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Inverses/317501: Find the inverse of the followin matrix, if the inverse exists.
A = [2 1 0]
[0 2 1]
[1 0 -1]
1 solutions

Answer 227380 by Fombitz(13828) About Me  on 2010-06-25 13:56:02 (Show Source):
You can put this solution on YOUR website!
[A]=%28matrix%283%2C3%2C2%2C1%2C0%2C0%2C2%2C1%2C1%2C0%2C-1%29%29
.
.
.
det[A]=-3
.
.
.
[A]inv=-%281%2F3%29%2A%28matrix%283%2C3%2C-2%2C1%2C1%2C1%2C-2%2C-2%2C-2%2C1%2C4%29%29


Exponential-and-logarithmic-functions/317470: find the product (please show work)
3p^2+14p+1/p^2-6p+9 * p^2-3p/25-9p^2
1 solutions

Answer 227375 by Fombitz(13828) About Me  on 2010-06-25 13:49:52 (Show Source):


Equations/317504: Solve.
x^2 + 18 - 4 = 0
1 solutions

Answer 227373 by Fombitz(13828) About Me  on 2010-06-25 13:45:48 (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+18+-+4+=+0
x%5E2+%2B+14+=+0
x%5E2+=-14
highlight%28x=0+%2B-+sqrt%2814%29i%29 where i=sqrt%28-1%29
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.
.
If you meant x%5E2+%2B+18x+-+4+=0, then
x%5E2+%2B+18x+-+4+=+0
Use the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-18+%2B-+sqrt%28+18%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+
x+=+%28-18+%2B-+sqrt%28+324%2B16+%29%29%2F2+
x+=+%28-18+%2B-+sqrt%28+340%29%29%2F2+
x+=+%28-18+%2B-+2sqrt%28+85%29%29%2F2+
highlight%28x+=+-9+%2B-+sqrt%28+85%29%29+


Polynomials-and-rational-expressions/317511: Let the length and width of a rectangle be 4y and y-3 respectively. If a square inside the rectangle has a side of length y-7, find the remaining area.
1 solutions

Answer 227371 by Fombitz(13828) About Me  on 2010-06-25 13:41:31 (Show Source):
You can put this solution on YOUR website!
The rectangle's area is,
A1=L%2AW=4y%28y-3%29=4y%5E2-12
The area of the square is,
A2=s%5E2=%28y-7%29%5E2=y%5E2-14y%2B49
The remaining area is,
A=A1-A2=4y%5E2-12-%28y%5E2-14y%2B49%29
highlight%28A=3y%5E2%2B14y-61%29


Expressions-with-variables/317500: Solve each system by the substitution method
x + 3y = 2
-x + y = 1
1 solutions

Answer 227370 by Fombitz(13828) About Me  on 2010-06-25 13:37:54 (Show Source):
You can put this solution on YOUR website!
1.x+%2B+3y+=+2
2.-x+%2B+y+=+1
From eq. 2,
y=x%2B1
Substitute into eq. 1,
x%2B3%28x%2B1%29=2
x%2B3x%2B3=2
4x=-1
highlight%28x=-1%2F4%29
THen from eq. 2,
y=-1%2F4%2B1
highlight%28y=3%2F4%29


Exponential-and-logarithmic-functions/317468: please show work:
x+7/x^2+x-56 - x+8/x^2-49
1 solutions

Answer 227369 by Fombitz(13828) About Me  on 2010-06-25 13:35:32 (Show Source):
You can put this solution on YOUR website!

Use a common denominator,%28x%2B8%29%28x-7%29%28x%2B7%29




Rational-functions/317515: I am being asked to rationalize the denominator.
(sqrt(6) + sqrt(5)) / (sqrt(6) - sqrt(5))
Can you help me with this?
Jerry
jerry@san.rr.com
1 solutions

Answer 227366 by Fombitz(13828) About Me  on 2010-06-25 13:29:47 (Show Source):


Equations/317510: Find the vertex, the line of symmetry of x is.
f(x) = 1/2 (x+8)^2 + 2
1 solutions

Answer 227364 by Fombitz(13828) About Me  on 2010-06-25 13:26:50 (Show Source):
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The equation is in vertex form,
y=a%28x-h%29%5E2%2Bk where (h,k) is the vertex.
The x coordinate of the vertex also specifies the axis of symmetry.
Comparing,
(h,k)=(-8,2)
The axis of symmetry occurs at x=-8.


