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Quadratic_Equations/341595: I need help solving x^2+20x=6
I know the formula should be x^2+bx but I need help understanding how to complete the square.
1 solutions

Answer 244626 by Fombitz(13828) About Me  on 2010-09-11 08:46:08 (Show Source):
You can put this solution on YOUR website!
x%5E2%2B20x=6
To complete the square, take 1%2F2 of the x-coefficient(b), square it, and add it to both sides.
%281%2F2%29%2820%29=10
10%5E2=100
x%5E2%2B20x%2B100=6%2B100
%28x%2B10%29%5E2=106
x%2B10=0+%2B-+sqrt%28106%29
highlight%28x=-10+%2B-+sqrt%28106%29%29


Linear-equations/341585: write equations for the vertical and horizontal lines passing through the point (-5,)
1 solutions

Answer 244625 by Fombitz(13828) About Me  on 2010-09-11 08:43:27 (Show Source):
You can put this solution on YOUR website!
Your ordered pair is incomplete.
The vertical line would be x=-5.
But without the y-coordinate, it can't be determined.
If the ordered pair was (-5,b), then the horizontal line would be y=b


Geometry_Word_Problems/341581: the area of a rectangle is 991 cm2 . if 991 is a prime number, what are the whole number dimensions of the rectangle. explain with reasoning
1 solutions

Answer 244624 by Fombitz(13828) About Me  on 2010-09-11 08:41:49 (Show Source):
You can put this solution on YOUR website!
Prime numbers only have factors of 1 and themselves.
So a rectangle with an area of 991 can only be either
1 cm wide by 991 cm long or 991 cm wide by 1 cm long.


Graphs/341574: 2x -3 > 3x -1
1 solutions

Answer 244623 by Fombitz(13828) About Me  on 2010-09-11 08:40:24 (Show Source):


Graphs/341569: 2x -3 > 23
1 solutions

Answer 244622 by Fombitz(13828) About Me  on 2010-09-11 08:37:48 (Show Source):


Reduction-of-unit-multipliers/341567: 2.5gm=xmg
1 solutions

Answer 244621 by Fombitz(13828) About Me  on 2010-09-11 08:36:54 (Show Source):
You can put this solution on YOUR website!
There are 1000mg/1g.
2.5g(1000mg/1g)=2500mg


Systems-of-equations/341556: for equation y=2x-4 select order of pairs that are solutions:
0,-4
-1,-6
2,3
-4,0
1 solutions

Answer 244619 by Fombitz(13828) About Me  on 2010-09-11 08:35:35 (Show Source):
You can put this solution on YOUR website!
Substitute values for x and y.
I'll do one you do the rest.
y=2x-4
x=0
y=-4
-4=2%280%29-4
-4=-4
True, so (0,-4) is a solution.
Now do the rest of the ordered pairs in the same way.


Linear-systems/341064: I am not sure what to do on this one
3(x-0.87)-2x=4.98
1 solutions

Answer 244527 by Fombitz(13828) About Me  on 2010-09-10 16:07:32 (Show Source):
You can put this solution on YOUR website!
Distribute the 3.
3%28x-0.87%29-2x=4.98
3x-2.61-2x=4.98
3x-2x=4.98%2B2.61
Take it from there and solve for x.


Geometry_Word_Problems/340808: I need help w/solving
2x-5=3x
____
4
1 solutions

Answer 244525 by Fombitz(13828) About Me  on 2010-09-10 16:06:04 (Show Source):
You can put this solution on YOUR website!

%282x-5%29%2F4=3x
2x-5=12x
Now solve for x.


Trigonometry-basics/340711: The accepted density for mercury is 13.6 g/mL. Calculate the percent error for each of these measurements.
(c) 13.9 g/mL
(d) 13.4 g/mL
1 solutions

Answer 244524 by Fombitz(13828) About Me  on 2010-09-10 16:05:07 (Show Source):
You can put this solution on YOUR website!
% Error=(Measured-Actual)/Actual x 100
.
.
.
c) E=%28%2813.9-13.6%29%2F13.6%29%2A100=2.21%
.
.
.
Do the next one, the same way.


Linear-equations/341049: Find m and b and graph.
y=4-3x
1 solutions

Answer 244522 by Fombitz(13828) About Me  on 2010-09-10 16:02:58 (Show Source):
You can put this solution on YOUR website!
The line is in slope-intercept form, y=mx%2Bb
m=-3
b=4
.
.
.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C4-3x%29


real-numbers/341052: Is 7.6 Rational or Irrational?
1 solutions

Answer 244521 by Fombitz(13828) About Me  on 2010-09-10 15:57:54 (Show Source):
You can put this solution on YOUR website!
Rational, it's the ratio of the two integers 76 and 10.
76%2F10=7.6


Functions/340858: Directions: For each function f, construct and simplify the difference quotient.
%28f%28x%2Bh%29-f%28x%29%29+%2F+h
f(x)=3x-5
- I have no problem with setting up the problem, but I have the most trouble with solving with fractions.

