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vleith answered: 2822 problems
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Linear_Equations_And_Systems_Word_Problems/184605: For what values of c will the system have:
infinitely many solution
1) 2x - 6y = c
6x - 18y = 30
2)no solution
x + 2y = 6
cx - 4y = 8

How do you do these questions? Can you explain how?
1 solutions

Answer 138550 by vleith(2825) on 2009-03-02 19:19:37 (Show Source):

You can put this solution on YOUR website!
infinitely many solution
1) 2x - 6y = c
6x - 18y = 30
infinitely many solution means the two 'lines' are really the same line
the second line above has two terms that are exactly 3 times the terms of the fisrt line (6x = 3*2x and -18y = 3 *(-6y)) so if c is 3*30, then the two lines are really the same line.
2)no solution
x + 2y = 6
cx - 4y = 8
No solution occurs when the 'answer' is something that can't happen
So let's double the first line to get
2x + 4y = 12
Now add the second line to it
2x + 4y = 12
cx -4y = 8
----------
(2+c)x = 20
any c that that makes (2+x) a non-zero number will result in an x that 'works'. However, if c = -2, then we get
(0*x) = 20
0 times anything is 0, so that yields
0 = 20
0=20 is impossible, so is c = -2 then ther eis no solution.,
make sense?

Linear-systems/184587: Solve the system of equations by graphing
x+y=8
x-y=-6
What is the solution of the system of equations?
1 solutions

Answer 138549 by vleith(2825) on 2009-03-02 19:12:59 (Show Source):

You can put this solution on YOUR website!
See this video --> http://collabvsl.wetpaint.com/page/Solving+Systems+of+Equations
The solution in this case is the point that is the intersection of the two given lines.
There are several methods to solve this.
We will use addition
x + y = 8
x - y = -6 add these two
-------------
2x = 2
x = 1
If x =1, then y is
x + y = 8
1 + y = 8
y = 7
So the solution is the point (1,7)
Check your answer using the second eqaution
x - y = -6
does 1 - 7 = -6 ??? yes it does !

Probability-and-statistics/184591: I NEED Help in statistics. Could someone please help me with this. Thank you.
The chair of the board of directors says, “There is a 45% chance this company will earn a profit, a 35% chance it will break even, and a 20% chance it will lose money next quarter.”
a. Find the probability they will not lose money next quarter.
b. Find the probability they will lose money next quarter.

1 solutions

Answer 138548 by vleith(2825) on 2009-03-02 19:08:18 (Show Source):

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a. Find the probability they will not lose money next quarter. This is the sum of the probability that the company makes money and breaks even (in either of those vcases, they didn't lose money). So 45 + 35 = 80%
b. Find the probability they will lose money next quarter. 20%

Miscellaneous_Word_Problems/184603: jen is putting a fence in her rectangular garden. The length of her garden is 12 feet and the width of her garden is 14 feet. how many feet of fencing will she need?
1 solutions

Answer 138546 by vleith(2825) on 2009-03-02 19:05:13 (Show Source):

You can put this solution on YOUR website!
what is the perimeter of a rectangle? The total length of the four sides.
Each rectangle has two sets of equal length sides. So the perimeter is
P= 2*lenght + 2*Width
P = 2*12 + 2*14
P = 24 + 28
P = 52 feet

Geometry_Word_Problems/184602: This question is from textbook geometry
if a triangle is formed with sides having lengths what type of triangle is 6 , 8 , and 10 ?
1 solutions

Answer 138545 by vleith(2825) on 2009-03-02 19:03:18 (Show Source):

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Any triangle with sides ina ratio of 3:4:5 is a right triangle.
Since a^2 + b^2 = c^2 for all right triangles, you can see this one fits that.

