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Recent problems solved by 'stanbon'
stanbon answered: 57182 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, >>NextLinear-systems/90658: solve the system by addition or substitution 20x - 5y = -12
y = 4x +3
Thank you.
1 solutions
Answer 65789 by stanbon(57250)   on 2007-07-29 10:30:43 (Show Source):
You can put this solution on YOUR website!solve the system by addition or substitution 20x - 5y = -12
y = 4x +3
--------------------------
Substitute y=4x+3 into the 1st equation to get:
20x - 5(4x+3) = -12
20x -20x -15 = -12
-15 = -12
This is a contradiction.
There is no solution for the system of equations.
------------
If you graph the two equations you will notice the lines are parallel:
Solving the 1st equation for y you get:
y = 4x+(12/5)
Graphing both equations you get:
Cheers,
Stan H.
|
absolute-value/90660: I dont know where I should post this question so here goes....please provide answer and show steps.
The function that relates weight in grams of a crystal (w) to the temperature t in degrees Fahrenheit in which it was grown is as follows (fictitious):
W(t) = 0.8t + 12
Find w(-6).
Thank you
1 solutions
Answer 65788 by stanbon(57250) on 2007-07-29 10:19:18 (Show Source):
|
Money_Word_Problems/90654: The start-up cost for producing widgets is $449, and each widget costs $91 to produce. Write the function relating x (number of widgets produced) with C(x) or the cost for producing that many widgets.
Thank you.
1 solutions
Answer 65787 by stanbon(57250) on 2007-07-29 10:01:38 (Show Source):
You can put this solution on YOUR website!The start-up cost for producing widgets is $449, and each widget costs $91 to produce. Write the function relating x (number of widgets produced) with C(x) or the cost for producing that many widgets.
--------------------
Let "x" be the number of widgets produced.
----------
EQUATION:
C(x) = 449 + 91x
==============
Cheers,
Stan H.
|
Expressions-with-variables/90587: Rewrite the middle term as the sum of two terms and then factor completely
15X^2-21x+6
Thank you
1 solutions
Answer 65774 by stanbon(57250) on 2007-07-28 23:12:35 (Show Source):
You can put this solution on YOUR website!Rewrite the middle term as the sum of two terms and then factor completely
15X^2-21x+6
-----------
Find two numbers whose product is 6*15=90
and whose sum is -21
---------
The numbers are -6 and -15
-------------
Replace -21x by -6x-15x to get:
=15x^2-6x-15x+6
Factor the 1st two and the last two terms separately:
=3x(5x-2)-3(5x-2)
=(5x-2)(3x-3)
=============
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/90592: Determine the far-left and far-right behavior of the graph of the polynomial function P(x) = 3x4 - 5x2 + 7.
1 solutions
Answer 65771 by stanbon(57250) on 2007-07-28 23:02:31 (Show Source):
You can put this solution on YOUR website!Determine the far-left and far-right behavior of the graph of the polynomial function P(x) = 3x^4 - 5x^2 + 7
Comment: As x gets larger and larger (positive or negative) the highest power term has the mostinfluence on the value of P(x).
-----------
Far left: As x approaches negative infinity P(x) approaches +infinity.
-----------
Far right: As x approaches positive infinity P(x) approaches + infinity
-------------
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/90595: Using Descartes Rule of Signs, determine the number of possible positive real roots of the polynomial 3x4 + 5x3 + 8x2 - 7x + 2.
1 solutions
Answer 65770 by stanbon(57250) on 2007-07-28 22:49:49 (Show Source):
You can put this solution on YOUR website!determine the number of possible positive real roots of the polynomial
f(x) = 3x^4 + 5x3 + 8x2 - 7x + 2
# of changes of sign = 2
# of Positive roots 2 or 0
--------------
f(-x) = 3x^4-5x^3 +8x^2 + 7x + 2
# of changes of sign = 2
# of Negative roots = 2 or 0
=================
Cheers,
Stan H.
|
Graphs/90597: I cannot wrap my brain around this for some reason.
A roof rises 7.25 ft over a horizontal distance of 16.62 ft. What is the slope of the roof to the nearest hundredth?
1 solutions
Answer 65769 by stanbon(57250) on 2007-07-28 22:39:02 (Show Source):
You can put this solution on YOUR website!A roof rises 7.25 ft over a horizontal distance of 16.62 ft. What is the slope of the roof to the nearest hundredth?
