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Recent problems solved by 'stanbon'
stanbon answered: 57311 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 , 57270..57299 , 57300..57329, >>NextProbability-and-statistics/204003: This question is from textbook thinking mathmatically
If two cards are drawn without replacement from a deck, find the probability that the second card is a spade, given that the first card was a spade.
1 solutions
Answer 153919 by stanbon(57384)   on 2009-07-23 10:10:30 (Show Source):
You can put this solution on YOUR website!If two cards are drawn without replacement from a deck, find the probability that the second card is a spade, given that the first card was a spade.
----------------------
P(2nd is spade|1st is spade) = 12/51
=====================================
Cheers,
Stan H.
|
Probability-and-statistics/204004: This question is from textbook thinking mathmatically
A family has five children. The probability of having a girl is 1/2. What is the probability of having no girls?
I came up with two answers but am unsure of either. This is for a take home exam and I musy show the work. Please help! Class is at two o'clock today!!!
1 solutions
Answer 153918 by stanbon(57384) on 2009-07-23 10:06:56 (Show Source):
You can put this solution on YOUR website!A family has five children. The probability of having a girl is 1/2. What is the probability of having no girls?
I came up with two answers but am unsure of either. This is for a take home exam and I musy show the work. Please help! Class is at two o'clock today!!!
----------------------------------------
Let x be the number of girls born in a family of 5.
P(x=0) = 5C0*)(1/2)^0*(1/2)^5
= 1*(1)*(1/32)
= 1/32
================================================
Cheers,
Stan H.
|
Functions/203991: Please help me solve this periodic functions question : 1. Write an equation for the following graph in the form y= asin kx
a) with a= 1/5, p= ∏/3
( ∏=pi) (1/5, ∏/3, are fractions)
1 solutions
Answer 153915 by stanbon(57384) on 2009-07-23 08:17:57 (Show Source):
You can put this solution on YOUR website!Please help me solve this periodic functions question : 1. Write an equation for the following graph in the form y= asin kx
a) with a= 1/5, p= ∏/3
------
Your problems are all the same.
For the sin function the period is always (2pi)/b
where "b" fits into the form y = asin(bx+c)+d
-------------------------------------------
Your Problem:
You are given that a = 1/5 and the period is pi/3
Therefore (2pi)/b = (pi/3)
So 6pi= pi*b
And b = 6
----
So your equation is y = (1/5)sin(6x)
==============================================
Cheers,
Stan H.
|
Probability-and-statistics/203977: 1.find all real values of 'w' for which the statement
C(w+1,2)=9•C(w,1) is true.
2. while shooting arrows, William can hit an apple 9 out of 10 times. what is the probability that he will hit it exactly 4 out of the next 7 times.
*both of them were really hard for me to figure out. I appreciate your help.
1 solutions
Answer 153914 by stanbon(57384) on 2009-07-23 08:12:29 (Show Source):
You can put this solution on YOUR website!1.find all real values of 'w' for which the statement
C(w+1,2)=9•C(w,1) is true.
--------------------
(w+1)!/[w-1)!2!] = 9w
---
Simplify:
[(w+1)w]/2 = 9w
w^2+w-18w = 0
w^2-17w = 0
w(w-17) = 0
Positive solution:
w = 17
-----------------------------------------------
2. while shooting arrows, William can hit an apple 9 out of 10 times. what is the probability that he will hit it exactly 4 out of the next 7 times.
P(x=4) = 7C4(0.9)^4(0.1)^3 = 0.02296..
============================================
Cheers,
Stan H.
|
Triangles/203960: HI EVERYONE. SORRY, BUT MY LAST QUESTION WAS WRITTEN WRONG! It should have been the following:
What should replace the term D to complete the following trigonometric identity?
(Answer needs to be a function of a.)
cos^2a + D = 1
Thanks again, -Nick.
1 solutions
Answer 153890 by stanbon(57384) on 2009-07-22 22:50:57 (Show Source):
You can put this solution on YOUR website!What should replace the term D to complete the following trigonometric identity?
(Answer needs to be a function of a.)
cos^2(a) + D = 1
----------------
D = sin^2(a)
====================
Cheers,
Stan H.
|
logarithm/203961: Hi all, I was hoping to get some help with the following log problem: I need to
evaluate the following using logarithmic rules: log(2) 4 - log(2) 2 + log(2) 1.
(The 2's in the brackets after log means the number is in place below it, I was unsure of how to show this correctly when typing out the equation.)
