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Recent problems solved by 'stanbon'
stanbon answered: 57222 problems
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53010..53039 , 53040..53069 , 53070..53099 , 53100..53129 , 53130..53159 , 53160..53189 , 53190..53219 , 53220..53249 , 53250..53279 , 53280..53309 , 53310..53339 , 53340..53369 , 53370..53399 , 53400..53429 , 53430..53459 , 53460..53489 , 53490..53519 , 53520..53549 , 53550..53579 , 53580..53609 , 53610..53639 , 53640..53669 , 53670..53699 , 53700..53729 , 53730..53759 , 53760..53789 , 53790..53819 , 53820..53849 , 53850..53879 , 53880..53909 , 53910..53939 , 53940..53969 , 53970..53999 , 54000..54029 , 54030..54059 , 54060..54089 , 54090..54119 , 54120..54149 , 54150..54179 , 54180..54209 , 54210..54239 , 54240..54269 , 54270..54299 , 54300..54329 , 54330..54359 , 54360..54389 , 54390..54419 , 54420..54449 , 54450..54479 , 54480..54509 , 54510..54539 , 54540..54569 , 54570..54599 , 54600..54629 , 54630..54659 , 54660..54689 , 54690..54719 , 54720..54749 , 54750..54779 , 54780..54809 , 54810..54839 , 54840..54869 , 54870..54899 , 54900..54929 , 54930..54959 , 54960..54989 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Nextexpressions/158526: This question is from textbook Algerbra 1
Placing planks at equel length end to end, jewels found that three planks where one foot short of the portch length, while four planks were two feet to long. How long was each plank?
1 solutions
Answer 116784 by stanbon(57290)   on 2008-09-22 23:21:48 (Show Source):
You can put this solution on YOUR website!Placing planks at equal length end to end, jewels found that three planks where one foot short of the porch length, while four planks were two feet to long. How long was each plank?
-------------------
EQUATION:
porch length = porch length
3p+1 = 4p-2
p = 3 ft.
Cheers,
Stan H.
|
Word_Problems_With_Coins/158293: Susan has saved $85.75 in quarters and loonies. She has one quarter more than three-fourths the number of loonies, how many coins of each type does she have.
I have tried this a zillion times using 2 separate equations and the elimination method a variety of ways, but cannot seem to get an answer that fits back. If someone can show me the proper equation to be using please then I can solve from there.
Thanks.
1 solutions
Answer 116670 by stanbon(57290) on 2008-09-21 23:49:38 (Show Source):
You can put this solution on YOUR website!Susan has saved $85.75 in quarters and loonies. She has one quarter more than three-fourths the number of loonies, how many coins of each type does she have.
------------------------
I believe a "looney" is one dollar. If that is right you get the following
equations:
Value Equation: 25Q + 100L = 8575
Quantity Equation: Q = (3/4)L + 1
-----------------------------------
Rearrange the equations:
4Q - 3L = 4
25Q + 100L = 8575
------------------------
Multiply the 1st equation by 25; Multiply the 2nd equation by 4.
100Q - 75L = 100
100Q + 400L = 4*8575
----------------------
Subtract the 1st equation from the 2nd to get:
475L = 4*8575 - 100
------------------------
I don't have a calculator with me so I'll leave solving "L"
to you. When you get "L" substitute into one of the early
equation to solve for Q.
--------------------------
Cheers,
Stan H.
|
Travel_Word_Problems/158306: Danielle drove from school to home averaging 20 mph. On the way back to school she averaged 30 mph. If the total driving time was 1.5 hours, how long did it take her to drive each way.
(i'm in 8th grade, and it just doesn't make sense to me) But I think this is what I am supposed to do, but I don't understand why it works.. if it does.
1 solutions
Answer 116669 by stanbon(57290) on 2008-09-21 23:39:29 (Show Source):
You can put this solution on YOUR website!Danielle drove from school to home averaging 20 mph. On the way back to school she averaged 30 mph. If the total driving time was 1.5 hours, how long did it take her to drive each way.