---------
slope = vertical/horizontal = 7.25/16.62 = 0.436
========================
Cheers,
Stan H.
|
Graphs/90598: One more that I cannot get even with working on it for 2 days!
an airplane covered 13 miles of its route while decreasing its altitude by 18,000 ft. Find the slope of the airplane's line of descent. Round to the nearest hundredth. (Hint: 1 mi = 5280 Ft)
1 solutions
Answer 65767 by stanbon(57250) on 2007-07-28 22:27:21 (Show Source):
You can put this solution on YOUR website!an airplane covered 13 miles of its route while decreasing its altitude by 18,000 ft. Find the slope of the airplane's line of descent. Round to the nearest hundredth. (Hint: 1 mi = 5280 Ft)
-----------
slope = vertical change/horizontal change
----------
slope = 18,000 ft/[13*5280 ft} = 0.2622...
===========
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/90596: With the help of synthetic division, find the zeros of the polynomial 2x3 + 9x2 - 32x + 21.
1 solutions
Answer 65766 by stanbon(57250) on 2007-07-28 22:20:52 (Show Source):
You can put this solution on YOUR website!find the zeros of the polynomial f(x) = 2x^3 + 9x^2 - 32x + 21.
--------
The coefficents add up to zro so x=1 is a zero of f(x)
--------
1)....2....9....-32....21
........2....11....-21...|..0
======================
Remainder is zero
Quotient is 2x^2+11x-21
Factor to get: (2x-3)(x+7)
x=3/2 or x=-7
===================
Cheers,
Stan H.
|
Trigonometry-basics/90493: Please help me solve this problem. thanks.
The angle of depression is measured from the top of a 43 ft. tower to a reference point on the ground. Its value is found to be 63 deg. How far is the base of the tower from the point on the ground?
1 solutions
Answer 65681 by stanbon(57250) on 2007-07-28 09:11:51 (Show Source):
You can put this solution on YOUR website!The angle of depression is measured from the top of a 43 ft. tower to a reference point on the ground. Its value is found to be 63 deg. How far is the base of the tower from the point on the ground?
-----------
Note: Angle of depression from the tree top is the same as angle of elevation
from the reference point on the ground.
--------------
Draw the picture: right triangle; side opposite the 63 deg angle is 43 ft.
The base is the adjacent side = x.
EQUATION:
tan(63)=opposite/adjacent = 43/x
x= 43/tan(63)
x= 21.91 ft.
==================
Cheers,
Stan H.
|
Trigonometry-basics/90491: Please help solve this one. thanks.
If a guy wire for a tree is 14 ft. long making a 41 degrees angle with the ground, how far is the base of the tree from the stake anchoring the wire.
1 solutions
Answer 65680 by stanbon(57250) on 2007-07-28 09:05:16 (Show Source):
You can put this solution on YOUR website!If a guy wire for a tree is 14 ft. long making a 41 degrees angle with the ground, how far is the base of the tree from the stake anchoring the wire.
------------
Draw the picture; you have a right triangle. The guy wire is the hypotenuse
You want the length of the base when the side opposite the 41 degree angle
is the tree.
You have an angle and the hypotenuse; the base is the side adjacent to the
41 degree angle.
EQUATION:
cos(41) = adjacent/hypotenuse = x/14
14cos(41) = x
x = 10.57 ft
============
Cheers,
Stan H.
|
Linear-equations/90490: This question is from textbook Beginning Algebra
Tutor...an explanation and a bit of help would be appreciated.
Could you tell me how to graph y=2x and y=x+1? I am not sure that I have done these two problems correctly and would like a little help. Thank you.
1 solutions
Answer 65679 by stanbon(57250) on 2007-07-28 08:59:22 (Show Source):
You can put this solution on YOUR website!graph y=2x
Plot two points and draw a line thru them:
If x=0,y=0
If x=2,y=4
================
graph y=x+1
Plot two points and draw a line thru them:
If x=0,y=1
If x=2,y=3
=============
Cheers,
Stan H.
|
Graphs/90488: Solve the system by graphing.
x – 2y = 8
x + y = –1
1 solutions
Answer 65677 by stanbon(57250) on 2007-07-28 08:49:30 (Show Source):
You can put this solution on YOUR website!Solve the system by graphing.
x – 2y = 8
x + y = –1
------------
Solve each equation for y:
y = (1/2)x -4
y = -x - 1
---------------
Plot two points for each graph and draw a line thru them:
For y=(1/2)x-4, if x=0,y=-4; if x=2,y=-3
------------
For y=-x-1, if x=0,y=-1; if x=2,y=-3
---------------
================
Cheers,
Stan H.
|
Travel_Word_Problems/90489: At 4 pm, Gigi and Madel left the music house. Gigi walked east and reached her house at 5 pm. Madel rode her bike west at 4:15 pm. Madel traveled twice as fast as Gigi. Their houses are 9 kilometers apart. How far did each travel?
1 solutions
Answer 65676 by stanbon(57250) on 2007-07-28 08:44:07 (Show Source):
You can put this solution on YOUR website!At 4 pm, Gigi and Madel left the music house. Gigi walked east and reached her house at 5 pm. Madel rode her bike west at 4:15 pm. Madel traveled twice as fast as Gigi. Their houses are 9 kilometers apart. How far did each travel?
