New! Get regular updates about newly solved problems via algebra.com's RSS system.

Recent problems solved by 'vleith'

vleith answered: 2822 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849, >>Next

Numeric_Fractions/203599: please help me on this question below:
Richard can paint the room alone in 5 days while Jose can paint the room alone in 3 days.in how many days will they be able to paint same room,working together?
with representation,equation,answer and checking.
thank you
1 solutions

Answer 153618 by vleith(2825) on 2009-07-20 06:14:19 (Show Source):

You can put this solution on YOUR website!
Rich can do 1%2F5

of a room in a day
Jose can do 1%2F3

of a room in a day
Together, they can do 1%2F5+%2B+1%2F3

room in a day
1%2F3+%2B+1%2F5

room in a day
So if they can paint 8/15 per day, then
%288%2F15%29+%2A+x+=+1

days
Just a little less than 2 days if they work together

Quadratic_Equations/203249: This question is from textbook
Please Help!!! Thanks Solve in the quadratic method and one other method. factoring, property of sq., or completing the square Show work.
3x^2 = 2x + 5
1 solutions

Answer 153344 by vleith(2825) on 2009-07-16 06:30:27 (Show Source):

You can put this solution on YOUR website!
3x%5E2+=+2x+%2B+5

so either (3x-5)=0 or (x+1)=0 , which means roots are 5/3 and -1
Look here for lots of tools to help sove these types of problems
http://www.algebra.com/tutors/all-solvers.mpl
Using quadratic equation

Solved by pluggable solver: SOLVE quadratic equation with variable

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

(in our case 3x%5E2%2B-2x%2B-5+=+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=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+64+%29%29%2F2%5Ca

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+64+%29%29%2F2%5C3+=+1.66666666666667

x%5B2%5D+=+%28-%28-2%29-sqrt%28+64+%29%29%2F2%5C3+=+-1

Quadratic expression 3x%5E2%2B-2x%2B-5

can be factored:
3x%5E2%2B-2x%2B-5+=+3%28x-1.66666666666667%29%2A%28x--1%29

Again, the answer is: 1.66666666666667, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-2%2Ax%2B-5+%29

Quadratic_Equations/203246: This question is from textbook
Please Help!!! Thanks
x varies directly as the square of s and inversely as t. How does x change when s is doubled? When both s and t are doubled?
1 solutions

Answer 153343 by vleith(2825) on 2009-07-16 06:25:21 (Show Source):

You can put this solution on YOUR website!
Given x%5Bs%5D+=+Ks%5E2%2Ft

So you can see that x varies directly with s^2 and inversely with t.
How does x change when s is doubled?
x%5Bs%5D+=+Ks%5E2%2Ft

doubling s means "the new value for s is now 2 times the original s ... so use 2s
x%5B2s%5D+=+K%282s%29%5E2%2Ft

compare

and see that x%5B2s%5D%2Fx%5Bs%5D

thus doubling s, makes x 4 times larger (makes sense since 2^2 = 4)

When both s and t are doubled?
x%5B2s2t%5D+=+K%282s%29%5E2%2F%282t%29

compare

and see that x%5B2s2t%5D%2Fx%5Bs%5D

thus doubling both s and t, doubles x

expressions/203168: Evaluate following expression
(1/5)y + (z/3) , y=1/2, z = 2
1 solutions

Answer 153282 by vleith(2825) on 2009-07-15 13:56:03 (Show Source):

You can put this solution on YOUR website!
%281%2F5%29y+%2B+%28z%2F3%29

at y=1/2 and z=2
%281%2F5%29%281%2F2%29+%2B+%282%2F3%29

Quadratic_Equations/203132: I am confused if anyone could help It would be appreciated.I don't understand how to finish the problem
Solve by completing the square.
2x^2 - 3x + 1 = 0
This is what I have so far
a=2 b=3 c=1
2x^2 - 3x + 1 = 0
x^2 - 3/2 x 1/2
x^2 - 3/2x + 3/4
now I am lost

1 solutions

Answer 153261 by vleith(2825) on 2009-07-15 07:28:16 (Show Source):

You can put this solution on YOUR website!