-------------------------------------
School to home DATA:
rate = 20 mph ; distance = x miles ; time = d/r = x/20 hrs
---------------------------
home to school DATA:
rate = 30 mph ; distance = x miles ; time = d/r = x/30 hrs
-----------------------------
EQUATION:
time + time = 1.5 hours
x/20 + x/30 = 3/2
Multiply thru by 60 to get:
3x + 2x = 90
5x = 90
x = 18 miles (distance each way)
-----------
time to drive from home to school = 18/20 = 9/10 hr = 54 minutes
time to drive from school to home = 18/30 = 3/5 hr = 36 minutes
======================
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/158309: Anna has 6 liters of 60% acid. How much water should she add to make a solution that is 40% acid?
1 solutions
Answer 116666 by stanbon(57290) on 2008-09-21 23:27:32 (Show Source):
You can put this solution on YOUR website!Anna has 6 liters of 60% acid. How much water should she add to make a solution that is 40% acid?
---------------------
Acid Equation: 0.6*6 + 0*x = 0.4(6+x)
0.36 = 0.24 + 0.4x
0.4x = 0.12
x = 3 liters (amount of water that must be added)
-----------
Cheers,
Stan H.
|
Geometry_Word_Problems/156936: This question is from textbook PRECALCULUS Mathmatics for Calculus 4th
I can't figure out how to even start this:
The hypotenuse of a right triangle has length 20 cm. The sum of the lengths of the other two sides is 28 cm. Find the lengths of the other two sides of the triangle.
1 solutions
Answer 115705 by stanbon(57290) on 2008-09-14 19:17:01 (Show Source):
You can put this solution on YOUR website!Let one of the sides be "x"; Let the other side be "28-x'
Use Pythagoras to find "s" and 28-x:
EQUATION:
x^2 + (28-x)^2 = 20^2
x^2 + 784 - 56x + x^2 = 400
2x^2 -56x + 384 = 0
x^2 - 28x + 192 = 0
(x-12)(x-16) = 0
x = 12 or x = 16
-----------
Cheers,
Stan H.
|
expressions/156695: How do I solve for x in the following:
(x x x) - 3 = 8x (the xxx in paranthesis is x times x times x)
thank you!
(it is a teacher created homework problem and not a problem in text. Even looked in text trying to find a model problem and could not. We are in the Mcdougal Littel Algebra 1 book.)
1 solutions
Answer 115565 by stanbon(57290) on 2008-09-13 18:03:43 (Show Source):
You can put this solution on YOUR website!solve for x in the following:
(x x x) - 3 = 8x
x^3 -8x -3 = 0
------------
I graphed it and found it crossed the x-axis at 2.148177...
---------------
Cheers,
Stan H.
|
expressions/156502: This question is from textbook Algebra
x^2+3x+2 x^2+5x+4
________ / _________
x^2+7x+12 x^2+5x+6
1 solutions
Answer 115480 by stanbon(57290) on 2008-09-13 07:17:27 (Show Source):
You can put this solution on YOUR website!x^2+3x+2 x^2+5x+4
________ / _________
x^2+7x+12 x^2+5x+6
------------------------------
Factor where you can to get:
(x+2)(x+1) (x+4)(x+1)
________ / _________
(x+3)(x+4) (x+3)(x+2)
--------------------------------
Invert the denominator and change to multiplication:
(x+2)(x+1) (x+3)(x+2)
________ * _________
(x+3)(x+4) (x+4)(x+1)
---------------------------------
Cancel factors that are common to a numerator and denominator,
such as (x+1), (x+3)
(x+2) (x+2)
________ * _________
(x+4) (x+4)
--------------------------------
= (x+2)^2 / (x+4)^2
=========================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/156628: A biologist estimated the population of seals on a group of islands over a span of 20 years after restrictions were put on hunting. Her data can be modeled by the equation P= 0.6x^4−19x^3+220x^2−850x+1900, where x is the number of years after the restrictions went into place, and P is the total population of seals. Evaluate the population for x = 15.
1 solutions
Answer 115479 by stanbon(57290) on 2008-09-13 06:56:01 (Show Source):
|
Geometry_proofs/156638: This question is from textbook
Given: Line segment BD is parallel to line segment AE
Prove: Triangle DCB ~ triangle ECA ?