-------------
Gigi DATA:
Time = 1 hr ; Distance = x km ; Rate = d/t = x kph
------------
Madel DATA:
Distance = 9-x km ; Rate = 2x kph ; Time = (9-x)/2x hrs
----------------
Comment: If Madel reached her house at the same time as Gigi reached
her house Madel's time is (3/4)hr.
---------------
EQUATION:
(9-x)/2x = 3/4
6x = 36-4x
10x = 36
x = 3.6 km (Gigi traveled this far)
9-3.6 = 5.4 (Mdel traveled this far)
==============
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/90417: a falling object is given by the function "S= -16t^2 + Vot + So" where "Vo" represents the initial velocity in ft/sec and "So" represents the initial height.
If a baseball is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot skyscraper, write the height equation using this information.
s = -16(t^2 + 32 + 40) drop the 40
s = divide by 16
__________________________
t + 2 and here's where I get lost
1 solutions
Answer 65639 by stanbon(57250) on 2007-07-27 22:27:45 (Show Source):
You can put this solution on YOUR website!a falling object is given by the function "S= -16t^2 + Vot + So" where "Vo" represents the initial velocity in ft/sec and "So" represents the initial height.
If a baseball is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot skyscraper, write the height equation using this information.
-----------
S(t) = -16t^2 + 32t + 40
===================
Cheers,
Stan H.
|
Inequalities/90418: Most insurance companies will replace a vehicle anytime and estimated repair exceeds 80% of it blue book value. Michelle's car had 6500 dollar in repairs after an accident. What can be concluded about its blue book value
1 solutions
Answer 65637 by stanbon(57250) on 2007-07-27 22:21:13 (Show Source):
You can put this solution on YOUR website!Most insurance companies will replace a vehicle anytime and estimated repair exceeds 80% of it blue book value. Michelle's car had 6500 dollar in repairs after an accident. What can be concluded about its blue book value
---------------
Let the blue book value be "x".
INEQUALITY:
6500 < 0.80x
8125 < x
The blue book value is greater than $8125.00
===============
Cheers,
Stan H.
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expressions/90438: This question is from textbook
6/x-2+?/2-x=13/x-2 can you please tell me how to set up the steps to solve this
equation and give me the answer to the ?
1 solutions
Answer 65636 by stanbon(57250) on 2007-07-27 22:14:48 (Show Source):
You can put this solution on YOUR website![6/x-2] + [?/2-x] = [13/x-2]
Rearrange the 2nd term as follows:
[6/x-2] - [?/x-2] = [13/x-2]
Now, multiply thru by (x-2) top get:
6 - ? = 13
? = -7
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Cheers,
Stan H.
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absolute-value/90435: how many birds and lions do you have in your zoo? If there are 30 heads and 100 feet.
1 solutions
Answer 65635 by stanbon(57250) on 2007-07-27 22:06:45 (Show Source):
You can put this solution on YOUR website!how many birds and lions do you have in your zoo? If there are 30 heads and 100 feet.
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Let # of birds be "b"; let number of lions be "l"
Head equation: b+l = 30
Feet equation: 2b+4l = 100
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l = 30-b
Substitute to get:
2b + 4(30-b) = 100
Solve for b:
2b+120-4b = 100
-2b = -20
b = 10 (# of birds)
l = 30 - 10 = 20 ( # of lions)
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/90405: Find the corresponding y values for x = -4, -3, -2, -1, 0, 1, 2 if y = x^2 + 2x- 3. help this is not sinking in at all.
1 solutions
Answer 65602 by stanbon(57250) on 2007-07-27 19:27:57 (Show Source):
You can put this solution on YOUR website!Find the corresponding y values for x = -4, -3, -2, -1, 0, 1, 2 if y = x^2 + 2x- 3. help this is not sinking in at all.
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Just put each value of x in place of x in the formula.
For example
If x = -3, y = (-3)^2 + 2(-3) -1 = 9 - 6 -1 = 2
If x = 2, y = (2)^2 + 2*(2) - 3 = 4+4-3=5
etc.
Cheers,
Stan H.
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Functions/90407: 7) The path of a falling object is given by the function where represents the initial velocity in ft/sec and represents the initial height.
a) If a rock is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot building, write the height equation using this information.
b) How high is the rock after 0.5 seconds?
c) After how many seconds will the rock reach maximum height?
d) What is the maximum height?
