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Recent problems solved by 'stanbon'
stanbon answered: 57252 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 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269, >>NextGraphs/102259: I need help with slopes and intercepts, I am dumb when it comes to math. This is really hard for me. Please HELP!. I heard you guys were the best.
I have to write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept.
1. Slope: -2; y-intercept: (0, 4)
2. Slope: 5; y-intercept: (0, -2)
3. Slope: ;3/4 y-intercept: (0, 8)
4. In which quadrant(s) are there no solutions for each line?
y = 3x + 2
Please help me!
1 solutions
Answer 74344 by stanbon(57320)   on 2007-10-04 11:32:27 (Show Source):
You can put this solution on YOUR website!write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept.
-----------------------------
The slope-intercept form is y=mx+b:
m is the slope and
b is the intercept
-------------------------
1. Slope: -2; y-intercept: (0, 4)
Eq: y = -2x+4
-----------------------------------------
2. Slope: 5; y-intercept: (0, -2)
Eq: y = 5x-2
-----------------------------------------
3. Slope: ;3/4 y-intercept: (0, 8)
Eq: y = (3/4)x + 8
-------------------------------------
4. In which quadrant(s) are there no solutions for each line?
y = 3x + 2
----
The graph indicates there are no solutions in the 4th Quadrant:
==================
Cheers,
Stan H.
|
Sequences-and-series/102288: -3,5,-4,8,-6,10,-5
I need to find the sigma for this set of numbers
Thank you
1 solutions
Answer 74339 by stanbon(57320) on 2007-10-04 11:17:06 (Show Source):
You can put this solution on YOUR website!-3,5,-4,8,-6,10,-5
I need to find the sigma for this set of numbers
----------------
Find the mean of the set: = 0.714
Subtract the mean from each data value.
Square this difference for each data value
Add these square values.
Divide by 7 if you are considering this set to be the population.
OR
Divide by 6 if you are considering this set to be a sample.
Using a TI calculator I get:
sigma = 6.227
OR
s = 6.726
-----------------
Cheers,
Stan H.
|
Functions/102268: Find the difference quotient for -f(x)= x^2-3x+5
1 solutions
Answer 74329 by stanbon(57320) on 2007-10-04 07:40:29 (Show Source):
You can put this solution on YOUR website!Find the difference quotient for -f(x)= x^2-3x+5
--------------
f(x)= -x^2+3x-5
f(x+h) = -[x^2+2hx+h^2]+3(x+h)-5
f(x+h) = -x^2-2hx-h^2+3x+3h-5
---------------
f(x+h)-f(x) = -2hx-h^2+3h
-----------------
Difference quotient = [f(x+h)-f(x)]/h
---------------
[f(x+h)-f(x)]/h = -2x-h+3
===================
Cheers,
Stan H.
|
Quadratic_Equations/102279: decide all values of b in the following equations that will
give one or more real number solutions.
(a) 3x^2 + bx - 3 = 0
(b) 5x^2 + bx + 1 = 0
(c) -3x^2 + bx - 3 = 0
1 solutions
Answer 74328 by stanbon(57320) on 2007-10-04 07:34:23 (Show Source):
You can put this solution on YOUR website!decide all values of b in the following equations that will
give one or more real number solutions.
(a) 3x^2 + bx - 3 = 0
(b) 5x^2 + bx + 1 = 0
(c) -3x^2 + bx - 3 = 0
-----------------------
Each of these is a quadratic equation.
To have Real Number solutions the discriminant must be > or = to zero.
-----------
a) a=3,b=b,c=-3
b^2-4ac>=0
b^2-4*3*-3>=0
b^2+36 >=0
b^2 >= -36
But b^2 is always >= -36 so b may have any Real Number value.
======================
Follow the same procedure on questions b) and c).