Triangles/317513: The base of a triangle is one-third as long as its height. If the area of the triangle is 24 square meters how long is its base?
1 solutions

Answer 227362 by Fombitz(13828) About Me  on 2010-06-25 13:23:44 (Show Source):
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The area of a triangle is,
A=%281%2F2%29bh=24
bh=48
%28h%2F3%29h=48
h%5E2=144
highlight%28h=12%29
Then,
b=h%2F3=12%2F3
highlight%28b=4%29


Mixture_Word_Problems/317183: Tickets for a school play sold for $2.50 for each adult and $1.00 for each child. The total receipts for 113 tickets sold were $221. Find the number of adult tickets sold.
1 solutions

Answer 227334 by Fombitz(13828) About Me  on 2010-06-25 11:08:22 (Show Source):
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Let A be the number of adult tickets, B the number of child tickets.
1.A%2BB=113
2.2.50A%2B1.00B=221
Multiply eq. 1 by -1 and add to eq. 2,
-A-B%2B2.5A%2BB=-113%2B221
1.5A=108
highlight%28+A=72%29
Then from eq. 1,
72%2BB=113
highlight%28B=41%29


Human-and-algebraic-language/317402: "A number cubed less the number tripled"
"The smoke stacks of the luxury liner cleared the bridge by 25 ft as it passed beneath it. Express the height of the stacks in terms of the bridge's height."
"As his reputation and referral business grew, Keith began to charge $75 per service call plus an hourly rate of $50 for the repair and maintenance of home computers. Express the cost of a service call in terms of the number of hours spent on the call."
1 solutions

Answer 227333 by Fombitz(13828) About Me  on 2010-06-25 11:05:22 (Show Source):
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"A number cubed less the number tripled"
N%5E3-3N
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.
.
"The smoke stacks of the luxury liner cleared the bridge by 25 ft as it passed beneath it. Express the height of the stacks in terms of the bridge's height."
S=B%2B25 where S is the stack height and B is the bridge height.
.
.
.
"As his reputation and referral business grew, Keith began to charge $75 per service call plus an hourly rate of $50 for the repair and maintenance of home computers. Express the cost of a service call in terms of the number of hours spent on the call."
C=75%2B50%2AH


Radicals/317457: 1.( 3x y ^ -1 )/ ( z ^ 2 ) =
2.( 3 x y ^ -2 )/ ( x ^ 3 ) =
1 solutions

Answer 227332 by Fombitz(13828) About Me  on 2010-06-25 11:02:58 (Show Source):


Systems-of-equations/317461: I have a problem in my math lab that I can not figure out here is what I have so far...
Solve by substitution method
3x+8y=18
-5x+y=13
solve for y, Y=13+5x
3x+8(13+5x)=18
remove the parenthesis
3x+104+40x=18
What is the coefficient of x? 43
Now solve for x.
The answer for x is -2 but I do not know how to get this answer can you please show me what i am doing wrong.
The answer I get is this 43x=132
Thank you
1 solutions

Answer 227330 by Fombitz(13828) About Me  on 2010-06-25 10:59:45 (Show Source):
You can put this solution on YOUR website!
You added instead of subtracted.
.
.
43x%2B104=18
43x=-86<--- Subtract 104 from both sides
x=-2<--- Divide both sides by 43


Money_Word_Problems/317349: joan had $1000 to invest. she invested part of the money in a COD that paid 4% annual simple interest, and the remainder in a mutual fund that paid 8% annual simple interest. the totsl interest of investments was $68.00. How much did Joan invest in each?
1 solutions

Answer 227328 by Fombitz(13828) About Me  on 2010-06-25 10:56:11 (Show Source):
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Let A be the amount in the COD, B in the mutual fund.
1.A%2BB=1000
.
.
0.04A%2B0.08B=68
2.4A%2B8B=6800
Multiply eq. 1 by -4 and add to eq. 2,
-4A-4B%2B4A%2B8B=-4000%2B6800
4B=2800
highlight%28B=700%29
Then from eq. 1,
A%2B700=1000
highlight%28A=300%29


Equations/317459: I have been working on this and can't seem to get the answer can you help? A rectangular table is four times as long as it is wide. The area of the table is 100ft^2. I can only get so far with it and keep getting the answer wrong. Can you show me how to do it so I can see where I am messing up.
1 solutions

Answer 227326 by Fombitz(13828) About Me  on 2010-06-25 10:52:38 (Show Source):
You can put this solution on YOUR website!
The area of a rectangle is,
1.A=L%2AW=100
"Four times long as wide"
2.L=4W
Substitute eq.2 in eq. 1,
L%2AW=100
%284W%29W=100
4W%5E2=100
Solve for W, then go back and solve for L using either equation.