Statements Reasons
Line segments
BD AE are parallel Given
Angles
CDB CEA, _______________________
CBD, CAE are congruent _______________________
_______________________
Triangles
DCB ~ ECA _______________________
_______________________
I don't know why I have such a problem figuring out proofs, but I do, I think at the angle congruent question they are looking for a theorem, and triangles, I think I need to prove, but I don't how. Can you help me. I am about to graduate in less than 2 weeks, and personally, I am losing my mind over proofs.
1 solutions
Answer 115478 by stanbon(57290) on 2008-09-13 06:51:01 (Show Source):
|
Polynomials-and-rational-expressions/156626: g^2 - g - 12/g^2 - 10g + 24 divided by g^2 - 9/g^2 - 7g + 6
1 solutions
Answer 115476 by stanbon(57290) on 2008-09-13 06:47:19 (Show Source):
You can put this solution on YOUR website!(g^2 - g - 12)/(g^2 - 10g + 24) / (g^2 - 9) / (g^2 - 7g + 6)
--------------------------------------------------------------
Factor where you can to get;
[(g-4)(g+3)] / [(g-6)(g-4)] / [(g-3)(g+3)] / [(g-6)(g-1)]
---------------------------------------------------------------
Invert the denominator and change to multiplication:
[(g-4)(g+3)] / [(g-6)(g-4)] * [(g-6)(g-1)][(g-3)(g+3)]
---------------------------------------------------------------
Cancel factors that are common to a numerator and a denominator,
such as (g-4), (g-6), (g+3):
[1/1] / [1/1)] * [(g-1)][(g-3)]
----------------------------------------------------------------
= (g-1)/(g-3)
=====================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/156639: A sum of money is made up of $5 bills and $10 bills. The total number of $5 bulls is at least 3 less than double the number of $10 bulls. That sum of money is a minimum of $65.
What would that look like as an inequality equation?
1 solutions
Answer 115474 by stanbon(57290) on 2008-09-13 06:28:27 (Show Source):
You can put this solution on YOUR website!A sum of money is made up of $5 bills and $10 bills.
------------------------------
The total number of $5 bills is at least 3 less than double the number of $10 bills.
Quantity Inequality: F >= 2T -3
----------------
That sum of money is a minimum of $65.
Value Inequality: 5F + 10T >= 65
----------------
That is what the inequalities look like.
===========================================
Cheers,
Stan H.
|
Inequalities/156642: Use the set builder notation to describe the complete solution.
7/4(3x-1/2)-4/3<5/3
1 solutions
Answer 115471 by stanbon(57290) on 2008-09-13 06:18:20 (Show Source):
You can put this solution on YOUR website!Use the set builder notation to describe the complete solution.
7/4(3x-1/2)-4/3<5/3
---------------------------------------------
(21/4)x - (7/8) - (4/3) < (5/3)
Add (4/3) to both sides to get:
(21/4)x - (7/8) < 3
Multiply thru by 8 to get:
42x - 7 < 24
Add 7 to both sides to get:
42x < 31
x < 31/42
----------------
Set Builder: {x| x < (31/42)}
=================================
Cheers,
Stan H.
|
Signed-numbers/156623: Find the difference of the given terms:
-15a squared b squared - (-6a squared b squared)
1 solutions
Answer 115468 by stanbon(57290) on 2008-09-13 06:11:41 (Show Source):
You can put this solution on YOUR website!Find the difference of the given terms:
-15a squared b squared - (-6a squared b squared)
----------------------------------------------------
-15a^2b^2 - (-6a^2b^2)
= -15a^2b^2 + (6a^2b^2)
= -9a^2b^2
=============
Cheers,
Stan H.
|
Rate-of-work-word-problems/156655: An application of rational function is T=(AB)/(A+B) Which gives the time T dictates for 2 workers to complete a particular task where A+B represent the time it would take for each individual worker to complete the identical task. Then how long is would take together.
My personal example:
It takes me 3.5 hours in 1 day to do my weekly house cleaning chores.
It takes my mother 4-5 hrs a day for 4 days to do her
housecleaning chores for the week.
I need the solution to be showed, and I need you to explain it to me please. Thank you.
1 solutions
Answer 115466 by stanbon(57290) on 2008-09-13 06:01:40 (Show Source):
You can put this solution on YOUR website!An application of rational function is T=(AB)/(A+B) Which gives the time T dictates for 2 workers to complete a particular task where A+B represent the time it would take for each individual worker to complete the identical task. Then how long is would take together.
