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Hector has a collection of nickels, dimes, and quarters totaling 122 coins. The number of dimes he has is 3 more than four times the number of nickels, and the number of quarters he has is 19 less than the number of dimes. How many coins of each kind does he have?
1 solutions
Answer 48479 by funmath(2925)   on 2007-01-27 06:21:38 (Show Source):
You can put this solution on YOUR website!Hector has a collection of nickels, dimes, and quarters totaling 122 coins. The number of dimes he has is 3 more than four times the number of nickels, and the number of quarters he has is 19 less than the number of dimes. How many coins of each kind does he have?
Let the number of Nickels be:x
Then the number of dimes is (3 more that 4 times nickels): 4x+3
Then the number of quarters is (19 less thatn the number of dimes: 4x+3-19=4x-16
The equation to solve is:
Nickels+dimes+quarters=122
(x)+(4x+3)+(4x-16)=122
9x-13=122
9x-13+13=122+13
9x+135
9x/9=135/9
x=15
:
Nickels: x=15
Dimes:4x+3=4(15)+3=63
Quarters: 4x-16=4(15)-16=44
:
Sanity check, do 15 nickels+63 dimes + 44 Quarters=122 coins?
15+63+44=122
122=122 Yes. I think we've got it!
Happy Calculating!!!
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Inequalities/68187: y>3. Determine the correct half-plane
1 solutions
Answer 48478 by funmath(2925) on 2007-01-27 06:10:35 (Show Source):
You can put this solution on YOUR website!y>3. Determine the correct half-plane
y=3 is a horizontal line going through 3 that looks like:
Because y>3 and not = to 3, you would use a dashed line instead of a solid one.
You would then shade above the line because y is greater than 3.
(I can't show you graphs of inequalities, but I hope that helped.)
Happy Calculating!!!
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Graphs/68189: Graph the inequality
4x + y is greater than or equal to 4
1 solutions
Answer 48477 by funmath(2925) on 2007-01-27 06:06:04 (Show Source):
You can put this solution on YOUR website!Graph the inequality
4x + y is greater than or equal to 4
Plot points the way you would an equality.
Let x=0 and solve for y:
 Plot (0,4)
Let x=1 and solve for y:
 Plot (1,0)
Because the inequality contains =, connect the two points with a solid line like this:
I don't have the capability of shading this graph for you, but you would shade above the line because y is greater than the rest of the graph.
Happy Calculating!!!
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Equations/68188: 6a/3xy + 2ab/5x^2y + 4b/2x^2 i tried to simplify this into a single fraction and came up with 60ax 12abx 60x^2y / 30x^2y lcd 30x^2y is this even close?
1 solutions
Answer 48476 by funmath(2925) on 2007-01-27 05:54:46 (Show Source):
You can put this solution on YOUR website! 6a/3xy + 2ab/5x^2y + 4b/2x^2 i tried to simplify this into a single fraction and came up with 60ax 12abx 60x^2y / 30x^2y lcd 30x^2y is this even close?
You were close.
:
 You're right the LCD is 30x^2y
 Which reduces by 6.
Happy Calculating!!!!
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Equations/68153: My Problem is 19h - 7 = 23 + 14h,its kinda of confusing 2 me
If you could help it would be Greatly appreciated
1 solutions
Answer 48461 by funmath(2925) on 2007-01-26 21:23:09 (Show Source):
You can put this solution on YOUR website!My Problem is 19h - 7 = 23 + 14h
19h-14h-7=23+14h-14h
5h-7=23
5h-7+7=23+7
5h=30
5h/5=30/5
Check by letting h=6 and see if the sides of the equation equal.
19(6)-7=23+14(6)
114-7=23+84
107=107 We're right!!!
Happy Calculating!!!
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Equations/68154: My Problem is 1 + 9a -8 = 8a
Can you help me please?
Thankz
1 solutions
Answer 48460 by funmath(2925) on 2007-01-26 21:18:43 (Show Source):
You can put this solution on YOUR website!My Problem is 1 + 9a -8 = 8a
9a-7=8a
9a-8a-7=8a-8a
a-7=0
a-7+7=0+7
Check by letting a=7 and see if both sides of the equation =.