Thanks everyone, -Nick.
1 solutions
Answer 153889 by stanbon(57384) on 2009-07-22 22:48:21 (Show Source):
|
Quadratic_Equations/203968: Hi guys, I was wondering whether anyone could help me to solve this quadratic equation for x: 3x^2 + 4x - 8 = 0.
Would be most appreciative if you could include steps on how to solve it also.
Thanks, -Nick.
1 solutions
Answer 153887 by stanbon(57384) on 2009-07-22 22:43:23 (Show Source):
You can put this solution on YOUR website!solve this quadratic equation for x: 3x^2 + 4x - 8 = 0.
-------------------
Use the quadratic formula to get:
x = [-4 +- sqrt(16 - 4*3*-8)]/6
---
x = [-4 +- sqrt(112)]/6
---
x = [-4 +- 4sqrt(7)]/6
---
x = (-2/3) +- (2/3)sqrt(7)
=================================
Cheers,
Stan H.
|
Functions/203965: Please help me solve this periodic functions question : 1. Write an equation for the following graph in the form y= asin kx
a)with a=3, p= ∏
( ∏= pi)
1 solutions
Answer 153886 by stanbon(57384) on 2009-07-22 22:39:10 (Show Source):
You can put this solution on YOUR website!Please help me solve this periodic functions question : 1. Write an equation for the following graph in the form y= asin kx
a)with a=3, p= ∏
------------------------------------------
I believe you are saying that the Period of the function is pi or 180 degrees.
----------------------------------
If so you have (2pi)/k = pi
k = 2
------------------
Therefore the equation is y = 3*sin(2x)
===============================================
Cheers,
Stan H.
|
logarithm/203966: Okay so I have been trying to solve this answer from my homework packet but i just dont remeber how to do it..If log(x+2)/log3-log(x-2)\log3=2, then what is x? HELP!!
1 solutions
Answer 153885 by stanbon(57384) on 2009-07-22 22:34:14 (Show Source):
You can put this solution on YOUR website!If log(x+2)/log3-log(x-2)\log3=2
------
Multiply thru by log(3) to get:
If log(x+2)-log(x-2) = 2log(3)
log[(x+2)/(x-2)] = log(9)
[(x+2)/(x-2)] = 9
Cross-multiply to solve for "x":
x+2 = 9x-18
8x = 20
x = 2.5
=================
Cheers,
Stan H.
|
Probability-and-statistics/203956: I have two probability questions.
1) from 8 shirts, 6 pair. of slacks, and 4 jackets how many different outfits can be made?
2) 9 points are placed on a circle, how many triangles can be formed using these points, three at a time as vertices?
thanks for the help.
1 solutions
Answer 153883 by stanbon(57384) on 2009-07-22 21:36:56 (Show Source):
You can put this solution on YOUR website!I have two probability questions.
1) from 8 shirts, 6 pair. of slacks, and 4 jackets how many different outfits can be made?
8*6*4 = 192 outfits
-------------------------------
2) 9 points are placed on a circle, how many triangles can be formed using these points, three at a time as vertices?
Every set of three points can determine a trianble because
no set of three points are on the same line.
Ans: 9C3 = (9*8*7)/(1*2*3) = 84
=======================================
Cheers,
Stan H.
|
Functions/203957: Hi all, Hopefully someone can show me how to do the following.
Given g(x) = sqrt(x - 1), find the following:
(a) the domain of g;
(b) the range of g.
Thanks again. -nick.
1 solutions
Answer 153882 by stanbon(57384) on 2009-07-22 21:32:15 (Show Source):
You can put this solution on YOUR website!Given g(x) = sqrt(x - 1), find the following:
(a) the domain of g;
x-1 cannot be negative:
x-1 >= 0
x >= 1
Domain: All Real Numbers that are greater than or equal to 1
====================================
(b) the range of g.
sqrt(x-1) can never be negative
Range is All Real Numbers greater than or equal to zero.
=====================================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/203942: The cliff divers of Acapulco amaze tourists with their diving skills. The velocity v of a diver is a function of the time t the diver has fallen, v=2 feet per second when t=0 seconds and v=66 feet per second when t=2 seconds.
a. Write a linear function that represents the velocity v as a function of time t.
b. Interpret the slope of this function in the context of the problem.
c. Interpret the y-intercept of this function in the context of the problem.
