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Pythagorean-theorem/347864: A triangle has sides of lengths 3,5 and x . determine all possible values of x so that the triangle is a right angle ?
1 solutions

Answer 248715 by Fombitz(13828) About Me  on 2010-09-25 07:28:29 (Show Source):
You can put this solution on YOUR website!
I think you mean right triangle.
Use the Pythagorean theorem where x is either a leg or the hypotenuse.
Leg:
x%5E2%2B3%5E2=5%5E2+
x%5E2%2B9=25+
x%5E2=16+
x=4+
.
.
.
Hypotenuse:
3%5E2%2B5%5E2=x%5E2+
9%2B25=x%5E2+
x%5E2=34+
+x=sqrt%2834%29+


Evaluation_Word_Problems/347870: as t approaches 0
find the limit of
( (sin^2) (3t) ) / (t^2)
1 solutions

Answer 248714 by Fombitz(13828) About Me  on 2010-09-25 07:26:08 (Show Source):
You can put this solution on YOUR website!
Use L'Hopital's rule.
.
.
.
f(x)=%28sin%283t%29%29%5E2
f1(x)=f'(x)=6sin%283x%29cos%283x%29
f2(x)=f''(x)=18cos%5E2%283x%29-18sin%5E2%283x%29
.
.
.
g(x)=x%5E2
g1(x)=g'(x)=2x
g2(x)=g''(x)=2
.
.
.
f2%28x%29%2Fg2%28x%29=9cos%5E2%283x%29-9sin%5E2%283x%29
lim+%28x-%3E0%2C+f2%28x%29%2Fg2%28x%29%29=9%281%29-9%280%29=highlight%289%29


Trigonometry-basics/347794: solve the equation tan x = 1 for the given interval of x
-pi/21 solutions

Answer 248712 by Fombitz(13828) About Me  on 2010-09-25 07:23:57 (Show Source):
You can put this solution on YOUR website!
tan%28x%29=1 when x=pi%2F4
.
.
.
Graphical verification
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.
.



Graphs/347829: it says solve by graphing the equation. 3x-4y=24 y=3/2x=3 to find a common point.can u help me step by step please.
1 solutions

Answer 248711 by Fombitz(13828) About Me  on 2010-09-25 07:20:08 (Show Source):
You can put this solution on YOUR website!
You have too many equal signs in your second equation.
Please correct.


Probability-and-statistics/347866:
1 solutions

Answer 248709 by Fombitz(13828) About Me  on 2010-09-25 07:18:19 (Show Source):
You can put this solution on YOUR website!
So the bin has 65 good, 12 bad, 77 total.
P(1st good)=65%2F77
P(2nd good)=65%2F77
P(3rd good)=65%2F77
P(4th good)=65%2F77
P(5th good)=65%2F77
P(all good)=%2865%2F77%29%2865%2F77%29%2865%2F77%29%2865%2F77%29%2865%2F77%29
P(all good)=0.4287
.
.
.
P=0.844 is the probability of picking the first good one out.
But you're doing it 5 times, so you need to multiply that value 5 times.


Numeric_Fractions/347789: Could you please help solve the following: 1/5(x-3)=3/15(2x-1). I tried it two different ways, but neither result works when I plug the value in for x. Thanks.
1 solutions

Answer 248680 by Fombitz(13828) About Me  on 2010-09-24 22:14:23 (Show Source):
You can put this solution on YOUR website!
%281%2F5%29%28x-3%29=%283%2F15%29%282x-1%29
Multiply both sides by 5.
x-3=2x-1
-x=2
highlight%28x=-2%29


Equations/347766: solve for x:
x+4/5+x-1/4=37/10
1 solutions

Answer 248679 by Fombitz(13828) About Me  on 2010-09-24 22:10:26 (Show Source):
You can put this solution on YOUR website!
Multiply both sides by 40.
40x%2B32%2B40x-10=148
80x%2B22=148
80x=126
highlight%28x=63%2F40%29


absolute-value/347758: solve the equation for the indicated variable
A=1/2h(B+b) for B
1 solutions

Answer 248677 by Fombitz(13828) About Me  on 2010-09-24 22:08:31 (Show Source):


absolute-value/347757: solve the equation
1/3(r+6)=1/6(r+8)
1 solutions

Answer 248676 by Fombitz(13828) About Me  on 2010-09-24 22:07:11 (Show Source):
You can put this solution on YOUR website!
%281%2F3%29%28r%2B6%29=%281%2F6%29%28r%2B8%29
Multiply both sides by 6.
2%28r%2B6%29=r%2B8
2r%2B12=r%2B8
highlight%28r=-4%29


logarithm/347765: How do I solve for X in this equation? log(small 2)(X+4) - log (small 2) (X-2)=3
1 solutions

Answer 248674 by Fombitz(13828) About Me  on 2010-09-24 22:05:53 (Show Source):


Equations/347771: find all solutions for x: square rt. of x^2+7=4
1 solutions

Answer 248672 by Fombitz(13828) About Me  on 2010-09-24 22:03:13 (Show Source):


Expressions-with-variables/347787: Solve the following linear equation where y-y sub 1= m (x-x sub 1) for m....
Please help me understand the above problem.
1 solutions

Answer 248670 by Fombitz(13828) About Me  on 2010-09-24 22:02:09 (Show Source):
You can put this solution on YOUR website!
y-y%5B1%5D=m%28x=x%5B1%5D%29
m=%28y-y%5B1%5D%29%2F%28x-x%5B1%5D%29
Where was the problem?