Cheers,
Stan H.
|
Linear-systems/102274: Solve the system by the addition method:
Eq 1 states: 3x = 3 + 2y
Eq 2 states: -4/3x + y = 1/3
1 solutions
Answer 74327 by stanbon(57320) on 2007-10-04 07:29:20 (Show Source):
You can put this solution on YOUR website!Solve the system by the addition method:
Eq 1 states: 3x = 3 + 2y
Eq 2 states: (-4/3)x + y = 1/3
------------------
Rearrange Eq 1 and multiply thru Eq 2 by 3 to get:
#3: 3x-2y=3
#4: -4x+3y=1
--------------
Multiply #3 by 3 and #4 by 2 to get:
#5: 9x-6y=9
#6:-8x+6y=2
-------------
Add to get:
x = 11
---------
Substitute into #3 to solve for y:
3*11-2y=3
2y = 30
y = 15
------------
Check the answer in -4x+3y=1
-4*11 + 3*15 = 1
-44+45 = 1
1=1
============
Cheers,
Stan H.
|
Equations/102278: (x/(4x-4)+(5/(x^2-1)=1/4 i keep coming up blank on this one for some reason thanks a lot for the help
1 solutions
Answer 74325 by stanbon(57320) on 2007-10-04 07:15:25 (Show Source):
You can put this solution on YOUR website!(x/(4x-4)+(5/(x^2-1)=1/4
---------
Factor to get:
x/[4(x-1)] + 5/[(x+1)(x-1)] = 1/4
--------------
lcm = 4(x-1)(x+1)
-----------------
Multiply thru by lcm to get:
x (x+1) + 5*4 = (x+1)(X-1)
Simplify:
x^2+x + 20 = x^2-1
x = -21
==============
Cheers,
Stan H.
|
Expressions-with-variables/102148: Add or subtract the following:
1) x-7/3 - 4/3 -----> on this I have either -11x/3 or 4x/3
2) 1/x + x+2/x --------> on this one I came up with 3x/x
3) 4x-3/x-7 - 2x+8/x-7 --------> here I am not sure but I got 2x-5/x-7
4) x^2/x+3 + 9/x+3 -------> here I don't understand how to use the power
5) x^2+2x/3x - x^2+5x+6/3x ------> this one I don't know at all :(
Thank you for your help.
1 solutions
Answer 74308 by stanbon(57320) on 2007-10-03 22:36:40 (Show Source):
You can put this solution on YOUR website!Add or subtract the following:
1) x-7/3 - 4/3 -----> on this I have either -11x/3 or 4x/3
Ans: x-(10/3)
-----------------------
2) 1/x + (x+2)/x --------> on this one I came up with 3x/x
Ans: (x+3)/x
------------------------
3) (4x-3)/(x-7) - (2x+8)/(x-7) --------> here I am not sure but I got 2x-5/x-7
Ans:[4x-3-2x-8]/)x-7
=[2x-11]/(x-7)
----------------------
4) x^2/x+3 + 9/x+3 -------> here I don't understand how to use the power
Ans: [x^2+9]/(x+3)
-----------------------
5) (x^2+2x)/3x - (x^2+5x+6)/3x ------> this one I don't know at all :(
Ans: [x^2+2x-x^2-5x-6]/3x
= [-3x-6]/3x
= [-3(x+2)]/3x
= [-(x+2)]/x
======================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/102188: what happens to y if y is inversely proportional to x, and x is tripled?
1 solutions
Answer 74305 by stanbon(57320) on 2007-10-03 22:28:47 (Show Source):
You can put this solution on YOUR website!what happens to y if y is inversely proportional to x, and x is tripled?
--------------
If y is inversely proportional to x, y = k/x
--------------
If you triple x you get y = k/(3x)
which can be written as h = (1/3)(k/x)
===============
So you see, if you triple the x you get (1/3) the y.
That is because y and x are inversely proportional;
as one get larger, the other gets smaller.
============================
Cheers,
Stan H.
|
Coordinate-system/102254: This question is from textbook MATHEMATICS 1 Algebra CPM Volume 1 Units 0-6
Hi,
I need to graph -x Squared and (-x) squared, with the substition for x being; 2, 0, -1, and -3 and i was wondering what is the difference between -x squared and (-x) squared.