1 solutions
Answer 153881 by stanbon(57384) on 2009-07-22 21:28:12 (Show Source):
You can put this solution on YOUR website!The cliff divers of Acapulco amaze tourists with their diving skills. The velocity v of a diver is a function of the time t the diver has fallen, v=2 feet per second when t=0 seconds and v=66 feet per second when t=2 seconds.
Write a linear function that represents the velocity v as a function of time t
---
Use the two points (0,2), and (2,66).
slope = (66-2)/2 = 32 per second
------------
intercept is v(0) = 2
-----------------
Equations:
v(t) = 32t + 2
---------------------------
b. Interpret the slope of this function in the context of the problem.
slope is the increase in falling-velocity per second.
-------------------------------
c. Interpret the y-intercept of this function in the context of the problem
At time = 0 seconds the velocity is 2 feet per second.
=====================================
Cheers,
Stan H.
|
Probability-and-statistics/203877: If the manager of a paint supply store wants estimate the mean amount of paint in a 1-gallon can to within +/- 0.004 gallon with 95% confidence and also assume that the standard deviation is 0.02 gallon, what sample size is needed?
1 solutions
Answer 153811 by stanbon(57384) on 2009-07-22 10:13:28 (Show Source):
You can put this solution on YOUR website!If the manager of a paint supply store wants estimate the mean amount of paint in a 1-gallon can to within +/- 0.004 gallon with 95% confidence and also assume that the standard deviation is 0.02 gallon, what sample size is needed?
-----------
n = [z*s/E]^2
------------
n = [1.96*0.02/0.004]^2 =
n = 96.04
rounding up you get n = 97 (required sample size)
=========================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/203851: It takes 45 min for 2 people to shovel a driveway. How long would it take 5 people to shovel the same driveway?
1 solutions
Answer 153807 by stanbon(57384) on 2009-07-22 08:21:21 (Show Source):
You can put this solution on YOUR website!It takes 45 min for 2 people to shovel a driveway. How long would it take 5 people to shovel the same driveway?
-----------------------
time and # of people are inversely related.
t = k/#
--------------
Find "k":
45 = k/2
k = 90
---
Equation for your problem: t = 90/#
--------
Your Problem:
t = 90/5
time = 18 minutes
============================
Cheers,
Stan H.
|
Probability-and-statistics/203865: The following data represents the monthly service fee in dollars if a customer’s account falls below the minimum required $1,500 balance for a sample of 26 banks for direct-deposit customers. Bancost2
12 8 5 5 6 6 10 10 9 7 10 7 7
5 0 10 6 9 12 0 5 10 8 5 5 9
a) Construct a 95% confidence interval for the population mean monthly service fee in dollars if a customer’s account falls below the minimum required balance.
b) Interpret the interval constructed in (a)
1 solutions
Answer 153806 by stanbon(57384) on 2009-07-22 07:43:11 (Show Source):
You can put this solution on YOUR website!The following data represents the monthly service fee in dollars if a customer’s account falls below the minimum required $1,500 balance for a sample of 26 banks for direct-deposit customers. Bancost2
12 8 5 5 6 6 10 10 9 7 10 7 7
5 0 10 6 9 12 0 5 10 8 5 5 9
a) Construct a 95% confidence interval for the population mean monthly service fee in dollars if a customer’s account falls below the minimum required balance.
The sample mean is 7.1538...
Sample standard dev. = 3.0554...
----
E = 1.96*s/sqrt(n) = 1.1745
----------
95% CI: 7.1538-1.1745 < u < 7.1538+1.1745
95% CI: 5.9793 < u < 8.3283
-----------------
b) Interpret the interval constructed in (a)
We are 95% confident the population mean lies
between those two numbers.
====================================
Cheers,
Stan H.
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Probability-and-statistics/203867: If the inspection division of a county weifhts and measures department wants to estimate the mean amount of soft-drink fill in 2-liter bottles to with +/- 0.01 liter with 95% confidence and also assumes that the standard deviation is 0.05 liter, what sample size is needed?
1 solutions
Answer 153805 by stanbon(57384) on 2009-07-22 07:28:05 (Show Source):
You can put this solution on YOUR website!If the inspection division of a county weights and measures department wants to estimate the mean amount of soft-drink fill in 2-liter bottles to within +/- 0.01 liter with 95% confidence and also assumes that the standard deviation is 0.05 liter, what sample size is needed?
------------------------------------------
Since E = z
sqrt(n) = z
n = [z*s/E]^2
-------------------
Your Problem:
n = [1.96*0.05/0.01]^2
n = 96.04
Rounding up you get n = 97 (this is the required sample size)
===========================
Cheers,
Stan H.