Graphs/184558: I'm not sure about this.
Graph the linear equation by finding and plotting its intercepts.
y=-5x
Thanks
1 solutions

Answer 138534 by vleith(2825) on 2009-03-02 17:28:43 (Show Source):

You can put this solution on YOUR website!
Intercepts are points that are on the axis. So one or the other coordinate of the point must be 0.
So
(0,y) and (x,0). Solve for them as follows.
Assume x =0, using y=-5x
y = -5*0 = 0
So the x intercept is (0,0)
Assume y=0. Using y = -5x
0 = -5x
0 = x
So the y intercept is (0,0)
What you have are 'two points that are the same point'. So you cannot plot the line using just the intercepts, since this line passes thru the origin.

Inequalities/184554: The problem 7x+3<=7(x+1)has got me!
My best solution.
7x+3<=7(x+1)
= 7x+3<=7x+7
= -3 -3
= 7x<=7x+4
=-7x -7x
= 0<=4
This is so frustrating. Thank you for any answers.

1 solutions

Answer 138531 by vleith(2825) on 2009-03-02 17:24:42 (Show Source):

You can put this solution on YOUR website!
Dont get frustrated. You got to the point where the 'solution' is 0<=4
Your frustration is 'that cant be'. Guess what, you're right. It can't be. When the 'solution' ends up being something that is not possible, then that means 'there is no solution to this problem'.
Thus, it is not possible for 7x+3<=7(x+1)

Graphs/184559: I need help please.
Complete each ordered pair so that it is a solution of the given linear equation.
x-2y=-5;( ,-3),(-9, )
The first ordered pair is ( ,-3)
The second ordered pair is (-9, )
Thank u!
1 solutions

Answer 138530 by vleith(2825) on 2009-03-02 17:21:18 (Show Source):

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Plug in the given half of the point ans then solve for the other one.
x-2y=-5;( ,-3),(-9, )
plug in -3 for y and solve for x
x - 2*(-3) = -5
x + 6 = -5
x = -11
(-11,-3)
Second point,
plug in -9 for x and solve for y
-9 - 2y = -5
-2y = 4
y = -2
(-9,-2)

Polynomials-and-rational-expressions/184194: This question is from textbook saxon algebra 2
Identify all real roots of x^3+x^2-34x+56=0
I worked it out to: 2, -3+ square root 11 and -3- square root 11. Am I correct?
1 solutions

Answer 138253 by vleith(2825) on 2009-02-28 15:31:19 (Show Source):

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2 is correct. The others are not. See the URLS below for tools to factor
x%5E3%2Bx%5E2-34x%2B56=0

http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic
http://www.calc101.com/webMathematica/long-divide.jsp#topdoit

Exponents-negative-and-fractional/184220: why can't you leave a negative number in the denominator? I know you mult. the top and bottom by -1 to keep the neg. out, I just need to know why is that the rule. trying to explain to a student/
1 solutions

Answer 138251 by vleith(2825) on 2009-02-28 15:24:04 (Show Source):

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It is just convention. There is 'no good reason' why the negative sign is usually associated with the numerator or even placed 'in front of' the fraction. It is just 'good practice'.

Polynomials-and-rational-expressions/184221: This question is from textbook Algebra 1(Concepts and Skills)
How do you factor a trinomial?
1 solutions

Answer 138250 by vleith(2825) on 2009-02-28 15:16:30 (Show Source):

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See this video for a discussion on factoring. Two fo the 4 examples are trinomials
http://www.teachertube.com/view_video.php?viewkey=e178941e511e7a36475c

Quadratic_Equations/184167: solve for x
x^2-7=0
1 solutions

Answer 138192 by vleith(2825) on 2009-02-28 05:09:32 (Show Source):

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x%5E2-7=0

AND

Surface-area/184114: A square field has 5m added to its length and 2m added to its width.The field then had an area of 130m^2.Find the length of the side of the original field.
1 solutions

Answer 138136 by vleith(2825) on 2009-02-27 16:11:18 (Show Source):

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Let the original field's sides be x.
The new field has length (x+5) and width (x+2)
Area of a rectangle is given as A+=+L%2AW

Use quadratic equation to solve

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 1x%5E2%2B7x%2B-120+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

Discriminant d=529 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+529+%29%29%2F2%5Ca