1 solutions
Answer 74304 by stanbon(57320) on 2007-10-03 22:24:02 (Show Source):
You can put this solution on YOUR website!what is the difference between -x squared and (-x) squared.
--------------
Try it with a number:
Let x=2
-2^2 = -4
but
(-2)^2 =+4
=============
Graphing y = -x^2 you get:
=============================
Graphing y = (-x)^2 you get:
=============================
Cheers,
Stan H.
|
Length-and-distance/102230: give a counter example that demonstrates that the converse of the statement is false.
if an angle measures 94 degrees then it is obtuse
1 solutions
Answer 74303 by stanbon(57320) on 2007-10-03 22:04:46 (Show Source):
You can put this solution on YOUR website!Statement: If an angle measures 94 degrees then it is obtuse.
Converse: If an angle is obtuse then it measures 94 degrees.
---------------
The converse is false; an angle of 100 degrees is obtuse and is not 94 degrees.
==================
Cheers,
Stan H.
|
Linear-equations/102250: Rewrite the equation below in general form Ax + By = C where A, B and C are the smallest integers possible and A > 0.
Enter the variable expression Ax + By separately from the constant term C
y=4/7x+2/17
1 solutions
Answer 74301 by stanbon(57320) on 2007-10-03 21:59:40 (Show Source):
You can put this solution on YOUR website!y=4/7x+2/17
----------
Multiply thru by 7*17 to get rid of the denominators:
7*17y = 17*4x + 7*2
119y = 68x + 14
68x -119y = -14
=================
Cheers,
Stan H.
|
Travel_Word_Problems/102163: Please help me solve this:
The Smith family drove to the state park at 60 miles per hour and returned on the same route at 50 miles per hour. Find the distance to the state park if the total driving time was 8.8 hours.
1 solutions
Answer 74299 by stanbon(57320) on 2007-10-03 21:56:38 (Show Source):
You can put this solution on YOUR website!The Smith family drove to the state park at 60 miles per hour and returned on the same route at 50 miles per hour. Find the distance to the state park if the total driving time was 8.8 hours.
-------------
To-the-Park DATA;
Rate = 60 mph ; distance = x miles ; time = d/r = x/60 hrs
-------------------
From-the-Park DATA:
Rate = 50 mph ; distance = x miles ; time = d/r = x/50 hrs
---------------------
EQUATION:
time +time = 8.8 hrs
x/60 + x/50 = 8.8
Multiply thru by 10 to get:
x/6 + x/5 = 88
[11x/30] = 88
11x = 30*88
x = 30*8
x = 240 miles (distance to the park)
==========
Cheers,
Stan H.
|
Angles/102206: This question is from textbook Geometry
Geometry is very confusing and I need some help with this problem because I don't understand it.
The measure of a supplement of angle is six times as large as a complement of the angle. Find the measures of the angle, its supplement, and its complement.
1 solutions
Answer 74297 by stanbon(57320) on 2007-10-03 21:50:51 (Show Source):
You can put this solution on YOUR website!The measure of a supplement of angle is six times as large as a complement of the angle. Find the measures of the angle, its supplement, and its complement.
--------------
Let the angle be "x"
Complement is "90-x"
Supplement is "180-x"
---------------
EQUATION:
180-x 6(90-x)
180-x = 540-6x
5x = 360
x = 72 degrees (the angle)
90-x = 18 degrees (the complement)
180-x = 108 degrees (the supplement)
============
Cheers,
Stan H.
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Numeric_Fractions/102234: Express each percent as a fraction in simplest form.
91 2/3%
1 solutions
Answer 74294 by stanbon(57320) on 2007-10-03 21:46:02 (Show Source):
You can put this solution on YOUR website!Express each percent as a fraction in simplest form.
