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1. The sum of two numbers is 18 and the sum of their squares is 164. Find the numbers.
2. Find two numbers that total 12 and whose squares total 90.
Thx!
1 solutions
Answer 994 by longjonsilver(2297)   on 2005-05-19 05:33:00 (Show Source):
You can put this solution on YOUR website!Look at my previous answers on types of questions like these.
Here is the first one to the equation stage. You can work it our from there...
Define 2 numbers to be x and y, so we know x+y = 18 --eqn1
Also  --eqn2
From 1, x=18-y. Sub this into eqn2 to give  . Expand this, simplify it and solve the quadratic equation to find y then find x from equation 1.
then try the second one yourself
Jon
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Probability-and-statistics/2360: Can some help me on this question of probability? Please show your work.
For this question pretend you are drawing cards without replacement from the infamous "Iraq's Most Wanted" deck issued by the U.S. Military. If you are drawing from the full deck of 55 cards, what are the following probabilities:
a. You draw a card that is not Saddam Hussein
b. You draw three cards, which end up being Saddam Hussein and his two sons.
c. You draw 14 cards and not one of them is Saddam Hussein.
1 solutions
Answer 993 by longjonsilver(2297) on 2005-05-19 05:27:50 (Show Source):
You can put this solution on YOUR website!55 cards? A deck of cards have 52 (+ 2 jokers).
Using a standard deck...
1. P(a certain card) = 1/52
2. P(3 certain cards, ABC) = P(1st is one of the 3) + P(2nd is one of the other 2) + P(3rd is the last one)
P(ABC) = 3/52 * 2/51 * 1/50 = 1/22100
3. P(not drawing card A in 14 attempts) = longwinded way, so you can see...
51/52 * 50/51 * 49/50 * 48/49 * ... * 38/39.
cancel out all the duplicate numbers to leave 38/52 = 0.731 to 3dp.
jon.
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Functions/2337: what is [fog](x) if f(x)= 2x +7 and g(x)= -3x+4. my list of possable answers is a.-6x-17 b.-6x+15 c.-6x+8 and d.-6x-10
1 solutions
Answer 982 by longjonsilver(2297) on 2005-05-18 11:06:54 (Show Source):
You can put this solution on YOUR website!ta.
assuming fog is my fg(x), then...
fg(x)
f(-3x+4)
so whereever you have x, you just put all this in...
2(-3x+4) + 7
-6x+8+7
fg(x)=15-6x
answer b. EASY EASY EASY but students are scared of functions for some reason.
jon
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Linear-equations/2335: Can you please explain how do the following problem?
If 2x+10=x+2
____ ____
2 10
what is the value of x -1?
P.D.The ______ below the 2x+10 means divided by 2 and same thing x+2 means is divided by 10.
1 solutions
Answer 978 by longjonsilver(2297) on 2005-05-18 10:46:03 (Show Source):
You can put this solution on YOUR website!with fractions, get rid of them first!. With 2 terms, you basically cross-multiply, but with more terms, you have to do it "properly", so i shall do this one properly, so you can see...
Look at the denominators and decide the smallest number that goes into all the denominators. Here it is 10. We therefore multiply everything by 10...we can do anything we like to an equation SO LONG AS WE DO THE SAME THING TO ALL THE TERMS! So,
The reason is that we can now simplify each term as:
Now multiply out the brackets and collect like terms together:
10x+50 = x + 2
9x+50 = 2
9x = -48
x = -48/9
jon
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Numbers_Word_Problems/2330: Three times the greater of two consecutive odd integers is five less than four times the smaller. Find the two numbers.
1 solutions
Answer 973 by longjonsilver(2297) on 2005-05-18 10:33:59 (Show Source):
You can put this solution on YOUR website!Define:
smallest odd integer = x
larger odd integer = y
we know y - x = 2 eg 19-17=2
and 3y = 4x - 5
so, getting rid of the y (from y=x+2), gives 3(x+2)=4x-5
3x+6=4x-5
6 = x-5
x=11
so y=13
Once you have the answer, just work through the question again with these, to see if it all makes sense.
jon.
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Quadratic_Equations/2297: 1. Given equation: y=xsquared-4x+2
solve the system of equation fors for y=xsquared-4x+2 (substitution method).
thanks,
Ally
1 solutions
Answer 971 by longjonsilver(2297) on 2005-05-18 08:00:29 (Show Source):
You can put this solution on YOUR website!y= 
Solve this means put y=0, so we get
Substitution method??
You either factorise the quadratic or use the formula. Here, use the formula, as i cannot factorise it.
x = 
x = 
x = 
x = 
x = 
x = 
x = 
these are your 2 answers, in an exact form.