Expressions-with-variables/317267: w-8/w-9 - w+1/w+9 + w-27/w^2-81
1 solutions

Answer 227325 by Fombitz(13828) About Me  on 2010-06-25 10:50:22 (Show Source):
You can put this solution on YOUR website!
Use the common denominator, w%5E2-81=%28w-9%29%28w%2B9%29
.
.







Inequalities/317221: Divide and Simplify.
3x - 18/10 / x-6/35x
1 solutions

Answer 227323 by Fombitz(13828) About Me  on 2010-06-25 10:39:57 (Show Source):
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Dividing by a fraction is equivlanet to multiplying by its reciprocal.


%28%283x-18%29%2F10%29%2F%28%28x-6%29%2F%2835x%29%29=%2821%2F2%29x


Exponents/317220: Divide:
(36b^2 + 18b^2 + 32b +39) / (6b + 5)
1 solutions

Answer 227321 by Fombitz(13828) About Me  on 2010-06-25 10:36:47 (Show Source):
You can put this solution on YOUR website!
Do you mean 36b%5E2 or 36b%5E3??


Rational-functions/317212: w=Cr^-2
a. Solve the equation for r.
b. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the Earth.)

100=3963r^-2
I am not sure if I am setting this problem up correctly? Can you let me know and give me some guidance as to what step to take first in solving?
1 solutions

Answer 227320 by Fombitz(13828) About Me  on 2010-06-25 10:34:43 (Show Source):
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a)w=C%2Fr%5E2
r%5E2w=C
r%5E2=C%2Fw
r=sqrt%28C%2Fw%29
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.
b)r=3963
w=100
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.
Find C.
C=wr%5E2
Plug in the values to find C.


Inequalities/317415: Which of the following CANNOT be a solution to 3x = 6 ≤ - 4x -2?
A: -8 B: -3 C: -8/14 D: -8/7 E: -1




1 solutions

Answer 227319 by Fombitz(13828) About Me  on 2010-06-25 10:31:37 (Show Source):
You can put this solution on YOUR website!
Correct your equation.
You have both an "=" sign and "<=" sign and you can't have both.


Numeric_Fractions/317450: Packets of washing powder can be bought individually for 2.35 each or in bulk at a rate of 50 packets for 100 dollars. Calculate the saving possible when bulk buying 200 packets. Express this savings as a percentage of the individual cost of the 200 packets. Give your answer correct to 2 decimal places.
1 solutions

Answer 227318 by Fombitz(13828) About Me  on 2010-06-25 10:30:27 (Show Source):
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Individually: 200%2A2.35=470
Bulk:200%28100%2F50%29=400
Savings:470-400=70
.
.
.
You could save $70 buying packets in bulk.
Percentage:%2870%2F470%29%28100%29=14.89=14.89%


Numbers_Word_Problems/317417: The sum of a nozero integer is twice the product of that number and 4. What is the number?
A: -2 B: 0 C: 2 D: 4 E: 7





1 solutions

Answer 227316 by Fombitz(13828) About Me  on 2010-06-25 10:27:21 (Show Source):
You can put this solution on YOUR website!
Can you re-phrase your question?
What does "sum of a nozero integer" mean?
Are you missing a term in that expression?


Human-and-algebraic-language/317419: you are collecting stamps in 16 cents and 21 cents denominations. You have total of $36.21, how many 16 cent stamps and how many 21 cent stamps do you have?
1 solutions

Answer 227315 by Fombitz(13828) About Me  on 2010-06-25 10:25:32 (Show Source):
You can put this solution on YOUR website!
There are multiple answers.
15, 161
36, 145
78, 113
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.
.
Do you have any additional information?