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Graphs/203808: Hi, can anyone please help with the following?
Write the equation of the straight line with a slope of -4 and a y-intercept of -3.
Would be most appreciated.
-Nick.
1 solutions
Answer 153782 by stanbon(57384) on 2009-07-21 21:18:44 (Show Source):
You can put this solution on YOUR website!Write the equation of the straight line with a slope of -4 and a y-intercept of -3.
-----------------
y = -4x - 3
====================
Cheers,
Stan H.
|
Probability-and-statistics/203799: This question is from textbook Introduction to Business Statistics
Hi Please help me with this problem. It is really hard and I'm not sure if I should be using a z-test or a t-test. Thanks for helping.
Reports say that the average teenager spends $39 during a shopping trip to the mall. The promotions director of a local mall has used a variety of strategies to attract area teens to his mall, including live bands and teenage appreciation days that feature special bargains for this age group. He believes teen shoppers at his mall respond to his promotional efforts by shopping there more often and spending more when they do. Mall management decides to evaluate the promotions director's success by surveying a simple random sample of 45 local teens and finding out how much they spend on their most recent shopping visit to the mall. Use a suitable hypothesis test in examining whether the mean mall shopping expenditure for teen sin this area might be higher than for US teens as a whole. Identify and interpret the p-value for the test. Using the 0.025 level of significance what conclusion do you reach?
Spent
40.33
46.06
37.98
50.81
19.03
59.36
31.81
45.98
45.07
40.94
51.06
52.36
45.68
72.28
37.07
40.57
17.44
55.28
41.26
52.34
8.39
61.54
49.94
59.13
44.99
55.47
42.17
26.79
37.30
56.98
36.51
52.23
46.55
52.06
11.84
57.28
51.73
50.24
66.58
18.39
19.15
37.50
22.17
48.98
40.63
1 solutions
Answer 153781 by stanbon(57384) on 2009-07-21 21:17:12 (Show Source):
You can put this solution on YOUR website!Reports say that the average teenager spends $39 during a shopping trip to the mall. The promotions director of a local mall has used a variety of strategies to attract area teens to his mall, including live bands and teenage appreciation days that feature special bargains for this age group. He believes teen shoppers at his mall respond to his promotional efforts by shopping there more often and spending more when they do. Mall management decides to evaluate the promotions director's success by surveying a simple random sample of 45 local teens and finding out how much they spend on their most recent shopping visit to the mall. Use a suitable hypothesis test in examining whether the mean mall shopping expenditure for teen sin this area might be higher than for US teens as a whole. Identify and interpret the p-value for the test. Using the 0.025 level of significance what conclusion do you reach?
Spent
40.33
46.06
37.98
50.81
19.03
59.36
31.81
45.98
45.07
40.94
51.06
52.36
45.68
72.28
37.07
40.57
17.44
55.28
41.26
52.34
8.39
61.54
49.94
59.13
44.99
55.47
42.17
26.79
37.30
56.98
36.51
52.23
46.55
52.06
11.84
57.28
51.73
50.24
66.58
18.39
19.15
37.50
22.17
48.98
40.63
-------------------
Ho: u = 39
Ha: u > 39
-----------------------
The sample mean is 23.05
The sample standard deviation is 14.54
-----------------------
Use a t-test on means tests.
------------------------
I ran a t-test and got the following results:
Test statistic: t = 1.8685...
p-value = 0.03418 which is greater than alpha = 0.025
------------------------
Conclusion:
Fail to reject Ho.
----------------
Interpretation: 3.418% of test results would provide
stronger evidence for rejecting Ho. Our criteria was
2.5%, so we fail to reject Ho.
======================================================
Cheers,
Stan H.
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Radicals/203800: This question is from textbook Intermediate Algebra
I have to multiply rational expression by using the distributive property.
3(square root7t)(2(square root7t) + 3(square root3t^2)), I believe that the it has to be distributed. Thank youu very much.
1 solutions
Answer 153778 by stanbon(57384) on 2009-07-21 20:45:32 (Show Source):
You can put this solution on YOUR website!I have to multiply rational expression by using the distributive property.
3(square root7t)(2(square root7t) + 3(square root3t^2)), I believe that the it has to be distributed.
----------------------------
Your problem is NOT in the form a(b+c) so you do not need to distribute.
--------------
= 6(7t) + 3t*sqrt(3)
================================
Cheers,
Stan H.