Here is solver you can use for this --> http://www.algebra.com/algebra/homework/quadratic/complete-square.solver

Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics

Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert 2x%5E2%2B-3x%2B1=0

to standard form by dividing both sides by 2:
We have: 1x%5E2%2B-1.5x%2B0.5=0

. What we want to do now is to change this equation to a complete square %28x%2Bsomenumber%29%5E2+%2B+othernumber

. How can we find out values of somenumber and othernumber that would make it work?
Look at %28x%2Bsomenumber%29%5E2

%28x%2Bsomenumber%29%5E2+=+x%5E2%2B2%2Asomenumber%2Ax+%2B+somenumber%5E2

. Since the coefficient in our equation 1x%5E2%2Bhighlight_red%28+-1.5%29+%2A+x%2B0.5=0

that goes in front of x is -1.5, we know that -1.5=2*somenumber, or somenumber+=+-1.5%2F2

. So, we know that our equation can be rewritten as %28x%2B-1.5%2F2%29%5E2+%2B+othernumber

, and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that %28x%2B-1.5%2F2%29%5E2+%2B+othernumber

is equivalent to our original equation 1x%5E2%2B-1.5x%2Bhighlight_green%28+0.5+%29=0

The highlighted red part must be equal to 0.5 (highlighted green part).

-1.5%5E2%2F4+%2B+othernumber+=+0.5

, or

othernumber+=+0.5--1.5%5E2%2F4+=+-0.0625

.
So, the equation converts to %28x%2B-1.5%2F2%29%5E2+%2B+-0.0625+=+0

, or

.

Our equation converted to a square %28x%2B-1.5%2F2%29%5E2

, equated to a number (0.0625).

Since the right part 0.0625 is greater than zero, there are two solutions:

, or

system%28+%28x%2B-1.5%2F2%29+=+0.25%2C+%28x%2B-1.5%2F2%29+=+-0.25+%29

system%28+x%2B-1.5%2F2+=+0.25%2C+x%2B-1.5%2F2+=+-0.25+%29

system%28+x+=+0.25--1.5%2F2%2C+x+=+-0.25--1.5%2F2+%29

Answer: x=1, 0.5.

Graphs/203137: pls answer..Urgent!
graph the equations
1. y= /absolute value of x-3/+2
2.y= -x^2 + 3
3. y= 2^x
1 solutions

Answer 153259 by vleith(2825) on 2009-07-15 07:19:24 (Show Source):

You can put this solution on YOUR website!
You can use www.wolframalpha.com to plot all that stuff

Sequences-and-series/203130: What is the next sequence of numbers; given: 4,18,200,20402
1 solutions

Answer 153254 by vleith(2825) on 2009-07-15 05:35:36 (Show Source):

You can put this solution on YOUR website!
given one term, to find the next one - follow these steps
1) Divide the first number by 2
2) Add one
3) Square
4) Multiply 2
So, given 4:
divide by 2 to get 2
Add 1 to get 3
Square to get 9
Multiply by 2 to get 18
Given 200:
1) 200/2 = 100
2) 100+1 = 101
3) 101^1 = 10201
4) Mult by 2 to get 20402
I know, clunky, but it holds for those 4 numbers anyway

Sequences-and-series/203033: This question is from textbook Pure Mathematics 1
Hi i would like help on geometric Sequences.
The Question says Find the common ratio of a geometric sequence which has a first term of 5 and a sum to infinity of 6.
The sum to infinity equation is S"infinity"=(a)/(1-r)
so i changed the a to a 5 and made it equal to 6 so the equation was 6=(5)/(1-r) the answer is 1/6 but i keep getting 5/6 can you please help
Thanx
Peder
1 solutions

Answer 153166 by vleith(2825) on 2009-07-14 06:41:43 (Show Source):

You can put this solution on YOUR website!
6=%285%29%2F%281-r%29

As my college calc prof once told me (actually many times told me), slow down. You have all the hard work done. It's the simple mistakes that bite you :)

Numbers_Word_Problems/203032: Find 2 consecutive even integers whose sum is 126.