1 solutions

Answer 244520 by Fombitz(13828) About Me  on 2010-09-10 15:57:06 (Show Source):
You can put this solution on YOUR website!
Shouldn't be a problem here.
f%28x%29=3x-5
.
.
f%28x%2Bh%29=3%28x%2Bh%29-5
f%28x%2Bh%29=3x%2B3h-5
.
.
f%28x%2Bh%29-f%28h%29=3x%2B3h-5-3x-%28-5%29
f%28x%2Bh%29-f%28h%29=3h
Now divide both sides by h.


Linear-systems/340960: for the following equation, state the value of the discriminant and then describe the nature of the solutions.
-3x^2-9x-5=0
The equation has one or two real solutions?
1 solutions

Answer 244519 by Fombitz(13828) About Me  on 2010-09-10 15:54:36 (Show Source):
You can put this solution on YOUR website!
a=-3
b=-9
c=-5
.
.
.
D=b%5E2-4ac
D=81-4%28-3%29%28-5%29
D=81-60
D=21
Since D%3E0 there are two unique irrational solutions.


Polynomials-and-rational-expressions/341388: I really need help with rational functions! Please help me with the following:
I need to find the zeroes, poles and asymptotes, then sketch
x(x-1)(x-5)/(x+1)(x-3)(x-4)
Thank you very much!
1 solutions

Answer 244518 by Fombitz(13828) About Me  on 2010-09-10 15:49:59 (Show Source):
You can put this solution on YOUR website!
Zeros make the numerator equal zero.
x%28x-1%29%28x-5%29=0
Three solutions:
x=0
.
.
.
x-1=0
x=1
.
.
.
x-5=0
x=5
.
.
.
Vertical asymptotes occur when the denominator equals zero.
%28x%2B1%29%28x-3%29%28x-4%29=0
Three solutions:
x%2B1=0
x=-1
.
.
.
x-3=0
x=3
.
.
.
x-4=0
x=4
.
.
.



Travel_Word_Problems/340655: How long does it take an automobile traveling at 63.2 km/h to become even with a car that is traveling in another lane at 49.2 km/h if the cars' bumpers are initially 137m apart? Answer your units in s.

1 solutions

Answer 244517 by Fombitz(13828) About Me  on 2010-09-10 15:37:36 (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
.
.
.
Convert meters to km.
D1=63.2t
D2=49.2t%2B137%2F1000
Find t when D1=D2
63.2t=49.2t%2B0.137
14t=0.137
t=137%2F14000 hrs.
There are 3600 seconds in 1 hour.
t=%28137%2F14000%29%2A%283600%2F1%29
t=2466%2F70sec.


Quadratic-relations-and-conic-sections/341469: Where does the parabola with the vertex (-4,5)and y-intercept -27 cross the x-axis?
1 solutions

Answer 244516 by Fombitz(13828) About Me  on 2010-09-10 15:34:11 (Show Source):
You can put this solution on YOUR website!
In vertex form,
y=a%28x-h%29%5E2%2Bk
y=a%28x-%28-4%29%29%5E2%2B5
y=a%28x%2B4%29%5E2%2B5
When x=0
16a%2B5=-27
16a=-32
a=-2
.
.
.
y=-2%28x%2B4%29%5E2%2B5=0
2%28x%2B4%29%5E2=5
%28x%2B4%29%5E2=5%2F2
x%2B4=0+%2B-+sqrt%285%2F2%29
highlight%28x=-4+%2B-+sqrt%2810%29%2F2%29
.
.
.



Average/340654: You have $100 and want to buy 100 items priced at $10, $3 and .50. What is the combination of items purchased when you must buy at least 1 of each?
1 solutions

Answer 244515 by Fombitz(13828) About Me  on 2010-09-10 15:26:25 (Show Source):
You can put this solution on YOUR website!
Let A be the number of $10 parts, B $3 parts, C $0.50 parts.
1.A%2BB%2BC=100
.
.
.
10A%2B3B%2B0.5C=100
2.20A%2B6B%2BC=200
From eq. 1,
C=100-A-B
Substitute into eq. 2,
20A%2B6B%2B100-A-B=200
19A%2B5B=100
The equation can only be satisfied when 19A is a multiple of 5.
In becomes a multiple of 5 when highlight%28A=5%29.
19%285%29%2B5B=100
95%2B5B=100
5B=5
highlight%28B=1%29
Then
C=100-1-5
highlight%28C=94%29


Angles/340644: A supplement of an angle is six times as large as a complement of the angle. Find the measures of the angle, its supplement, and its complement.
1 solutions

Answer 244514 by Fombitz(13828) About Me  on 2010-09-10 15:13:40 (Show Source):
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1.A%2BC=90
2.A%2BS=180
3.S=6C
Subtract eq. 1 from eq. 2,
A%2BS-A-C=180-90
S-C=90
Substitute from eq. 3,
6C-C=90
5C=90
highlight%28C=18%29degrees
Then
S=6%2818%29
highlight%28S=108%29degrees
.
.
.
A=90-18
highlight%28A=72%29degrees


Equations/340645: How do you solve problems like 4/x-3 = 8/x
Could you also show me the work so I know how to do other problems similar to this?
1 solutions