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Human-and-algebraic-language/203796: A girl walked 1/3 of the way at 3 mph and got a car ride the rest of the way at 30 mph. What was her average speed?
1 solutions
Answer 153776 by stanbon(57384) on 2009-07-21 20:41:55 (Show Source):
You can put this solution on YOUR website!A girl walked 1/3 of the way at 3 mph and got a car ride the rest of the way at 30 mph. What was her average speed?
--------------------
average speed = total distance/total time
-------------------
Your Problem:
Let the total trip distance be x miles:
---
Walking time = distance/rate = [(1/3)x]/[3 mph] = x hrs
Riding time = distance/rate = [(2/3)x]/[30 mph] = 20x hrs.
----------------------------
Therefore average speed = x miles/(21x hrs) = (1/21) mph
================================================================
Cheers,
Stan H.
|
Probability-and-statistics/203798: A certain jar consists of seven green marbles, five black and four red marbles. If three marbles are drawn at random, find the probability that all three marbles are the same color.
If needed, round to two decimal places.
1 solutions
Answer 153775 by stanbon(57384) on 2009-07-21 20:24:36 (Show Source):
You can put this solution on YOUR website! A certain jar consists of seven green marbles, five black and four red marbles. If three marbles are drawn at random, find the probability that all three marbles are the same color.
-----------------
P(3 green or 3 black or 3 red) = P(3 green) + P(3 black) + P(3 red)
= [7C3/16C3] + {5C3/16C3) + (4C3/16C3)]
= [35+10+4]/560
= 49/560
===============
Cheers,
Stan H.
|
Travel_Word_Problems/203792: If I drive x mph for t hours and then y mph for 2t hours. Then what is expression for the average speed.
1 solutions
Answer 153770 by stanbon(57384) on 2009-07-21 18:49:36 (Show Source):
You can put this solution on YOUR website!If I drive x mph for t hours and then y mph for 2t hours. Then what is expression for the average speed.
-------------------------------
average speed = (total distance)/(total time)
-----
distance = rate*time
-------------------
Your Problem:
total distance = (xt)+ (2yt) = (x+2y)t miles
----------------------
total time = t + 2t = 3t hours
---------------------------
Therefore, average speed = [(x+2y)t]/(3t) = (x+2y)/3 mph
===============================================================
Cheers,
Stan H.
|
Pythagorean-theorem/203782: 1. We can use the Pythagorean theorem to solve problems that involve right triangles. Provide an example of a day-to-day situation that involves right triangles and the use of the theorem.
I already answered this before and my teacher asked me another question to go with the example and she confused because my answer was wrong. So can you help me please?
1 solutions
Answer 153767 by stanbon(57384) on 2009-07-21 18:13:58 (Show Source):
You can put this solution on YOUR website!We can use the Pythagorean theorem to solve problems that involve right triangles. Provide an example of a day-to-day situation that involves right triangles and the use of the theorem.
----------------------------------
If the catcher stands on homplate how far does he throw
the baseball to achieve an "out" at 2nd base.
----------------------------------
A ski-jumper starts his run at a height of 300 ft. and lands
on the ground 600 ft from the base of the tower where he
started. What was the length of his path from the top to
the ground?
----------------
Use Google to search for Pythagorean Applications to find
all the examples you could ever want.
-------------------
Cheers,
Stan H.
-------------------
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logarithm/203783: ok. i have never understood logarithmic equations
do u mind helping?
4log(1-5x)= 2
i remeber having to do somthing like puting a 4 after log and it cancels and moves to the 2... something like that... can u show me the steps on how to solve logarithms :-]
1 solutions
Answer 153764 by stanbon(57384) on 2009-07-21 18:02:08 (Show Source):
You can put this solution on YOUR website!4log(1-5x)= 2
--------------------
A "log" is an exponent
---
In your problem 4 times the "exponent" = 2
So the "exponent" must be 2/3 or 1/2.
----------------------
So log(1-5x) = 1/2
-----
You might ask: Exponent of what?
Since your problem does not show the base,
the word "log" means the base is 10.
-----------
So 1-5x = 10^(1/2)
----
Solve for "x"
5x = 1-sqrt(10)
x = -0.4325...
===============================
Cheers,
Stan H.
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Problems-with-consecutive-odd-even-integers/188053: Twice the lesser of two consecutive odd integers decreased by the greater integer is 53. What are the integers?