1+9(7)-8=8(7)
1+63-8=56
64-8=56
56=56 We're right!!!
Happy Calculating!!!
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Linear_Equations_And_Systems_Word_Problems/68164: The cost of producing a number of items x is given by C=mx+b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item)
a.) if the fixed cost is $40 and the variable cost is $10, write the cost equaton
1 solutions
Answer 48459 by funmath(2925) on 2007-01-26 21:13:07 (Show Source):
You can put this solution on YOUR website!The cost of producing a number of items x is given by C=mx+b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item)
a.) if the fixed cost is $40 and the variable cost is $10, write the cost equaton
In the formula  , m=variable cost and b=fixed cost
m=10 and b=40
Therefore:
Happy Calculating!!!
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Equations/68155: My problem is 4t = 2(7t + 15)
Can you help me out?
Thankz
1 solutions
Answer 48458 by funmath(2925) on 2007-01-26 21:10:47 (Show Source):
You can put this solution on YOUR website!My problem is 4t = 2(7t + 15)
4t=2(7t)+2(15)
4t=14t+30
4t-14t=14t-14t+30
-10t=30
-10t/-10=30/-10
Check by letting t=-3 and see if both sides equal:
4(-3)=2(7(-3)+15)
-12=2(-21+15)
-12=2(-6)
-12=-12 We're right!!!
Happy Calculating!!!
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Equations/68156: My problem is 7 + w - 10 = 2w
Can you help me out?
Thank You
1 solutions
Answer 48457 by funmath(2925) on 2007-01-26 21:07:07 (Show Source):
You can put this solution on YOUR website!My problem is 7 + w - 10 = 2w
w-3=2w
w-w-3=2w-w
-3=w
Check by letting w=-3 and see if both sides of the equation equal.
7+(-3)-10=2(-3)
7-13=-6
-6=-6 We're right!!!
Happy Calculating!!!
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Square-cubic-other-roots/68174: Is this irrational or rational:
- 4throot sqrt 16
Would this be irrational? I think it would because to me the negative sign before it confuses me but I believe it is irrational. Am I correct? Thank you!
1 solutions
Answer 48452 by funmath(2925) on 2007-01-26 20:55:09 (Show Source):
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Linear-equations/68146: What is the slope, x-intercept, and y-intercept of the following line?
3x + 4y = 9
1 solutions
Answer 48431 by funmath(2925) on 2007-01-26 16:49:51 (Show Source):
You can put this solution on YOUR website!What is the slope, x-intercept, and y-intercept of the following line?
3x + 4y = 9
The slope intercept form of a line is:  where m=slope and (0,b)=y-intercept.
 the slope, m=-3/4
 the y-intercept, (0,b)=(0,9/4)
Happy Calculating!!!
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Rational-functions/68140: For f(x)=1/x^2-2x-8, find the interval(s) where f(x)<0.
Express the following statement as a formula with the value of the constant of proportionality determined with the given conditions: w varies directly as x and inversely as the square of y. If x=15 and y=5, then w=36.
The electrical resistance R of a wire varies directly as its length L and inversely as the square of its diameter. A wire 20 meters long and 0.6 centimeters in diameter made from a certain alloy has a resistance of 36 ohms. What is the resistance of a piece of wire 60 meters long and 1.2 centimeters in diameter made from the same material?
The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve a 1 swcond period?
Thanks for asssiting me in studying for my final exam.
1 solutions
Answer 48430 by funmath(2925) on 2007-01-26 16:45:54 (Show Source):
You can put this solution on YOUR website!For f(x)=1/x^2-2x-8, find the interval(s) where f(x)<0.
x-4=0 when x=4 and x+2=0 when x=-2
So your possible intervals are (-infinity,-2), (-2,4), or (4, infinity)
for (-infinity,-2) test -3
 1/7 is not <0 so reject this interval.
for (-2,4) test 0
 -1/8 is <0 so accept this interval.
for (4,infinity) test 5
 1/7 is not <0 so reject this interval.