91 2/3%
=(275/3)%
=(275/[3*(100/3)]
= [27500/3][1/100]
= [27500/3]%
= 9166.667%
==============
Another way to do this:
91 2/3%
91.666666666666
= 9166.66666..../100
= 9166.6666...%
=====================
Cheers,
Stan H.
Cheers,
Stan H.
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Equations/102243: This question is from textbook prentice hall
1.03-0.62x=0.71-0.22x
&
1.7t+8-1.62t=0.4t-0.32+8
&
0.7n-15+n=2n-8-0.4n I DO NOT KNOW HOW TO SOLVE THESE PROBLEMS I NEED HELP ALL 3 PROBLEMS
1 solutions
Answer 74290 by stanbon(57320) on 2007-10-03 21:36:52 (Show Source):
You can put this solution on YOUR website!1.03-0.62x=0.71-0.22x
Multiply thru by 100 to get rid of those pesky decimals:
103 - 62x = 71 - 22x
Subtract 71 from both sides to get:
32 -62x = -22x
Add 62x to both sides to get:
32 = 40x
Divide by 40 to get:
x = 32/40 = 4/5 or 0.8
-----------------------
The other two problems can be worked in the same way.
Good luck.
--------------
Cheers,
Stan H.
&
1.7t+8-1.62t=0.4t-0.32+8
&
0.7n-15+n=2n-8-0.4n
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Equations/102241: Hello good evening,
Could you please assist me with the following question...I know it might be simple, however I haven't done grade 11 math in years, now that my son is in it kind of feel dumb. I have no text book as this question he got wrong in a quiz.
(3x^3y^4)^5 (so this is 3x to the power of 3, y to the power of 4 all in brackets to the power of 5.
Hope this makes sense.
Have a fabulous night and thanks again!!
1 solutions
Answer 74287 by stanbon(57320) on 2007-10-03 21:29:03 (Show Source):
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Geometric_formulas/102235: what is the perimeter of a square if the length of the diagonal = 5?
1 solutions
Answer 74286 by stanbon(57320) on 2007-10-03 21:26:52 (Show Source):
You can put this solution on YOUR website!what is the perimeter of a square if the length of the diagonal = 5?
Draw a square; draw a diagonal; label the sides as "x"; label the
diagonal as 5.
-----------
Use Pythagoras to get:
x^2 + x^2 = 5^2
2x^2 = 25
x = 5/sqrt2 or [5sqrt5]/2 or (5/2)sqrt5
--------------
Perimeter = 4*side
Perimeter = 4*(5/2)sqrt5
Perimeter = 10sqrt5
==================
Cheers,
Stan H.
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real-numbers/102233: This question is from textbook Algebra Structure and method
Hello. I was wondering if you could please assist me with this math problem. I've been having a lot of trouble with it. By the way, the / symbol means that the two numbers on each side the numerator and denominator.
-5a-(-1/2b)+31/2a-1/2b= ?
Thank you very much.
1 solutions
Answer 74285 by stanbon(57320) on 2007-10-03 21:22:46 (Show Source):
You can put this solution on YOUR website!-5a-(-1/2b)+31/2a-1/2b= ?
-----------
Comment:
You need to repost this problem in such a way that we
can tell where numberators begin and end.
For example, is the 1st fraction
(-5a-(-1/2b)+31)/2a
or is it
(-5a-(-1/2b)+ 31)/(2a-1)/2b
or what is it?
It is not enough to say the / separates numerator from denominator.
=============
Cheers,
Stan H.
|
Graphs/102214: This question is from textbook
Can you please help me graph x>2y on a coordinate plane?
1 solutions
Answer 74265 by stanbon(57320) on 2007-10-03 19:59:23 (Show Source):
You can put this solution on YOUR website!Can you please help me graph x>2y on a coordinate plane?
-------------
Solve for y:
y<(1/2)x
--------------
Graph the line y=(1/2)x as a dashed line thru the points (0,0), (2,1)
That is the boundary of the solution of your problem
Darken all the points where y<(1/2)x that is all the points that are
below the line. That would be the half-plane below the boundary line.