Use your calculator to work the approx answers out, say to 2 decimal places.
jon
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Travel_Word_Problems/2306: None of the cars finished the race here is what happend
car A broke 1/9th into last 3rd of race. How far did car A go?
car B completed the first 1/2 of 13/16th of the race how far did car B go?
car C broke with 1/3 left of race how far did car C go?
car D broke with 1/5 of the last 5th of race completed, how far did D go?
car E went 1/2 as far as car B how far did car E go?
Car F went 2/3 as far as car B how far did car f go?
Who went the farthest? who went the shortest.
1 solutions
Answer 969 by longjonsilver(2297) on 2005-05-18 07:49:12 (Show Source):
You can put this solution on YOUR website!A did 2/3 + (1/9 of 1/3) = 2/3 + 1/9 x 1/3) = 2/3 + 1/27 = 18/27 + 1/27 = 19/27
B did 1/2x13/16 = 13/32
C did 2/3
D did 4/5 + (1/5 of 1/5) = 4/5 + 1/25 = 20/25 + 1/25 = 21/25
E did 1/2 of 13/32 = 1/2 x 13/32 = 13/64
F did 2/3 of 13/32 = 2/3 x 13/32 = 13/48
Both E and F did less than B, so ignore them. It is between A, B, C and D. Looking at B, this is a small fraction compared to the other 3.
Converting to decimals on calculator (you didn't say i couldn't)...
A = 0.704
C = 0.666
D = 0.84
Answer...D went furthest.
B was shortest of A,B,C and D and then E and F are both fractions of B, so it had to be one of E or F. 1/2 is less than 2/3, so E went shortest distance.
jon
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Numbers_Word_Problems/2314: One number is 16 more than another. If the smaller number is subtracted from 2/3 of the larger, the result is 1/4 of the sum of the two numbers. find the numbers
1 solutions
Answer 967 by longjonsilver(2297) on 2005-05-18 07:31:00 (Show Source):
You can put this solution on YOUR website!Let larger number be x
Let smaller number be y
x = y + 16 --eqn1
(2/3)x - y = (x+y)/4 --eqn2
eqn2 becomes, by multiplying every term by 12...
8x - 12y = 3x + 3y
5x = 15y
x = 3y --eqn3
sub 3 into 1 for x, to give
3y = y + 16
2y = 16
y = 8
so, x = 24
check these by using them in the question and making sure that you do get the correct answers that way.
jon
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Quadratic_Equations/2276: I'm trying to solve an equation I've been working on, but it's been a long time since my algebra days...
I want to solve this equation for t, as a function of x and p:
x = 2pt(1-t) + t^2
I get stuck when I smoosh around the terms to:
x = 2pt - 2pt^2 + t^2
I'm not sure if this can be reduced to a quadratic equation or not -- I'm stuck!
Is there a solution?
1 solutions
Answer 965 by longjonsilver(2297) on 2005-05-18 07:22:06 (Show Source):
You can put this solution on YOUR website!
you can put this into the quadratic formula and solve for t but there are too many variable that the square root doesn't really simplify and you end up with a mess.
Are you sure you want to keep all t, p and x in the equation? Is there nothing else that relates p to x, for example so that we can remove one of these?
jon
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Geometry_Word_Problems/2256: what is the measure of each exterior angle,one angle at each vertex,of a regular nonagon
1 solutions
Answer 963 by longjonsilver(2297) on 2005-05-18 07:11:57 (Show Source):
You can put this solution on YOUR website!a 9-sided figure can be split into 7 triangles. 7 triangles have 7*180 degrees for its interior angles = 1260 degrees.
As it is a regular nonagon, each interior angle is the same, so 1260/9 = 140 degrees. So, each exterior angle must be 180-140 = 40degrees.
Jon
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Linear-equations/2271: 6(x+1) = 12(x-3)
then you get
6x+6=12x-36
My question at this point is: How do you know which side to start with. Not sure whether to start with +6 or -36 or 6x or 12x.
1 solutions
Answer 962 by longjonsilver(2297) on 2005-05-18 06:20:11 (Show Source):
You can put this solution on YOUR website!it doesn't matter...
either collect x terms together first:
-6x+6=-36
-6x = -42
x=(-42)/(-6)
x=7
or collect the pure numbers together first:
6x = 12x-42
-6x = -42
x = (-42)/(-6)
x = 7
jon
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Linear-equations/2320: 1). how would you find the slope that passes through the points of (-4 ,-1)and (-3 ,-3 )? and
2). find the slope of the graph 5x -3y = 6
3). simplify :(ab^4)(ab^2).
4). simplify :[(m^3n^4)(m^2n^3)]/[(mn)(m^2n)]
5). solve:y=x+3
3y+x=5
6). simplify: [(3^2)^4]^2
please show me how to do these problems because i have some more to do.