------------------------------------------
My personal example:
It takes me 3.5 hours in 1 day to do my weekly house cleaning chores.
It takes my mother 4-5 hrs a day for 4 days to do her
housecleaning chores for the week.
--------------------------------------
T=(AB)/(A+B)
A = 3.5 hrs
B = 5 hrs (Note: You can't say "4 to 5"; you must select a number)
----------
Then T = [3.5*5] / [3.5 + 5]
T = 17.5/8.5
T = 2.05.. hrs.
====================
Cheers,
Stan H.
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Linear_Algebra/156658: can i ask u how to show that B is a subset of V
as V={(a,b,c)|a-b=c} and B={(0,-1,1),(1,-1,2)}
1 solutions
Answer 115464 by stanbon(57290) on 2008-09-13 05:50:30 (Show Source):
You can put this solution on YOUR website!can i ask u how to show that B is a subset of V
as V={(a,b,c)|a-b=c} and B={(0,-1,1),(1,-1,2)}
--------------------------------
V is the set of all triplets of the form (a,b,c) that satisfy
the condition that a-b=c.
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But (0,-1,1) is a triplet where 0-(-1)=1;
And (1,-1,2) is a triplet where 1-(-1)=2.
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Since both elements of B satisfy the conditions of V,
B is a subset of V.
=========================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/156643: for the following function, c computes a value, where if you add millions of dollars to the value, the result is the cost of implementing a city recycling project when x, as a perentage(not its decimal equivalent) citizens participate. C(x)= 1.5x/100-x
a. Using this model, determine the cost if 60% of the citizen's participate.
b. Using this model, find the percentage of participation that can be expected if $5 million is spent on this recycling project? Set up an equation and solve algebraically. Round to the nearest whole percent.
1 solutions
Answer 115455 by stanbon(57290) on 2008-09-12 22:48:16 (Show Source):
You can put this solution on YOUR website!C(x)= 1.5x/100-x
a. Using this model, determine the cost if 60% of the citizen's participate.
C(60) = 1.5*60/(100-60) = 90/40 = 9/4 = $2.25 million
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b. Using this model, find the percentage of participation that can be expected if $5 million is spent on this recycling project?
5 = 1.5x/(100-x)
500 -5x = 1.5x
6.5x = 500
x = 76.92%
================
Cheers,
Stan H.
Set up an equation and solve algebraically. Round to the nearest whole percent.
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Linear_Equations_And_Systems_Word_Problems/156644: Jonathan plays midget hockey. Last season, three times the number of assists he made was less than the number of goals he scored. At the end of the season he had more than 58 points (assists and goals).
Write in two inequality equations
1 solutions
Answer 115449 by stanbon(57290) on 2008-09-12 22:02:52 (Show Source):
You can put this solution on YOUR website!Jonathan plays midget hockey.
-------------------------------
Write in two inequality equations
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Last season, three times the number of assists he made was less than the number of goals he scored.
INEQUALITY:
3a < g
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At the end of the season he had more than 58 points (assists and goals).
a + g > 58
----------------
Cheers,
Stan H.
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Polynomials-and-rational-expressions/156645: Subtract and simplify
(8-v)/(v-2) - (4v-9)/(v-2)
i got -v+8/v-2 -4v-9/-v+2... do i go a step further? Is there a step beyond this?
1 solutions
Answer 115448 by stanbon(57290) on 2008-09-12 21:57:40 (Show Source):
You can put this solution on YOUR website!Subtract and simplify
(8-v)/(v-2) - (4v-9)/(2-v)
-------------------------------
Multiply numerator and demoniator of the 2nd fraction by -1
to get:
(8-v)/(v-2) + (4v-9)/(v-2)
Now the denominators are the same so combine the numerators to get;
= [8-v+4v-9] / [v-2]
= [3v-1] / [v-2]
=======================
Cheers,
Stan H.
