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Number-Line/350027: if a < b, then -a > -b. Why is this? Explain and suppose, a = 4 and b = 1 and write in a number line
1 solutions

Answer 250170 by jim_thompson5910(28476) About Me  on 2010-09-30 00:28:36 (Show Source):
You can put this solution on YOUR website!
a+%3C+b Start with the given inequality.


a-b+%3C+cross%28b-b%29 Subtract b from both sides.


a-b+%3C+0 Simplify


cross%28a-a%29-b+%3C+0-a Subtract 'a' from both sides.


-b+%3C+-a Simplify


-a%3E-b Flip the inequality (this is possible since x%3Ey is the same as y%3Cx and vice versa)


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider making a donation at my tutoring website. Thank you.

Jim


Expressions-with-variables/349985: trying to help my son with his 6th grade math. writing algebraic expressions can you let me know if these are correct? 200 less than half of a number 1/2n-200 2nd problem the square of the product of 6 and a number (6xn)squared
1 solutions

Answer 250142 by jim_thompson5910(28476) About Me  on 2010-09-29 22:51:05 (Show Source):
You can put this solution on YOUR website!
"200 less than half of a number" translates to %281%2F2%29n-200 or you can write it as n%2F2-200


"the square of the product of 6 and a number " translates to %286n%29%5E2. Leave the 'x' out because "6n" means "six times 'n'"


Proportions/349984: Solve this proportion:
6/2x = 5/x+8
1 solutions

Answer 250141 by jim_thompson5910(28476) About Me  on 2010-09-29 22:49:14 (Show Source):
You can put this solution on YOUR website!
6%2F%282x%29=5%2F%28x%2B8%29 Start with the given equation.


6%28x%2B8%29=5%282x%29 Cross multiply.


6x%2B48=10x Distribute and multiply.


6x=10x-48 Subtract 48 from both sides.


6x-10x=-48 Subtract 10x from both sides.


-4x=-48 Combine like terms on the left side.


x=%28-48%29%2F%28-4%29 Divide both sides by -4 to isolate x.


x=12 Reduce.


----------------------------------------------------------------------

Answer:

So the solution is x=12


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Rational-functions/349980: 9%2F3x-4%2F2x%5E2
1 solutions

Answer 250137 by jim_thompson5910(28476) About Me  on 2010-09-29 22:25:13 (Show Source):
You can put this solution on YOUR website!
9%2F3x-4%2F2x%5E2 Start with the given expression.


3%2Fx-2%2Fx%5E2 Reduce


3x%2Fx%5E2-2%2Fx%5E2 Multiply the first fraction by x%2Fx to get that denominator equal to the LCD x%5E2


%283x-2%29%2Fx%5E2 Subtract the fractions.


So 9%2F3x-4%2F2x%5E2=%283x-2%29%2Fx%5E2


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Expressions-with-variables/349978: a cd cost $ 3.50 more than a tape
write an expresion for the total cost of i cd and 1 tape
1 solutions

Answer 250135 by jim_thompson5910(28476) About Me  on 2010-09-29 22:17:07 (Show Source):
You can put this solution on YOUR website!
Let t = cost of one tape.


Since "a cd cost $ 3.50 more than a tape", this means that a cd costs t%2B3.5 dollars.


Add up these two costs to get t%2Bt%2B3.5=2t%2B3.5


So the total cost of a cd and a tape is 2t%2B3.5 dollars.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Equations/349977: 11-4d=71
1 solutions

Answer 250134 by jim_thompson5910(28476) About Me  on 2010-09-29 22:15:29 (Show Source):
You can put this solution on YOUR website!
11-4d=71 Start with the given equation.


-4d=71-11 Subtract 11 from both sides.


-4d=60 Combine like terms on the right side.


d=%2860%29%2F%28-4%29 Divide both sides by -4 to isolate d.


d=-15 Reduce.


----------------------------------------------------------------------

Answer:

So the solution is d=-15


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Angles/349901: I am trying to help a friend out. She needs help with an angle of this: problem is...(x-20) and (x+20). The lesson she is on (She thinks it is a Saxton math book) is: Proving Lines Paralell. Please hurry to help. I am working on the same one and we BOTH stuck.
1 solutions

Answer 250133 by jim_thompson5910(28476) About Me  on 2010-09-29 22:14:52 (Show Source):
You can put this solution on YOUR website!
Is there a picture involved with the two angles?