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+529+%29%29%2F2%5C1+=+8

x%5B2%5D+=+%28-%287%29-sqrt%28+529+%29%29%2F2%5C1+=+-15

Quadratic expression 1x%5E2%2B7x%2B-120

can be factored:
1x%5E2%2B7x%2B-120+=+1%28x-8%29%2A%28x--15%29

Again, the answer is: 8, -15. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-120+%29

or factor as
0+=+%28x-8%29%28x%2B15%29

Either way, the possible original sides are 8 or -15. Since the original field cannot have a negative length side, the answer must be 8meters on each side

Expressions-with-variables/184115: 1-3(5b-2)=4-(7b+3)
What is b? I'd really like to know HOW to solve this.
1 solutions

Answer 138135 by vleith(2825) on 2009-02-27 16:04:47 (Show Source):

You can put this solution on YOUR website!
use the same rules you use for arithmetic.
1-3%285b-2%29=4-%287b%2B3%29

first use distribution
1+-+15b+%2B+6+=+4+-+7b+-+3

collect like terms
7+-+15b+=+1+-+7b

now isolate the terms with variables
7+-1+=+15b+-+7b

simplify

now solve for b
6%2F8+=++b

simplify

Check your answer by plugging 3/4 in for b and verifying that boths sides are the same

Triangles/184063: hi,
Please help me my problem.If a shape that has three sides and three angles,can we call that a triangle?If the sides of the triangles are unsraight lines ,how can we call that?How can I know its angles and sides by computing?
please ..please..help me...thank you very much for yor answer.Thank you very much!! ! !

1 solutions

Answer 138134 by vleith(2825) on 2009-02-27 15:59:34 (Show Source):

You can put this solution on YOUR website!
If a shape that has three sides and three angles,can we call that a triangle? Generally speaking - no. In order to be a 'euclidean triangle' the sides must be line segments. (that is, they cannot be curved). See http://www.mathopenref.com/triangle.html
If the sides of the triangles are unstraight lines ,how can we call that? A 3 sided polygon.
How can I know its angles and sides by computing? I'll assume you mean on a triangle. Use the law of sines --> http://en.wikipedia.org/wiki/Law_of_sines

Proportions/184073: I would like help with the following problem

Solve by using a proportion. If the answer does not come out evenly,
round it to the nearest hundredth.
You read 500 words in 3 minutes. At that rate, how many words would
you read in 20 minutes?

All correct answers are greatly appreciated.Thank You:)
1 solutions

Answer 138133 by vleith(2825) on 2009-02-27 15:53:25 (Show Source):
You can put this solution on YOUR website!
Same idea here. use ratios

Proportions/184075: I would like help with the following problem

A flagpole is 12.5 m tall. It casts a 17.5-m shadow. How tall is a
nearby radio tower that casts a 61.25-m shadow?

All help with my problem is greatly appreciated.Thank You:)
1 solutions

Answer 138132 by vleith(2825) on 2009-02-27 15:51:41 (Show Source):
You can put this solution on YOUR website!
Use ratios

Equations/184103: graph the following linear equation
f(x)= 3/4x + 2
1 solutions

Answer 138131 by vleith(2825) on 2009-02-27 15:48:01 (Show Source):

You can put this solution on YOUR website!
graph%28400%2C400%2C-10%2C10%2C+-10%2C10%2C+0.75x+%2B+2%29

Exponential-and-logarithmic-functions/184111: log 3 (5x+1)=2
1 solutions

Answer 138130 by vleith(2825) on 2009-02-27 15:46:40 (Show Source):

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Convert to log 10
http://www.mathwords.com/c/change_of_base_formula.htm
log3%285x%2B1%29+=+%28log%285x%2B1%29%29%2F%28log3%29%29

log3%285x%2B1%29+=+%28log%285x%2B1%29%29%2F%28log3%29%29

Now that it is converted, solve
%28log%285x%2B1%29%29%2F%280.477%29+=+2

Quadratic_Equations/184112: Aki's Bycycle Designs has determined that when x hundred bicycles are built, the average cost per bycycle is given cy C(x)=0.7x^2-1.3x+10.679, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
I don't know where to begin with this problem, can someone please help me with it? I would really appreciate it.
1 solutions

