solution on YOUR website!a rectangle has a length twice its width.
A square with the same area has a side 2 units longer than the width of the rectangle.
Find the dimensions of the rectangle.
------------
Let width of rectangle be "x"
Then length of rectangle is "2x"
Area of rectangle is 2x^2
--------------
Square area = (side)^2 = 2x^2
Side of square = xsqrt(2)
------------------
EQUATION:
side ofsquare = width of rectangle + 2
xsqrt(2) = x+2
Square both sides to get:
2x^2 = x^2+4x+4
x^2-4x-4=0
x = [4 +- sqrt(16-4*-4)]/2
x = [4 +- sqrt(32)]/2
x = [2 +- 2sqrt(2)]
x = 2(1+sqrt(2)) or approximately 4.828...(this is the width of the rectangle)
==============
Cheers,
Stan H.
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