Probability-and-statistics/349808: Hello
Disease 1 and Disease 2 are prevalent among people in a certain population. It is assumed that 10% of the population will contract disease 1 sometime during their lifetime, 15% will contact disease 2 eventually,and 3% will contract both diseases.
a)Find the probability that a randomly chosen person from this population will contract at least one disease.
b)find the conditional probability that a randomly chosen person from this population will contact both diseases, given that he or she has contracted at least disease.

Thank You
1 solutions

Answer 250027 by jim_thompson5910(28476) About Me  on 2010-09-29 17:48:57 (Show Source):
You can put this solution on YOUR website!
a) Hint: P(Contract at least one disease) = P(Contract Disease 1) + P(Contract Disease 2) - P(Contract both diseases)

b) Hint: P(Contract both given having contracted at least one) = P(Contracting both) divided by P(Contract at least one disease)


Equations/349818: 5x+12-2x=7-(4x+2)
1 solutions

Answer 250025 by jim_thompson5910(28476) About Me  on 2010-09-29 17:44:58 (Show Source):
You can put this solution on YOUR website!
5x%2B12-2x=7-%284x%2B2%29 Start with the given equation.


5x%2B12-2x=7-4x-2 Distribute.


3x%2B12=7-4x-2 Combine like terms on the left side.


3x%2B12=-4x%2B5 Combine like terms on the right side.


3x=-4x%2B5-12 Subtract 12 from both sides.


3x%2B4x=5-12 Add 4x to both sides.


7x=5-12 Combine like terms on the left side.


7x=-7 Combine like terms on the right side.


x=%28-7%29%2F%287%29 Divide both sides by 7 to isolate x.


x=-1 Reduce.


----------------------------------------------------------------------

Answer:

So the answer is x=-1


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


percentage/349816: If the percent of increase is 16% and the new number is 522, how do we find the original number?
1 solutions

Answer 250024 by jim_thompson5910(28476) About Me  on 2010-09-29 17:44:09 (Show Source):
You can put this solution on YOUR website!
Let x = the original number.


If you have a 16% increase, then you're basically adding 16% of that original number to the original number.


In other words: 16% increase of some number = Some number + 16% of same number


Symbolically, this means that x%2B0.16x=1.16x. Because we know that the new number is 522, we know that 1.16x=522


I'll let you finish.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Numeric_Fractions/349812: What is the product of 5a\3 + 5\3a? The slashes are to make the problem a fraction okay not a division sign.=)
1 solutions

Answer 250023 by jim_thompson5910(28476) About Me  on 2010-09-29 17:41:31 (Show Source):
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So %28%285a%29%2F3%29%2A%285%2F%283a%29%29=25%2F9


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Jim


Equations/349813: find the unit rate : a computers fan rotates 2000 times in 4o seconds
1 solutions

Answer 250022 by jim_thompson5910(28476) About Me  on 2010-09-29 17:39:40 (Show Source):
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The computer fan rotates 2000%2F40+=+200%2F4+=+50 times in one second


Equations/349806: x over 2+x over 4 = 4
1 solutions

Answer 250014 by jim_thompson5910(28476) About Me  on 2010-09-29 17:25:00 (Show Source):
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x%2F2%2Bx%2F4=4 Start with the given equation.


4%28x%2Fcross%282%29%2Bx%2Fcross%284%29%29=4%284%29 Multiply both sides by the LCD 4 to clear any fractions.


2x%2Bx=16 Distribute and multiply.


3x=16 Combine like terms on the left side.


x=%2816%29%2F%283%29 Divide both sides by 3 to isolate x.


----------------------------------------------------------------------

Answer:

So the answer is x=16%2F3 which approximates to x=5.333.


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Travel_Word_Problems/349802: How long will it take to drive 330 miles if I go 55 mph and start at 11pm?
1 solutions

Answer 250011 by jim_thompson5910(28476) About Me  on 2010-09-29 17:23:34 (Show Source):
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Using d=rt, we get 330=55t. Solve for 't' to get t=330%2F55=6. So it takes 6 hours which means that you'll arrive at 11 pm + 6 hours = 5 am


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Inequalities/349800: The question is 6 the solution. the problem is y-8>2y-3
and then I am given these inequalites to work with 6,-19,-15,-2 This is new to me so I don't even know where to start.
1 solutions

Answer 250008 by jim_thompson5910(28476) About Me  on 2010-09-29 17:20:46 (Show Source):
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First, let's solve the given inequality


y-8%3E2y-3 Start with the given inequality.


y%3E2y-3%2B8 Add 8 to both sides.


y-2y%3E-3%2B8 Subtract 2y from both sides.