Exponential-and-logarithmic-functions/317241: Find the product please show work:
6p^2+14p+15/p^2-6p+p * p^2-3p/25-9p^2
1 solutions

Answer 227312 by Fombitz(13828) About Me  on 2010-06-25 10:16:23 (Show Source):


Miscellaneous_Word_Problems/317425: find the indicated output for f(x)=2 smal 2 =3x
1 solutions

Answer 227310 by Fombitz(13828) About Me  on 2010-06-25 10:10:22 (Show Source):
You can put this solution on YOUR website!
Can you clarify what you mean by "f(x)=2 smal 2=3x"?


Trigonometry-basics/317421: A passenger in an airplane at an altitude of 10 kilometers sees two towns directly to the east of the plane. The angle of depression of town a is 55 degrees and the angle of depression of town b is 28 degrees. How far apart are the towns?
1 solutions

Answer 227309 by Fombitz(13828) About Me  on 2010-06-25 10:07:01 (Show Source):
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Use trigonometry.
tan%2855%29=OPP%28a%29%2FADJ
OPP%28a%29=10tan%2855%29=14.28 km
.
.
.
tan%2828%29=OPP%28b%29%2FADJ
OPP%28b%29=10%2Atan%2828%29=5.32 km
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.
.
DELTA=14.28-5.32=8.96 km


Miscellaneous_Word_Problems/317428: 9x-4y=-16
4y-9x=16
1 solutions

Answer 227306 by Fombitz(13828) About Me  on 2010-06-25 09:59:23 (Show Source):
You can put this solution on YOUR website!
1.9x-4y=-16
2.-9x%2B4y=16
.
.
.
There are infinitely many solutions.
Line 1 and Line 2 are the same line.
Every solution of line 1 is a solution of line 2.


Functions/317416: If f (4) = 3, what is the slope when f (6) = -2?
A: -5/2 B: -1/2 C: -2/5 D: 2/5 E: 2




1 solutions

Answer 227305 by Fombitz(13828) About Me  on 2010-06-25 09:57:08 (Show Source):
You can put this solution on YOUR website!
Use the formula for slope,
m=%28f%28x2%29-f%28x1%29%29%2F%28x2-x1%29
m=%28-2-3%29%2F%286-4%29=-5%2F2
A) is the correct answer.


Travel_Word_Problems/317265: An airplane is flying at a speed of 350 mi/h at an altitude of one mile. The plane passes directly above a radoar station at time t=0
a. Express the distance s (in miles) between the plane and the radar station as a function of the horizontal distance d (in miles) that the plane has flown.
b. Express d as a function of the t (in hours) that the plane has flown.
c. Use composition to express s as a function of t.
1 solutions

Answer 227304 by Fombitz(13828) About Me  on 2010-06-25 09:53:38 (Show Source):
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a) The horizontal distance (d), the one mile altitude, and s form a right triangle.
Use the Pythagorean theorem.
s%5E2=1%5E2%2Bd%5E2
s%5E2=d%5E2%2B1
highlight%28s=sqrt%28d%5E2%2B1%29%29
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b) highlight%28d=350t%29
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c) s%28t%29=sqrt%28%28350t%29%5E2%2B1%29
highlight%28s%28t%29=sqrt%28122500t%5E2%2B1%29%29


Surface-area/317266: The rectangular prism pictured below has a square left side and an open right side. Its surface area in terms of a and b is
1 solutions

Answer 227303 by Fombitz(13828) About Me  on 2010-06-25 09:49:51 (Show Source):
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No picture provided.
Please repost.


Complex_Numbers/317423: WHAT IS COMPLEX NUMBER
1 solutions

Answer 227302 by Fombitz(13828) About Me  on 2010-06-25 09:49:20 (Show Source):
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Complex numbers are constructions made up of a two real numbers, x,y, and an imaginary part,i, in the form,z=x%2Biy.
The important property of i is i=sqrt%28-1%29 which makes it useful to solve equations of the form,x%5E2%2Ba%5E2=0, among others.
The solutions for x%5E2%2Ba%5E2=0 are x=ai and x=-ai.
x%5E2=-a%5E2
x%5E2=%28-1%29%28a%5E2%29
sqrt%28x%5E2%29=sqrt%28%28-1%29%28a%5E2%29%29
x=0+%2B-+a%2Asqrt%28-1%29
x=0+%2B-+ai
There are many application for complex numbers that provide meaningful interpretations in the real world. Search the internet for examples and properties of complex numbers.