================
Cheers,
Stan H.
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Mixture_Word_Problems/102198: How many tons of hay at $125 per ton and $75 per ton must be purchased to have 100 tons of hay worth $9000?
1 solutions
Answer 74262 by stanbon(57320) on 2007-10-03 19:49:48 (Show Source):
You can put this solution on YOUR website!How many tons of hay at $125 per ton and $75 per ton must be purchased to have 100 tons of hay worth $9000?
----------------------
Let # of tons of $125 hay be "x" ; value of that is 125x dollars.
------------------------
# of tons of $75 hay is "100-x" ; value of that is 75(100-x)=7500-75x dollars
-------------------------
EQUATION:
value + value = 9000 dollars
125x + 7500-75x = 9000
50x = 1500
x = 30 (# of tons of $125 per ton hay that must be purchased)
100-x = 70 (# of tons of $75 per ton hay that must be purchased)
================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/102194: Explain how to find the vertex of a parabola. What is the significance of the vertex?
1 solutions
Answer 74255 by stanbon(57320) on 2007-10-03 19:31:45 (Show Source):
You can put this solution on YOUR website!If the equation of the parabola is y=ax^2+bx+c
then the vertex is at [-b/2a , f(-b/2a)]
------------------
The vertex is the turning point of the parabola.
-------------------
If a>0 the vertex is the minimum point of the graph of the parabola.
If a<0 the vertex is the maximum point of the graph of the parabola.
=================
Cheers,
Stan H.
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Geometry_Word_Problems/102157: My biggest weakness in math is problems with cylinders so please help me out.
A cylindrical container including a top and bottom is made from no more than 108(pi) cm-squared of sheet metal. If the radius of the top is 3cm what is the maximum volume that the container can hold?
1 solutions
Answer 74253 by stanbon(57320) on 2007-10-03 19:13:44 (Show Source):
You can put this solution on YOUR website!A cylindrical container including a top and bottom is made from no more than 108(pi) cm-squared of sheet metal. If the radius of the top is 3cm what is the maximum volume that the container can hold?
------------------------
If radius is 3 cm, area of the top is 9pi sq. cm.
Top + bottom = 18pi sq.cm.
=============================
Surface area of the side is 108pi cm^2 - 18pi cm^2 = 90pi cm^2
------------------------------
Formula for the surface of the area = 2pi*r*h
So, 2pi*r*h cm^2 = 90pi cm^2
rh = 45
But r=3
So, h = 45/3 = 15 cm
--------------------------
Volume = pir^2h
Volume = pi*3^2*15
Volume = 135pi cm^3
===================
Cheers,
Stan H.
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Travel_Word_Problems/102159: The local train heading for Westford at 60km/h and the express train heading for Eastford at 80km/h pass each other at Centerville while heading in opposite directions along a straight roadbed. Westford and Eastford are 195 km apart, and if the local train makes one 15 minute stop after passing Centerville the express completes its run before the local does. What is the maximum distance to the nearest kilometer between Westford and Centerville.
1 solutions
Answer 74249 by stanbon(57320) on 2007-10-03 18:59:12 (Show Source):
You can put this solution on YOUR website!The local train heading for Westford at 60km/h and the express train heading for Eastford at 80km/h pass each other at Centerville while heading in opposite directions along a straight roadbed. Westford and Eastford are 195 km apart, and if the local train makes one 15 minute stop after passing Centerville the express completes its run before the local does. What is the maximum distance to the nearest kilometer between Westford and Centerville.
-----------------------
Find time they meet at Centerville.