Answer 244513 by Fombitz(13828) About Me  on 2010-09-10 15:10:43 (Show Source):
You can put this solution on YOUR website!
Multiply both sides by the product of the denominators.
4%2F%28x-3%29=8%2Fx
In this case, x%28x-3%29,
4x=8%28x-3%29
4x=8x-24
4x=24
highlight%28x=6%29


Travel_Word_Problems/340658: Hans and Heidi departed in opposite directions from the bus stop. Hans left at 1 p.m. and Heidi left at 2 p.m. Hans drove his bus 50 miles per hour and Heidi drove hers at 60 miles per hour. At what time were the two drivers 270 miles apart?
1 solutions

Answer 244512 by Fombitz(13828) About Me  on 2010-09-10 15:08:59 (Show Source):
You can put this solution on YOUR website!

Rate*Time=Distance
R%2At=D
.
.
.
During that hour, Hans drove 50 miles.
D1=50%2B50%2At
.
.
.
D2=60t
.
.
.
Find t when D1=D2,
50%2B50t=60t
10t=50
t=5 hrs.
They will meet 5 hours after Heidi left.


Linear-equations/341466: a line passes through the point (-4,-3 and a slope of 3 write the equation for this line
1 solutions

Answer 244511 by Fombitz(13828) About Me  on 2010-09-10 15:06:19 (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-%28-3%29=3%28x-%28-4%29%29
y%2B3=3%28x%2B4%29


Equations/341468: 750=2x+4y
what are the values of x and y?
1 solutions

Answer 244510 by Fombitz(13828) About Me  on 2010-09-10 15:04:59 (Show Source):
You can put this solution on YOUR website!
To solve for 2 variables, you need 2 independent equations.
You only have 1.
The best you can do is solve for x in terms of y or y in terms of x.


Money_Word_Problems/340652: an inheretance earned 6.1%interest compounded continously. after 5 years he had 51426.94.
What was the original inheretance?
1 solutions

Answer 244509 by Fombitz(13828) About Me  on 2010-09-10 15:03:45 (Show Source):


Numbers_Word_Problems/340649: find three consecutive odd integers such that sum of the smallest and 4 times the largest is 61
1 solutions

Answer 244508 by Fombitz(13828) About Me  on 2010-09-10 15:00:16 (Show Source):
You can put this solution on YOUR website!
The three integers are,
N
N%2B2
N%2B4
.
.
.
N%2B4%28N%2B4%29=61
N%2B4N%2B16=61
5N=45
N=9
The integers are 9,11, and 13.


Trigonometry-basics/340968: Find the right part of the identity.
CSC B/Sec B =
1 solutions

Answer 244507 by Fombitz(13828) About Me  on 2010-09-10 14:55:41 (Show Source):


Equations/341465: 70x^2y^4/4x^3y
I have to simplify this rational equation. This is what I have so far:
= 7*10*x*x*y*y*y*y/1*4*x*x*x*y
= 7*10*y*y*y/1*4*x*y
= 70y^3/4xy
Does this look right?
1 solutions

Answer 244503 by Fombitz(13828) About Me  on 2010-09-10 14:52:35 (Show Source):
You can put this solution on YOUR website!
It's easier to use the laws of exponents rather than expand the expressions.
Further simplification is possible in your answer.
.
.
.
%2870x%5E2y%5E4%29%2F%284x%5E3y%29+=%2870%2F4%29x%5E%282-3%29y%5E%284-1%29
%2870x%5E2y%5E4%29%2F%284x%5E3y%29+=%2815%29x%5E%28-1%29y%5E%283%29
%2870x%5E2y%5E4%29%2F%284x%5E3y%29+=%2815y%5E3%29%2Fx


Numbers_Word_Problems/341018: The sum of two numbers is 70. Their quotient is 13. what are the two numbers?
1 solutions

Answer 244502 by Fombitz(13828) About Me  on 2010-09-10 14:49:38 (Show Source):
You can put this solution on YOUR website!
Let the two numbers be A and B.
1.A%2BB=70
2.A%2FB=13
From eq. 2,
A=13B
Substitute into eq. 1,
13B%2BB=70
14B=70
highlight%28B=5%29
A=13%285%29
highlight%28A=65%29


Length-and-distance/341390: what is the distance between a & b A(2,2) B(5,5)
1 solutions

Answer 244491 by Fombitz(13828) About Me  on 2010-09-10 13:41:41 (Show Source):
You can put this solution on YOUR website!
Use the distance formula,
D%5E2=%28x1-x2%29%5E2%2B%28y1-y2%29%5E2
D=sqrt%28%285-2%29%5E2%2B%285-2%29%5E2%29%29


Expressions-with-variables/341451: Factor Completely;
3x^8-15x7^15+15x^6
1 solutions

Answer 244490 by Fombitz(13828) About Me  on 2010-09-10 13:39:50 (Show Source):
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Check this term, 15x7^15.


Mixture_Word_Problems/341445: how many liters of 25% alcohol must be mixed with 40 liters of a 35 % alcohol solution?
1 solutions

Answer 244489 by Fombitz(13828) About Me  on 2010-09-10 13:39:05 (Show Source):