Expressions-with-variables/347709: Solve the following literal equation:
Solve f= 1/r sub 1 + 1/r sub 2 for r sub 1
I do not understand these subs...Please help explain
1 solutions

Answer 248636 by Fombitz(13828) About Me  on 2010-09-24 19:31:41 (Show Source):
You can put this solution on YOUR website!
Don't get hung up on that.
f=1%2Fa%2B1%2Fb where a=r%5B1%5D, b=r%5B2%5D
Multiply both sides by ab
abf=b%2Ba
abf-a=b
a%28bf-1%29=b
a=b%2F%28bf-1%29
r%5B1%5D=r%5B2%5D%2F%28f%2Ar%5B2%5D-1%29


Equations/347712: Sam evaluated the expression x2y for x = 7 and y = 9. He got a value of 49. Which of the following statements is correct.
A) Sam's answer is correct.
B) Sam forgot to multiply.
C) Sam squared wrong.

1 solutions

Answer 248634 by Fombitz(13828) About Me  on 2010-09-24 19:28:48 (Show Source):


Expressions-with-variables/347733: 1%2Fw%2B1-1%2F2w=3%2F40
1 solutions

Answer 248633 by Fombitz(13828) About Me  on 2010-09-24 19:27:46 (Show Source):
You can put this solution on YOUR website!
Multiply both sides by 40w,
40%2B40w-20=3w
20%2B40w=3w
Now solve for w.


Evaluation_Word_Problems/347579: Use the Squeeze Theorem to evaluate the limit as x approaches infinity (sinx)/x

1 solutions

Answer 248549 by Fombitz(13828) About Me  on 2010-09-24 16:14:54 (Show Source):
You can put this solution on YOUR website!
-1%3C=sin%28x%29%3C=1
-1%2Fx%3C=sin%28x%29%2Fx%3C=1%2Fx
.
.
.
So as x-%3Einfinity
1%2Fx-%3E0
-1%2Fx-%3E0
So then,
sin%28x%29%2Fx-%3E0 because it is squeezed between those two functions.


Trigonometry-basics/347678: graph 2 periods of the given function y = 3 sec x
1 solutions

Answer 248546 by Fombitz(13828) About Me  on 2010-09-24 16:10:57 (Show Source):


Radicals/347687: how do you simplify 15x^2+75x-1260

1 solutions

Answer 248529 by Fombitz(13828) About Me  on 2010-09-24 15:22:56 (Show Source):
You can put this solution on YOUR website!
Divide all terms by 15, since all terms are divisible by 3 and 5.


Mixture_Word_Problems/347686: This is a homework problem I can't figure out: A party mix is made by adding nuts that sell for $2.50 per kg to a cereal mixture that sells for $1.00 per kg. How much of each should be added to get 30 kg of a mix that will sell for $1.70 per kg?
1 solutions

Answer 248527 by Fombitz(13828) About Me  on 2010-09-24 15:22:09 (Show Source):
You can put this solution on YOUR website!
Let A be the amount of $2.50/kg nuts.
Let B be the amount of $1.00/kg cereal.
.
.
.
Total weight equation:
1.A%2BB=30
Concentration/Price equation:
2.5A%2B1B=1.7%2830%29
2.2.5A%2BB=51
Subtract eq. 1 from eq. 2,
2.5A%2BB-A-B=51-30
1.5A=21
highlight%28A=14%29kg
Now that you have A use either equation to solve for B.


Quadratic_Equations/347685: How do I solve this problem? (x-6)(x+8)=3(x-2)
1 solutions

Answer 248525 by Fombitz(13828) About Me  on 2010-09-24 15:18:05 (Show Source):
You can put this solution on YOUR website!
Use the FOIL method to expand the left hand side.
x%5E2%2B8x-6x-48=3x-6
x%5E2%2B2x-48=3x-6
x%5E2-x-42=0
Factor,
%28x-7%29%28x%2B6%29=0
Two solutions:
x-7=0
highlight%28x=7%29
.
.
.
x%2B6=0
highlight%28x=-6%29
.
.
.
As a check, verify the solutions by plugging them into the original equations.


Problems-with-consecutive-odd-even-integers/347640: the sum of three consecutive odd integers is 5 less than 4 times the smallest such integer. what are the three odd integers?
1 solutions

Answer 248522 by Fombitz(13828) About Me  on 2010-09-24 15:15:34 (Show Source):
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Let the integers be N, N%2B2, and N%2B4.
N%2BN%2B2%2BN%2B4=4N-5
3N%2B6=4N-5
-N=-11
N=11
The integers are 11,13, and 15.
.
.
.
11%2B13%2B15=4%2811%29-5
39=44-5
39=39
True, good solution.


Linear_Algebra/347684: For what value of x would the expression below be undefined?