-y%3E-3%2B8 Combine like terms on the left side.


-y%3E5 Combine like terms on the right side.


y%3C%285%29%2F%28-1%29 Divide both sides by -1 to isolate y. note: Remember, the inequality sign flips when we divide both sides by a negative number.


y%3C-5 Reduce.


----------------------------------------------------------------------

Answer:

So the answer is y%3C-5


So ANY number that is less than -5 is a solution to the original inequality.


So for example, 6 is NOT a solution as it is NOT less than -5. However, -19 and -12 are both solutions since they are both less than -5.


Alternatively, you can plug in each possible solution into the given inequality and evaluate each side. If you get a true statement, then that given possible solution is actually a solution. If you get a false statement, then it's not a solution.


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Jim


Travel_Word_Problems/349792: . Choose the best answer to the following question. If X is the set of positive multiples of 2, and Y is the set of positive multiples of 3, then the intersection of X and Y is:
1 solutions

Answer 250005 by jim_thompson5910(28476) About Me  on 2010-09-29 17:05:50 (Show Source):
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Notation Note: Intersection of X and Y =


= Set of positive multiples of 2 AND 3


= Set of positive multiples of 6 (since 2*3 = 6)


Triangles/349752: In the figure in the link below angle CDB is a straight angle. If the measure of angle ADC= 2x-24 , measure of ADE is x+74, and measure of ADB is 9x-148, what is the measure of CDE? please help i dont understand how to solve it

http://s231.photobucket.com/albums/ee131/babydolla101/?action=view¤t=angle.png
1 solutions

Answer 250003 by jim_thompson5910(28476) About Me  on 2010-09-29 17:02:32 (Show Source):
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Hint: ADE = ADC+CDE. So this means that CDE = ADE-ADC

Also, because CDB is a straight line, we know that CDB = 180. From the picture, ADC+ADB = CDB. So ADC + ADB = 180.


Let me know if this helps or not.


Expressions-with-variables/349749: (2Y+5)+Y=-22
1 solutions

Answer 249978 by jim_thompson5910(28476) About Me  on 2010-09-29 15:25:08 (Show Source):
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2y%2B5%2By=-22 Start with the given equation.


3y%2B5=-22 Combine like terms on the left side.


3y=-22-5 Subtract 5 from both sides.


3y=-27 Combine like terms on the right side.


y=%28-27%29%2F%283%29 Divide both sides by 3 to isolate y.


y=-9 Reduce.


----------------------------------------------------------------------

Answer:

So the answer is y=-9


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Jim


Linear-equations/349745: Write the equation in slope-intercept form for the line passing through each pair of points (-1,3) and (2,-5)
1 solutions

Answer 249976 by jim_thompson5910(28476) About Me  on 2010-09-29 15:19:32 (Show Source):
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First let's find the slope of the line through the points and


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-5-3%29%2F%282--1%29 Plug in y%5B2%5D=-5, y%5B1%5D=3, x%5B2%5D=2, and x%5B1%5D=-1


m=%28-8%29%2F%282--1%29 Subtract 3 from -5 to get -8


m=%28-8%29%2F%283%29 Subtract -1 from 2 to get 3


So the slope of the line that goes through the points and is m=-8%2F3


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-3=%28-8%2F3%29%28x--1%29 Plug in m=-8%2F3, x%5B1%5D=-1, and y%5B1%5D=3


y-3=%28-8%2F3%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-3=%28-8%2F3%29x%2B%28-8%2F3%29%281%29 Distribute


y-3=%28-8%2F3%29x-8%2F3 Multiply


y=%28-8%2F3%29x-8%2F3%2B3 Add 3 to both sides.


y=%28-8%2F3%29x%2B1%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


y=%28-8%2F3%29x%2B1%2F3 Simplify


So the equation that goes through the points and is y=%28-8%2F3%29x%2B1%2F3


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Jim


Equations/349739: can you solve these following questions plaese
19-h-h=-13
14+6a-8=18
25=7+3k-12
5n-16-8n=-10

1 solutions

Answer 249974 by jim_thompson5910(28476) About Me  on 2010-09-29 15:11:19 (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started. Please only post one problem at a time.

# 1



19-h-h=-13 Start with the given equation.


-2h%2B19=-13 Combine like terms on the left side.


-2h=-13-19 Subtract 19 from both sides.