1 solutions
Answer 65600 by stanbon(57250) on 2007-07-27 19:23:53 (Show Source):
You can put this solution on YOUR website!7) The path of a falling object is given by the function where represents the initial velocity in ft/sec and represents the initial height.
a) If a rock is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot building, write the height equation using this information.
h(t) = -16t^2+32t+40
b) How high is the rock after 0.5 seconds?
h(0.5) = -16*(0.5)^2+32*0.5+40
h(0.5) = 52 ft.
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c) After how many seconds will the rock reach maximum height?
Maximum occurs at t=-b/2a = -32/(2*-16) = 1 second
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d) What is the maximum height?
h(1) = -16+32+40 = 56
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Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/90316: Please help me- I cannot get this I have tried to get you help a few times on this. I am getting nowhere. please please help. Thank you
Suppose you wanted to construct a fence around a garden plot in the form of a rectangle. On the neighbor’s side it’s going to need heavy-duty fencing that costs $2.00 per foot. The other three sides can be made of standard fencing material that costs $1.20 foot. You have $200 to spend.
1. How many different rectangles would it be possible to enclose for $200?
2. Write an equation using two variables for the total cost of the fence. Use x and y to represent the width and length of the rectangle. Solve the equation for one of the variables (either x or y).
3. Given that Area = (x)(y), now write the area function for this problem using ONLY ONE VARIABLE (by making a substitution using the equation from #2).
4. What dimensions will give the maximum area inside the fence?
5. What will be the maximum area?
1 solutions
Answer 65599 by stanbon(57250) on 2007-07-27 19:18:41 (Show Source):
You can put this solution on YOUR website!Suppose you wanted to construct a fence around a garden plot in the form of a rectangle. On the neighbor’s side it’s going to need heavy-duty fencing that costs $2.00 per foot. The other three sides can be made of standard fencing material that costs $1.20 foot. You have $200 to spend.
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Draw the rectangle; let the fence on the neighbors side have length x.
The side opposite it is also of length x.
Let the other two sides have length y.
1. How many different rectangles would it be possible to enclose for $200?
Plenty
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2. Write an equation using two variables for the total cost of the fence. Use x and y to represent the width and length of the rectangle. Solve the equation for one of the variables (either x or y).
Cost Equation: 2x + 1.2x + 1.2y + 1.2y = 200
3.2x + 2.4y = 200
y = (-3.2/2.4)x + (200/2.4)
y = (-4/3)x + (250/3)
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3. Given that Area = (x)(y), now write the area function for this problem using ONLY ONE VARIABLE (by making a substitution using the equation from #2).
Area = x[(-4/3)x + (250/3)] = -(4/3)x^2+(250/3)x
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4. What dimensions will give the maximum area inside the fence?
Maximum area occurs at x=-b/2a = -(250/3)/[2(-4/3)] = 31.25 ft (width)
Then y = (-4/3)*(125/4)+(250/3) = -125/3 + 250/3 = 125/3 = 41.66 ft (length)
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5. What will be the maximum area?
Area = x*y = 31.25*41.66 = 1301.85 sq ft.
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Cheers,
Stan H.
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real-numbers/90391: Consecutive Even Integers. Find four consecutive integers whose sum is 340.
1 solutions
Answer 65597 by stanbon(57250) on 2007-07-27 18:13:38 (Show Source):
You can put this solution on YOUR website! Find four consecutive integers whose sum is 340.
x + (x+1) + (x+2) + (x+3) = 340
4x + 6 = 340
4x = 334
But x = 334/4 is not an integer.
It seems that there are no four consecutive integers whose sum is 340.
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Cheers,
Stan H.
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Miscellaneous_Word_Problems/90392: what was the percentage increase in the age 75+ population of Europe from 1970 to 1995?
Population of Europe by Age Groups
Age 0-14 Age 15-64 Age 65+ Age 75+ Total
1950 143,175 359,162 44,981 14,553 547,318
1970 166,367 421,432 68,642 22,762 656,441
1995 139,464 487,110 101,338 38,139 727,912
Source: European Rural Development (ERD) Project.
A)63.4%
B)65.1%
C067.6%
D)68.9%
1 solutions
Answer 65595 by stanbon(57250) on 2007-07-27 17:46:18 (Show Source):
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Equations/90394: Problem #1 7r/12=-14
Problem #2 1/3 s + 7/9 = 4/3 s
Use the appropriate property os eqaulity to solve each problem.
1 solutions
Answer 65593 by stanbon(57250) on 2007-07-27 17:34:18 (Show Source):
You can put this solution on YOUR website!Problem #1
7r/12=-14
Divide both sides by 7 to get:
r/12 = -2
Multiply both sides by 12 to get:
r = -24
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Problem #2
1/3 s + 7/9 = 4/3 s
Multiply thru by 9 to get:
3s + 7 = 12s
Subtract 3s from both sides to get:
9x = 7
Divide both sides by 9 to get:
x = 7/9
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Cheers,
Stan H.
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