1 solutions
Answer 153762 by stanbon(57384) on 2009-07-21 17:49:16 (Show Source):
You can put this solution on YOUR website!Twice the lesser of two consecutive odd integers decreased by the greater integer is 53. What are the integers?
------------------------------------------
Lesser: 2x-1
Larger: 2x+1
-------------------
Equation:
2(2x-1)-(2x+1) = 53
4x-2-2x-1 = 53
2x-3 = 53
2x = 56
--------------
Lesser: 2x-1 = 55
Larger: 2x+1 = 57
=========================
Cheers,
Stan H.
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Travel_Word_Problems/203758: Please help me solve, Iam unsure how to set up the problem... it shows in the book but I cannot understand the explanation
#6. If a car travels 1/100 kilometer each second, how many kilometers does it travel in an hour?
I tried this 1/100*120 seconds... this is not right, I dont understand why.
1 solutions
Answer 153760 by stanbon(57384) on 2009-07-21 17:36:07 (Show Source):
You can put this solution on YOUR website!#6. If a car travels 1/100 kilometer each second, how many kilometers does it travel in an hour?
---
There are 60 seconds in a minute and 60 minutes in an hour,
so there are 3600 seconds in an hour.
-------------
Your Problem:
[(1/100)km/sec]sec = [36]km
====================================
Cheers,
Stan H.
====================================
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Linear-systems/203755: This question is from textbook Elementary and Intermediate Algebra
I really need help understanding how to answer these questions using the addition method...I want to learn this!!! For some reason I am just not getting it???
12.) x-2y=-1
-x+5y=11
16.) 3x+5y=-11
x-2y=11
22.) 2x=2-y
3x+y=-1
Thank you, thank you, thank you!!!!
1 solutions
Answer 153728 by stanbon(57384) on 2009-07-21 12:29:45 (Show Source):
You can put this solution on YOUR website!I really need help understanding how to answer these questions using the addition method...I want to learn this!!! For some reason I am just not getting it???
12.)
x-2y=-1
-x+5y=11
---
Add the two equations to solve for "y":
3y = 10
y = 10/3
-----
Substitute into either of the two original equations to solve for "x":
x = 2y-1
x = 2(10/3)-1
x = 20/3 - 3/3
x = 17/3
-------------------
Ans: (17/3 , 10/3)
======================================
16.)
3x+5y=-11
x-2y=11
---
Multiply the 2nd equation by 3 to get:
3x+4y = -11
3x-6y = 33
-----------------
Subtract the 2nd from the 1st so you can solve for "y":
10y = -44
y = -22/5
-----------
Substitute into x = 2y+11 to solve for "x":
x = 2(-22/5)+(55/5)
x = 11/5
-------
Ans: (11/5 , -22/5)
=================================================
22.)
2x=2-y
3x+y=-1
---
Rearrange:
2x + y = 2
3x + y = -1
--------
Subtract 1st from 2nd to solve for "x":
x = -3
---
Substitute into y = -2x+2 to solve for "y":
y = -2(-3)+2
y = 8
------------------
Ans: (-3 , 8)
======================================
Cheers,
Stan H.
======================================
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Quadratic_Equations/203752: Please walk me throught this: (Imaguinary solutions of quadratic equations)
Solve: 2x^2 + 1 = 0
1 solutions
Answer 153726 by stanbon(57384) on 2009-07-21 12:19:41 (Show Source):
You can put this solution on YOUR website!Please walk me throught this: (Imaginary solutions of quadratic equations)
Solve: 2x^2 + 1 = 0
--------------------------
2x^2 = -1
x^2 = -1/2
x = +/- [sqrt(2)/2)i
=========================
Cheers,
Stan H.
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Rational-functions/203695: This question is from textbook College Algebra
Find all the rational zeros of the function h(x)=3x^5+2x^4-3x-2
1 solutions
Answer 153678 by stanbon(57384) on 2009-07-20 21:58:59 (Show Source):
You can put this solution on YOUR website!Find all the rational zeros of the function h(x)=3x^5+2x^4-3x-2
-----------------------------------
The coefficients add up to zero so x=1 is a root.
Use synthetic division to find the other roots.
------------------------------------------
1)....3....2....-3....-2
.......3....5.....2...|..0
Quotient: 3x^2 + 5x + 2
Find the zeroes:
3x^2+3x + 2x+2 = 0
3x(x+1) + 2(x+1) = 0
(x+1)(3x+2) = 0
x = -1 or x = -2/3 or x = 1
======================================
Cheers,
Stan H.
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