-2h=-32 Combine like terms on the right side.


h=%28-32%29%2F%28-2%29 Divide both sides by -2 to isolate h.


h=16 Reduce.


---------------------------------

Answer:

So the answer is h=16

========================================================
# 2




14%2B6a-8=18 Start with the given equation.


6a%2B6=18 Combine like terms on the left side.


6a=18-6 Subtract 6 from both sides.


6a=12 Combine like terms on the right side.


a=%2812%29%2F%286%29 Divide both sides by 6 to isolate a.


a=2 Reduce.


----------------------------------------

Answer:

So the answer is a=2


Sequences-and-series/349738: The expression x squared can be used to find the nth term in a sequence. What is the 5th term in that sequence?
A.)31
B.)25
C.)16
D.)7
1 solutions

Answer 249971 by jim_thompson5910(28476) About Me  on 2010-09-29 15:05:55 (Show Source):
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Assuming that the first term is n=1, the 5th term is n=5. This means that the fifth term is 5%5E2=25


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Jim


Square-cubic-other-roots/349735: What is the square root of 9 over 49?
Please hurry and answer =] my test depends on it haha!
1 solutions

Answer 249969 by jim_thompson5910(28476) About Me  on 2010-09-29 14:54:48 (Show Source):
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Ask yourself this: What number multiplied by itself gives you 9? Also, what number multiplied by itself gives you 49?


Linear-equations/349734: find y-intercept of y=4x-64
1 solutions

Answer 249967 by jim_thompson5910(28476) About Me  on 2010-09-29 14:51:22 (Show Source):
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Plug in x=0 to get y=4%280%29-64=0-64=-64. So when x=0, y=-64 which means that the y-intercept is (0,-64)


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Jim


Inequalities/349732: explain why a < b, then -a > -b
1 solutions

Answer 249966 by jim_thompson5910(28476) About Me  on 2010-09-29 14:47:51 (Show Source):
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a+%3C+b Start with the given inequality.


a-b+%3C+cross%28b-b%29 Subtract b from both sides.


a-b+%3C+0 Simplify


cross%28a-a%29-b+%3C+0-a Subtract 'a' from both sides.


-b+%3C+-a Simplify


-a%3E-b Flip the inequality (this is possible since x%3Ey is the same as y%3Cx and vice versa)


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Jim


expressions/349727: Add or subtract as indicated, Simplify. Show factoring, cancelling, and the steps to finding the lowest common denominator. (Assume that no denominator is 0.)

(x+5)(2)/x(2)+2x-15 + 2/4x-12
I really need help very soon, I am stuck and don't even know where to begin. Thank you! :)
1 solutions

Answer 249965 by jim_thompson5910(28476) About Me  on 2010-09-29 14:44:55 (Show Source):
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%28%28x%2B5%29%5E2%29%2F%28x%5E2%2B2x-15%29%2B2%2F%284x-12%29 Start with the given expression.


%28%28x%2B5%29%28x%2B5%29%29%2F%28x%5E2%2B2x-15%29%2B2%2F%284x-12%29 Break up the first numerator


%28%28x%2B5%29%28x%2B5%29%29%2F%28%28x%2B5%29%28x-3%29%29%2B2%2F%284x-12%29 Factor the first denominator.


Highlight the common terms.


Cancel out the common terms.


%28x%2B5%29%2F%28x-3%29%2B2%2F%284x-12%29 Simplify


%28x%2B5%29%2F%28x-3%29%2B2%2F%284%28x-3%29%29 Factor the second denominator.


Take note that the LCD is 4%28x-3%29. So we need to get every denominator equal to the LCD so we can add the fractions.


%284%28x%2B5%29%29%2F%284%28x-3%29%29%2B2%2F%284%28x-3%29%29 Multiply the first fraction by 4%2F4 to get that fraction to have the denominator equal to the LCD.


%284x%2B20%29%2F%284x-12%29%2B2%2F%284x-12%29 Distribute.


%284x%2B20%2B2%29%2F%284x-12%29 Add the fractions.


%284x%2B22%29%2F%284x-12%29 Combine like terms.


%282%282x%2B11%29%29%2F%284x-12%29 Factor out a '2' from the numerator.


%282%282x%2B11%29%29%2F%282%282x-6%29%29 Factor out a '2' from the denominator.


%28highlight%282%29%282x%2B11%29%29%2F%28highlight%282%29%282x-6%29%29 Highlight the common terms.