Answer 138129 by vleith(2825) on 2009-02-27 15:35:33 (Show Source):

You can put this solution on YOUR website!
If you know calculus, take the derivative, set that to 0 and solve for x.
If you don't know that yet, find the minimum of the parabola. Here is a URl with the formula on it --> http://www.tpub.com/math1/17e.htm

Exponents/184113: What is the answer to r to the negitive 5th s to the 4th t divided by rs to the negitive 2nd t to the negitive 5th
1 solutions

Answer 138128 by vleith(2825) on 2009-02-27 15:21:49 (Show Source):

You can put this solution on YOUR website!
You mean this ?
%28r%5E%28-5%29%2As%5E4%2At%29%2F%28%28rs%29%5E%28-2%29%2At%5E%28-5%29%29

%28%28rs%29%5E2%2As%5E4%2At%2At%5E5%29%2F%28r%5E5%29

%28r%5E2%2As%5E2%2As%5E4%2At%2At%5E5%29%2F%28r%5E5%29

Polynomials-and-rational-expressions/184104: please help me solve this problem
Reduce an expression to lowest terms.
-2b2-6b-4/b2-1

1 solutions

Answer 138126 by vleith(2825) on 2009-02-27 15:15:53 (Show Source):

You can put this solution on YOUR website!
+%28-2b%5E2-6b-4%29%2F%28b%5E2-1%29

%28-2%28b%5E2%2B3b%2B2%29%29%2F%28%28b%2B1%29%28b-1%29%29

%28-2%28b%2B1%29%28b%2B2%29%29%2F%28%28b%2B1%29%28b-1%29%29

You might find this URL handy --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic

Miscellaneous_Word_Problems/184108: What is the population density of a city with 425,000 people in 1,872 square miles? express each ratio as a fractionin simplist form. If we completed correctly, we came up with 53125/234 - is this the correct answer?
1 solutions

Answer 138125 by vleith(2825) on 2009-02-27 15:09:47 (Show Source):

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That's what I got.

Polynomials-and-rational-expressions/184109: please help me solve this problem on factor out the GCF in the expression
6x3+18x2+24x
1 solutions

Answer 138124 by vleith(2825) on 2009-02-27 15:05:35 (Show Source):

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6x%5E3%2B18x%5E2%2B24x

So the GCF is 6x

Triangles/184083: Not sure if this question goes here, but I am having a horrible time trying to figure this out, so any help is greatly appreciated. Thank you.
The perimeter of a triangular dog pen has one side represented by 3x, another side represented by x +19 and the third side represented by 2x + 6. Find the algebraic expression for the perimeter. Find the numerical perimeter if the value of x is 5 feet.
1 solutions

Answer 138091 by vleith(2825) on 2009-02-27 09:34:09 (Show Source):

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The perimeter is the sum of the triangles sides.
Perimeter+=+3x+%2B+%28x%2B19%29+%2B+%282x+%2B6%29

If x = 5, then
Perimeter+=+6%2A5+%2B+25

feet

Functions/184084: could someone please help.
The equation of the line that goes through the point ( 7 ,2 ) and is parallel to the line 5 x + 3 y = 5 can be written in the form y = mx+b where m is:
and where b is:

1 solutions

Answer 138090 by vleith(2825) on 2009-02-27 09:31:28 (Show Source):

You can put this solution on YOUR website!
Get the original equation in the form y+=+mx+%2B++b

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line

Since any two parallel lines have the same slope we know the slope of the unknown line is -%285%2F3%29