1 solutions
Answer 961 by longjonsilver(2297) on 2005-05-18 06:14:12 (Show Source):
You can put this solution on YOUR website!i have done gradients of straight lines before..look at my explanations there.
gradient is (change in y)/(change in x)
Re-arrange any straight line to y=mx+c..then m is the gradient.
so 5x-3y = 6
-3y = -5x+6 OR...
3y = 5x-6
y = (5/3)x-2
gradient is +5/3
3. 
4. 
5. linear equations... see the many examples i have done before.
6. 
jon
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Geometry_Word_Problems/2279: Is it possible to have a regular polygon with interior angles measuring 15 degrees? If so how many sides does it have?
1 solutions
Answer 960 by longjonsilver(2297) on 2005-05-18 06:02:00 (Show Source):
You can put this solution on YOUR website!the sum of the interior angles of a polygon are:
3 sides = 1*180
4 sides = 2*180
5 sides = 3*180
6 sides = 4*180
.
.
.
13 sides = 11*180
see a pattern?
n sides = (n-2)*180
So for a regular polygon, each angle would be this divided the number of sides. And can this be 15?
so 
180n - 360 = 15n
165n = 360
n = 2.1818
so it is NOT possible, since this is not a whole number (remember n is the number of sides).
jon
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Age_Word_Problems/2325: "Grandpa how old are you?"Billy asked. His grndfather retorted,"why,the average age of you grandmother and me is seventy years,Billy." "But how old are you_?" he asked again,seemiing impatient.
"Well,let me put it another way: I am twice as old as your grandmother was when I was her present age.Perhaps you can figure out both our ages by using some of that algebra you learned today." Scratching his head,Billy went to his room.
1 solutions
Answer 958 by longjonsilver(2297) on 2005-05-18 05:51:38 (Show Source):
You can put this solution on YOUR website!define:
x = grandpa's age now
y = grandma's age now.
1. 
 --eqn1
2. when he was her age: he was y, she was y-(x-y) where (x-y) is the difference in their ages. Use numbers to check this..just make some up and look at how you would work it out with numbers.
x = 2(y-(x-y)) --eqn2. this is a tricky one to get.
Re-arranging gives...
x = 2(2y-x)
x = 4y - 2x
3x = 4y --eqn3
sub 1 into 3 for x, gives
3(140-y) = 4y
420-3y= 4y
7y=420
y=60
so x=80
check...grandma was 40 when he was her age now, 60. And Grandpa's current age of 80 is twice that..so correct.
jon.
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logarithm/2287: If log5 6=1.1133 and log5 2=0.4307, what is the value of log5 12?
1 solutions
Answer 957 by longjonsilver(2297) on 2005-05-18 05:18:48 (Show Source):
You can put this solution on YOUR website!when you say log5 i take it you mean log to the base 5? If so, we have...
(i will ignore writing the 5 - take it as read):
log 12 is the same as log(6*2) which is the same as log6+log2
as you know log6 and log2 from your question, just add them together :-)
Jon
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Circles/2313: I have 100 feet of fence. What shape would maximize the enclosure. Thanks
1 solutions
Answer 953 by longjonsilver(2297) on 2005-05-18 04:35:21 (Show Source):
You can put this solution on YOUR website!as you don't say prove it...i shall tell you the answer: a cirle.
calculate the area of the circle then a square...any other shape just gets less effective, as the perimeter increases but the area does not.
Jon.
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Geometry_Word_Problems/2324: Hi there,
I'm trying to help my little sister on her geometry final. She is supposed to present a problem and for a pyramid with a hexagon base to her entire class. The problem here is that she needs to create a visual aid (pyramid w/hexagon base) based on a real building but we can't find one. If you know one can you please let me know? Thank you so much.
Desperate older sister
1 solutions
Answer 950 by longjonsilver(2297) on 2005-05-18 04:26:36 (Show Source):
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Linear-equations/2327: how do you graph the equation 2y-4=4x & then solve for y & then find 3 solutions
1 solutions
Answer 949 by longjonsilver(2297) on 2005-05-18 04:16:42 (Show Source):
You can put this solution on YOUR website!Get any straight line equation in the form y=mx+c...m is the gradient and c is the y-intercept. Any straight line will cross the x-axis once ONLY (unless the line is parallel to the x-axis, then no crossing).
The x-value at which the line crosses the x-axis is called the SOLUTION or ROOT of the equation. So, there will NOT be 3 solutions!!!
solution...
2y = 4x + 4
so, y = 2x + 2
gradient is +2
y-intercept is at y=2
when y=0, x=-1 --> this is the root (or solution)
so draw your axes, plot these two points and draw a straight line between them. Done!
Jon
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