5x - 18
x - 7

1 solutions

Answer 248521 by Fombitz(13828) About Me  on 2010-09-24 15:13:20 (Show Source):
You can put this solution on YOUR website!
I assume you mean like this (5x-18)/(x-7)=%285x-18%29%2F%28x-7%29.
The expression is undefined when the denominator equals zero.
x-7=0
Solve for x.


Sequences-and-series/347669: find using algebra the first five terms of the sequence when the 99th and 100th in the sequence are 351 and 353

1 solutions

Answer 248518 by Fombitz(13828) About Me  on 2010-09-24 15:03:42 (Show Source):
You can put this solution on YOUR website!
a%28n%29=a%281%29%2B%28n-1%29d
a%2899%29=a%281%29%2B98%2Ad=351
a%28100%29=a%281%29%2B99%2Ad=353
a%28100%29-a%2899%29=a%281%29%2B99d-a%281%29-98d
a%28100%29-a%2899%29=d
d=353-351
d=2
Then,
a%281%29%2B98d=351
a%281%29%2B98%282%29=351
a%281%29=351-196
a%281%29=155
.
.
.
a%282%29=a%281%29%2Bd=155%2B2=157
a%283%29=a%281%29%2B2d=155%2B4=159
I think you see how to get the next 2 values so I'll leave that to you.


absolute-value/347679: |-2w+5|=11
1 solutions

Answer 248516 by Fombitz(13828) About Me  on 2010-09-24 14:47:34 (Show Source):
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-2w%2B5=11 and -%28-2w%2B5%29=11
-2w=6 and -2w%2B5=-11
w=-3 and -2w=-16
w=-3 and w=8
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.
.


Numbers_Word_Problems/347670: The distance s, in feet, that an object will fall in t seconds is given by s=16tsquared + vt, where v is the initial velocity of the object in feet per second.
1 solutions

Answer 248515 by Fombitz(13828) About Me  on 2010-09-24 14:44:11 (Show Source):
You can put this solution on YOUR website!
Yes, and what's your question?


Equations/347667: find the equation of the line whose slope (m) is -3/4 and which passes through the (8,-2)
1 solutions

Answer 248514 by Fombitz(13828) About Me  on 2010-09-24 14:36:43 (Show Source):
You can put this solution on YOUR website!
Use the point-slope form of a line,
y-yp=m%28x-xp%29
y-%28-2%29=-%283%2F4%29%28x-8%29
y%2B2=-%283%2F4%29x%2B6
highlight%28y=-%283%2F4%29x%2B4%29


Inequalities/347672: Please help me solve this equation by method of substitution y=x(3) I tried substituting 14 for x. The main equation is x + y = 56 where y =x(3). After the substitution I got 14 + 42 = 56 and 42=14(3). Is that correct?
1 solutions

Answer 248513 by Fombitz(13828) About Me  on 2010-09-24 14:35:22 (Show Source):
You can put this solution on YOUR website!
No, that's not correct.
How did you come up with 14?
.
.
.
1.y=3x
2.x%2By=56
Now substitute eq. 1 into eq. 2, that's where the substitution comes in.
x%2B%283x%29=56
4x=56
x=14
That's where the 14 comes from.
Now use either equation and the result for x to find y.
From eq. 1,
y=3%2814%29
y=42
So the solution is x=14 and y=42.
You verify the solution by plugging it back into your original equations.


Trigonometry-basics/347675: y = 2 tan 2x graph two periods of the given tangent function
1 solutions

Answer 248512 by Fombitz(13828) About Me  on 2010-09-24 14:30:29 (Show Source):


Geometry_Word_Problems/347616: A bicycle tire travels about 50.27 inches during one rotation of the wheel. What is the diameter of the tire?

1 solutions

Answer 248511 by Fombitz(13828) About Me  on 2010-09-24 14:09:46 (Show Source):
You can put this solution on YOUR website!
DUPLICATE See Miscellaneous_Word_Problems/347592


Divisibility_and_Prime_Numbers/347621: Show all the three digit number that are divible either by 2 either by 3 and those by 2 and 3
1 solutions

Answer 248508 by Fombitz(13828) About Me  on 2010-09-24 14:04:03 (Show Source):
You can put this solution on YOUR website!
You can generate them yourself.
.
.
2:100,102,104,...,998 <--- Just add 2 to the previous number
.
.
3:102,105,108,...,999 <--- Just add 3 to the previous number
.
.
6:102,108,114,...,996 <--- Just add 6 to the previous number


Quadratic-relations-and-conic-sections/347596: evaluate the following determinants.
-2 -1 0
-3 5 -2
0 8 -1
1 solutions

Answer 248507 by Fombitz(13828) About Me  on 2010-09-24 13:58:43 (Show Source):
You can put this solution on YOUR website!
D=-19
I used EXCEL's MDETERM function with your matrix.
.
.
.
You could also calculate by hand,
D=-2%285%28-1%29-%28-2%29%288%29%29-1%28-2%280%29-%28-1%29%28-3%29%29
D=-2%28-5%2B16%29-1%28-3%29
D=-2%2811%29%2B3
D=-22%2B3
D=-19