Therefore the interval where f(x)<0 is (-2,4)
:
Express the following statement as a formula with the value of the constant of proportionality determined with the given conditions: w varies directly as x and inversely as the square of y. If x=15 and y=5, then w=36.
Therefore, the formula is: 
:
The electrical resistance R of a wire varies directly as its length L and inversely as the square of its diameter. A wire 20 meters long and 0.6 centimeters in diameter made from a certain alloy has a resistance of 36 ohms. What is the resistance of a piece of wire 60 meters long and 1.2 centimeters in diameter made from the same material?
Convert 20 m to cm's: 
60m=6000cm
 ohms
:
The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve a 1 swcond period?
:
Period=T Length=L
L=1.5 ft
Good Luck on Your Final!
Happy Calculating!!!!
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Linear-equations/68129: evaluate each function for the value specified
f(x)=x^2-7x+10, find (a)f(0),(b) f(5), and (c) f(-2)
Please help this relates to the function notation, I dont
understand how to do this problem.
1 solutions
Answer 48425 by funmath(2925) on 2007-01-26 16:12:39 (Show Source):
You can put this solution on YOUR website!evaluate each function for the value specified
Substitute the number in for x and simplify.
f(x)=x^2-7x+10, find
(a)f(0)
:
(b) f(5)
:
(c) f(-2)
:
Happy Calculating!!!
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Linear-equations/68130: rewrite each equation as a function of x
-3x+4y= 11
Please help with this equation
Thanks
1 solutions
Answer 48422 by funmath(2925) on 2007-01-26 16:02:51 (Show Source):
You can put this solution on YOUR website!rewrite each equation as a function of x
-3x+4y= 11
-3x+3x+4y=11+3x
4y=3x+11
 If you need to use function notation, replace y with f(x)
If this doesn't look exactly the way the book says that it should, it could also look like this:
Happy Calculating!!!
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Functions/68142: If f (X) = 5x-1, find the following
f (a-2)
Please help me solve this thank you
these are function notation problems
1 solutions
Answer 48420 by funmath(2925) on 2007-01-26 15:58:00 (Show Source):
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Quadratic_Equations/68137: solve the following:
18x^2 + 9x - 2 = 0
1 solutions
Answer 48416 by funmath(2925) on 2007-01-26 15:41:06 (Show Source):
You can put this solution on YOUR website!solve the following:
18x^2 + 9x - 2 = 0 Factor
18x^2+12x-3x-2=0
(18x^2+12x)+(-3x-2)=0
6x(3x+2)-1(3x+2)=0
(6x-1)(3x+2)=0 Set each parentheses = to 0.
6x-1=0 or 3x+2=0
6x-1+1=0+1 or 3x+2-2=0-2
6x=1 or 3x=-2
6x/6=1/6 or 3x/3=-2/3
 or 
Happy Calculating!!!!
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Quadratic_Equations/68138: I had a problem I was working on with the quadratic equation rule.
Eventually I worked the problem down to 
The answer I'm suppose to get from there is 
I don't see how this is possible.
1 solutions
Answer 48410 by funmath(2925) on 2007-01-26 15:20:39 (Show Source):
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Functions/67978: How do I evaluate each function for the value specified.
f(x) = x 2 - 7x +10; find (a) f (0), (b) f (5), and (c) f (2).
1 solutions
Answer 48331 by funmath(2925) on 2007-01-25 08:07:04 (Show Source):
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absolute-value/67973: solve the inequality, with answer in interval notation
|2x-3| is less than or equal to 20
1 solutions
Answer 48329 by funmath(2925) on 2007-01-25 06:47:38 (Show Source):
You can put this solution on YOUR website!solve the inequality, with answer in interval notation
|2x-3| is less than or equal to 20
Because this is a less than situation it is an and situation and can be solved simultaneously like this.
Interval notation:
[-17/2,23/2]
Happy Calculating!!!
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