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Equations/156647: Express the following rational expressions in lowest terms y^5-3y^3+8y^2 over 5y
1 solutions
Answer 115446 by stanbon(57290) on 2008-09-12 21:54:25 (Show Source):
You can put this solution on YOUR website!Express the following rational expressions in lowest terms y^5-3y^3+8y^2 over 5y
------------------------------------
(y^5-3y^3+8y^2) / (5y)
= [y^2(y^3-3y+8)]/[5y]
= [y(y^3 - 3y + 8)]/5
==========================
Cheers,
Stan H.
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Travel_Word_Problems/156637: This question is from textbook Prentice Hall Mathematics Algebra 2
30) Two planes left an airport at noon. One flew east at a certain speed and the other flew west twice the speed. The planes were 2700 mi (miles) apart in 3 h (hours). How fast was each plane flying?
50) Michael drove to a friend's house at a rate of 40 mi/h (miles per hour). He returned by the same route at a rate of 45 mi/h. The driving time for the round trip was 4 h (hours). What is the distance Michael traveled
1 solutions
Answer 115440 by stanbon(57290) on 2008-09-12 21:12:52 (Show Source):
You can put this solution on YOUR website!Two planes left an airport at noon.
One flew east at a certain speed ;
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the other flew west twice the speed.
--------------------------------------
The planes were 2700 mi (miles) apart in 3 h (hours).
How fast was each plane flying?
---------------------------
Combined plane data:
distance = 2700 miles ; time = 3 hrs ; rate = 2700/3 = 900 mph
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1st plane rate = x
2nd plane rate = 2x
Combined plane rate = 3x mph
---------------------------------
EQUATION:
combines rate = combined rate
3x = 900
x = 300 mph (1st plane's speed)
2s = 600 mph (2nd plane's speed)
====================================
50) Michael drove to a friend's house at a rate of 40 mi/h (miles per hour).
Outward DATA:
rate = 40 mph ; distance = x miles ; time = d/r = x/40 hrs
----------------------------------
He returned by the same route at a rate of 45 mi/h.
Return DATA:
rae = 45 mph ; distance = x miles ; time = d/r = x/45 hrs.
----------------------------------
The driving time for the round trip was 4 h (hours). What is the distance Michael traveled
------
EQUATION:
time + time = 4 hrs
x/40 + x/45 = 4
85x = 4*40*45
x = 84.71 miles (distance to his friend's house)
---------------------------------------------------
Cheers,
Stan H.
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Quadratic_Equations/156550: In 1994, the life expectancy of males in a certain country was 69.6 years. In 2001, it was 73.3 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994.
The linear function E(t)that fits the data is,
E(t)= t+
(Round to the nearest tenth.)
1 solutions
Answer 115439 by stanbon(57290) on 2008-09-12 20:49:29 (Show Source):
You can put this solution on YOUR website!In 1994, the life expectancy of males in a certain country was 69.6 years.
In 2001, it was 73.3 years.
Let E represent the life expectancy in year t and let t represent the number of years since 1994.
----------------------
You have two points(0,69.6) (7.73.3)
slope = (73.3-69.6)/(7-0) = 0.5286
intercep = 69.6
The linear function E(t)that fits the data is,
E(t)= 0.5296t + 69.6
----------------------------
(Round to the nearest tenth.)
===================================
Cheers,
Stan H.
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Geometry_Word_Problems/156624: This question is from textbook Prentice Hall Mathematics Algebra 2
33) The sides of a rectangle are in the ratio 3 : 2. What is the length of each side if the perimeter of the rectangle is 55 cm?
34) The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 30 cm?
1 solutions
Answer 115435 by stanbon(57290) on 2008-09-12 20:18:20 (Show Source):
You can put this solution on YOUR website!The sides of a rectangle are in the ratio 3 : 2. What is the length of each side if the perimeter of the rectangle is 55 cm?
--------------------
Let length be 3x and let width bwe 2x.
-------------
EQUATION:
Perimeter = 2(length + width) = 55 cm
2(3x+2x) = 55 cm
2*5x = 55 cm
2x = 11 cm
x = 6.5 cm
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2x = 11 cm (width)
3x = 3*6.5 = 19.5 cm (length)
=======================
34) The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 30 cm?
EQUATION:
2x + 4x + 5x = 30 cm
11x = 30 cm
x = (30/11) cm
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3x = 90/11 cm
4x = 120/11 cm
5x = 150/11 cm
=====================
Cheers,
Stan H.
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