%28cross%282%29%282x%2B11%29%29%2F%28cross%282%29%282x-6%29%29 Cancel out the common terms.


%282x%2B11%29%2F%282x-6%29 Simplify.


So %28%28x%2B5%29%5E2%29%2F%28x%5E2%2B2x-15%29%2B2%2F%284x-12%29 simplifies to %282x%2B11%29%2F%282x-6%29


In other words, %28%28x%2B5%29%5E2%29%2F%28x%5E2%2B2x-15%29%2B2%2F%284x-12%29=%282x%2B11%29%2F%282x-6%29


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Jim


Rectangles/349726: A rectangle is 4 units wide. How many square units does the rectangle cover if it is 6,7,8, or 9 units long?
1 solutions

Answer 249961 by jim_thompson5910(28476) About Me  on 2010-09-29 14:26:02 (Show Source):
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6 units long: Area = 4*6 = 24 square units


7 units long: Area = 4*7 = 28 square units


I'll let you do the last two.


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Jim


Equations/349714: Which of these shows 36/24 in simplest form?
A. 3/2
B. 4/3
C. 2/3
D. 6/4

1 solutions

Answer 249959 by jim_thompson5910(28476) About Me  on 2010-09-29 14:09:23 (Show Source):
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Solved by pluggable solver: Reducing Fractions Calculator
In order to reduce 36%2F24, the numerator and denominator must share a common factor. This common number must evenly divide into both of them without any remainder or decimal.


In order to completely reduce the fraction, you must divide the numerator and the denominator by the greatest common factor (GCF). The GCF of 36 and 24 is 12 (note: click here if you need help with finding the GCF). So divide both the numerator and denominator by 12



In other words, to reduce the fraction you do this
%28numerator%2FGCF%29%2F%28denominator%2FGCF%29=Reduced_Fraction



%2836%2F12%29%2F%2824%2F12%29 Plug in the numerator, denominator, and the GCF


%283%29%2F%2824%2F12%29 Now divide 36 by 12 to get 3. This is now the new numerator.


3%2F2 Now divide 24 by 12 to get 2. This is now the new denominator.



So

%2836%2F12%29%2F%2824%2F12%29=3%2F2




This means that 36%2F24 reduces to 3%2F2



In other words, 36%2F24=3%2F2






So the answer is A) 3%2F2


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Problems-with-consecutive-odd-even-integers/349711: A positive odd number plus a positive odd number equals a...?
A. positive odd number
B. positive even number
C. negative even number
D. negative odd number

1 solutions

Answer 249956 by jim_thompson5910(28476) About Me  on 2010-09-29 14:01:43 (Show Source):
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Any positive odd number is of the form 2n%2B1 where n%3E=0 (and n is an integer). So another positive odd number may look like 2m%2B1 where m%3E=0 (and m is an integer). Also, we can make the condition that m%3C%3En


Add the two numbers to get %282n%2B1%29%2B%282m%2B1%29=%282m%2B2n%29%2B%281%2B1%29=2%28m%2Bn%29%2B2=2%28m%2Bn%2B1%29


Notice how 2%28m%2Bn%2B1%29 is of the form 2q which is even where 'q' is some integer. Ie q=m%2Bn%2B1


So 2%28m%2Bn%2B1%29 is an even number which means that the sum of two positive odd numbers is ALWAYS a positive even number.



Example: 3 and 5 are positive odd numbers and 3+5 = 8 is an even number.


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Rectangles/349692: 2x+2(x-10)
1 solutions

Answer 249939 by jim_thompson5910(28476) About Me  on 2010-09-29 12:59:05 (Show Source):
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2x%2B2%28x-10%29=2x%2B2x-20=4x-20 which means that 2x%2B2%28x-10%29=4x-20


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test/349601: i asked 2 questions and can not access the answers help please
they are supposed to be posted at
www.algebra.com/tutors/students/your-answer.mlp?question349588 and #349586 how do I access the solutions

1 solutions

Answer 249938 by jim_thompson5910(28476) About Me  on 2010-09-29 12:57:35 (Show Source):
You can put this solution on YOUR website!
See the following links below:


http://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.349588.html

http://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.349586.html


Matrices-and-determiminant/349687: why is there a minus sign in the determinant
1 solutions

Answer 249931 by jim_thompson5910(28476) About Me  on 2010-09-29 12:52:44 (Show Source):
You can put this solution on YOUR website!
We would need to see the problem to have any idea of what you're referring to.