(its from the slope of y=%28-%285%2F3%29%29%2Ax%2B%285%2F3%29

which is also -%285%2F3%29

). Also since the unknown line goes through (7,2), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29

where m is the slope and ( x%5B1%5D

) is the given point

y-2=%28-%285%2F3%29%29%2A%28x-7%29

Plug in

, and

y-2=%28-%285%2F3%29%29%2Ax%2B%28%285%2F3%29%29%287%29

Distribute -%285%2F3%29

Multiply

Add

to both sides to isolate y

y=%28-%285%2F3%29%29%2Ax-0%2F3%2B6%2F3

Make into equivalent fractions with equal denominators

y=%28-%285%2F3%29%29%2Ax%2B6%2F3

Combine the fractions

y=%28-%285%2F3%29%29%2Ax%2B2

Reduce any fractions

So the equation of the line that is parallel to y=%28-%285%2F3%29%29%2Ax%2B%285%2F3%29

and goes through (

) is

So here are the graphs of the equations y=%28-%285%2F3%29%29%2Ax%2B%285%2F3%29

and

graph of the given equation y=%28-%285%2F3%29%29%2Ax%2B%285%2F3%29

(red) and graph of the line y=%28-%285%2F3%29%29%2Ax%2B2

(green) that is parallel to the given graph and goes through (

)

Polynomials-and-rational-expressions/183359: Suppose that you square two consecutive whole numbers and subtract the smaller square from the larger. Is it possible that the difference is an even number
provide an example please

1 solutions

Answer 137681 by vleith(2825) on 2009-02-23 14:01:24 (Show Source):

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Let one number be x. Then the other one is (x+1)
%28x%2B1%29%5E2+-+x%5E2

2x will always be even. So 2x+1 is always odd
4 , 5
25-16 = 9 which is odd

Miscellaneous_Word_Problems/183377: One pump fills a tank 4 times as fast as another pump. If the pumps work together, they fill the tank in 28 minutes. How long does it take for each pump to fill the tank?
It takes the faster pump ______ minutes to fill the tank when working alone and it takes the slower pump ______ minutes.
1 solutions

Answer 137680 by vleith(2825) on 2009-02-23 13:57:17 (Show Source):

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Let the slow pump rate be X. Then the fast pump rate is 4X
Together they can pump at X+4X = 5X
The slow pump will be 1/5 as fast. So it will take 28*5 minutes
The faster pump will be 4/5 as fast. So it will take (28*5)/4 minutes

Equations/183376: How to reach the end results for x/2+1=3, 3x/2+1=4 and 2x/3+1=5. break these down please
1 solutions

Answer 137679 by vleith(2825) on 2009-02-23 13:54:11 (Show Source):

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Use the following process for each. We'll do the first one, then you cna use the same idea to do the other two.
x%2F2%2B1=3

Isolate the term with x by subtracting the constant on the left (sub 1 from both sides). To get
x%2F2+=+2

Now get x 'by itself'. In this case, multiply both sides by 2
x+=+4

For the next one
3x%2F2%2B1=4

Isolate the term with x
3x%2F2+=+3

Now get x 'by itself'. Multiply by 2/3
x+=+%282%2F3%29%2A3

You can do the last one

Average/183337: x(x-6) = 7
If I solve it: x^2-6x = 7
how do i continue from here? It is solving an equation but how do i reach x= ?
1 solutions

Answer 137660 by vleith(2825) on 2009-02-23 10:09:53 (Show Source):

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x%5E2-6x+=+7

Now you can factor it or use the quadratic equation.
Let;s factor this one
%28x-7%29%28x%2B1%29=+0

so x = 7 or x= -1
Check using this URL --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic

Mixture_Word_Problems/183339: One thrid of a number is 5 less than half of the same number. What is the number?
ISNB -13 978-0-395-97722-4
ISBN-10 0-395-97722-3
1 solutions

Answer 137659 by vleith(2825) on 2009-02-23 10:05:15 (Show Source):

You can put this solution on YOUR website!
Let x be the number. You are told
x%2F3+=+x%2F2++-+5

multiply thru by 6
2x+=+3x+-+30

Is 10 five less than 15?

See tutors' answers!

Recent problems solved by 'vleith'