----------------------------
Local train DATA:
Rate = 60 kmh ; distance = x km; time = x/60 hrs
---------------
Express train DATA:
Rate = 80 kmh ; distance = (195-x) km ; time = (195-x)/80 hrs
------------------------------
EQUATION:
time = time
x/60 = (195-x)/80
x/3 = (195-x)/4
4x = 585-3x
7x = 585
x = 83.571 km (distance local train traveled to meeting point)
195-x= 111.429 km (distacne express trin traveled to meeting point)
---------------
Looks like it is 111.429 km from Eastport to Centerville.
=====================
Cheers,
Stan H.
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Graphs/102162: P(5,7) to Q(x,y) what is the delta x and delta y from P to Q?
1 solutions
Answer 74243 by stanbon(57320) on 2007-10-03 18:35:40 (Show Source):
You can put this solution on YOUR website!P(5,7) to Q(x,y) what is the delta x and delta y from P to Q?
------------------------
delta x = x-5
delta y = y-7
============================================
cheers,
Stan H.
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Linear-systems/102155: Hi, Can you please help with this equation? I have a test first thing tomorrow morning and I am very stuck. I know what the answers should be, (x=1.5 and y=-0.8) but and having trouble getting there.
The equation is as follows:
1.2(x+4)-2.5(3y-2) = 2
4/5(3x-5)+ 3/2(3y-4) = -10
This is what I've got so far:
1.2(x+4)-2.5(3y-2) = 2
.08(3x-5)+1.5(3y-4) = -10
1.2x + 4.8 -7.5y+5 = 2
2.4x-4 + 4.5y-6 = -10
1.2x + 9.8 -7.5y = 2
2.4x -10 + 4.5y = -10
2.4x x -7.5 -10x-7.5 +4.5y-7.5 = 10x-7.5
-18x +75 -33.75y = -75
1.2x-18x +9.8+75 - 7.5y-33.75y = -75+2
16.8x + 84.8 - 41.25y = 77
1 solutions
Answer 74239 by stanbon(57320) on 2007-10-03 18:32:30 (Show Source):
You can put this solution on YOUR website!1.2(x+4)-2.5(3y-2) = 2
Multiply thru by 10 to get rid of the decimals:
12(x+4) - 25(3y-2) = 20
12x+48-75y+50 = 20
12x-75y= -78
Divide thru by 3 to get:
4x - 25y = -26
---------------------
(4/5)(3x-5)+ (3/2)(3y-4) = -10
Multiply thru by 10 to get rid of the denominators:
8(3x-5) + 15(3y-4) = -100
24x-40+45y-60 = -100
24x+45y = 0
8x+15y = 0
-----------------------
Solve this system of equations:
1st: 4x - 25y = -26
2nd: 8x + 15y = 0
----------------
Multiply 1st by "2" to get:
3rd: 8x - 50y = -52
------------------
Subtract 2nd from 3rd to get:
-65y = -52
y = (4/5) or 0.8
----------------
Substitute into 2nd to solve for "x"
8x + 15(4/5) =0
8x + 12 = 0
x = -1.5
--------------
Final solution:
x= -1.5
y= 0.8
=========================
Check the answer in 1.2(x+4)-2.5(3y-2) = 2
1.2((-1.5)+4)-2.5(3*0.8-2) = 2
1.2(2.5) - 2.5(0.4) = 2
3 - 1 = 2
2 = 2
===============
Cheers,
Stan H.
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Quadratic_Equations/102153: Please help me solve correctly and show algebraic support.
(X + 4)^(1/2) = X-6
I am so lost. Thank you so much.
1 solutions
Answer 74231 by stanbon(57320) on 2007-10-03 18:13:37 (Show Source):
You can put this solution on YOUR website!(X + 4)^(1/2) = X-6
-----------
Square both sides to get:
x+4 = x^2-12x+36
Rearrange:
x^2-13x+32 = 0
------------
x = [13 +- sqrt(169-4*32)] / 2
x = [13 +- sqrt41]/2
x = 41.62 or x = 3.298
----------
Check these answers in the original equation:
x= 41.62 is a valid answer; x=3.298 is extraneous
because the right side of the equation would be
negative.
=============
Cheers,
Stan H.
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