1 solutions

Answer 153165 by vleith(2825) on 2009-07-14 05:58:35 (Show Source):

You can put this solution on YOUR website!
This is a common type of intro algebra problem.
Let the smaller even integer be represented by

. Then the next larger even integer is x%2B2

You are told the sum of the two numbers is 126. So
x+%2B+%28x%2B2%29+=+126

Now simplify and solve for x
2x+%2B+2+=+126

So the integers are 62 and 64

Linear-equations/203025: If f(x)=-3x^4+x^10-x^7-23, then the largest amount of zeros(including multilicities) that f could have is: 4,10,7,or 21? thanks.
1 solutions

Answer 153164 by vleith(2825) on 2009-07-14 05:55:23 (Show Source):

You can put this solution on YOUR website!
Look at the power of the highest order term. That tells you how many roots there are.
In this case, the high order term is x^10... so there are 10 roots

Linear-systems/202913: -4x+7y=9
2y=-5x-22
solve using addition method
1 solutions

Answer 153077 by vleith(2825) on 2009-07-13 08:52:28 (Show Source):

You can put this solution on YOUR website!
2y=-5x-22

Mult by 7

mult by 2

Now add them
-8x+%2B+14y+=+18

----------------------
27x+=+-136

Now solve for y and you're there

Miscellaneous_Word_Problems/202901: The intensity of illumination on a surface varies inversely as the square of the distance of the light from the surface. If the illumination from a source is 64 foot candles when the distance is 9 feet, then find the illumination when the distance is 12 feet. Would it be 6, 8, 32 or 36 foot candles. Could someone please help me with this been trying but need some assistance, thanks.
1 solutions

Answer 153073 by vleith(2825) on 2009-07-13 07:45:31 (Show Source):

You can put this solution on YOUR website!
Intensity changes inversely with distance squared
I%5B%28d%29%5D+=+K%2Fd%5E2

I%5B%2812%29%5D+=+%2881%2AI%5B%289%29%5D%29%2F144

You are given I%5B%289%29%5D+=+64

. Thus

Linear_Equations_And_Systems_Word_Problems/202722: Please help me solve this problem. Thank you!!!!
The body mass index, I can be used to determine an individual’s risk for heart disease. An index less than 25 indicates a low risk. The body mass index is given by the formula, or model, I=700W/H2(small 2), where W= weight, in pounds, and H= height, in inches, in inches. Francis weights 198 pounds and stands 76 inches tall. What is his approximate body mass index? Find an inequality describing all weights W that Francis can have and be in the low-risk category.
Francis’s approximate body mass index is ?
(Round to the nearest whole number.)
{W/W < (approximate) ? lb}
(Round to the nearest whole number.)

1 solutions

Answer 152897 by vleith(2825) on 2009-07-11 13:29:01 (Show Source):

You can put this solution on YOUR website!
Answered many time out here already. See
http://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.202169.html

Miscellaneous_Word_Problems/202651: A crew of 6 can complete a job in 8 hours. How many hours would it take a group of 4 to complete the job?
1 solutions

Answer 152844 by vleith(2825) on 2009-07-10 16:11:11 (Show Source):

You can put this solution on YOUR website!
This a really poor question. It is quite possible that a job that can be done by 6 people, cannot be done by 4 people no matter what the job is. Also, there is nothing to let you know if the 4 person group is subset of the 6. So perhaps the skills held by the 6 person group are not skills the 4 person group has.
That said, I am sure the intent is as follows:
The job requites 6*8= 48 person/hours
If there are 4 people working, the 48/4 = 12. So the group of 4 will take 12 hours to complete the job.

Miscellaneous_Word_Problems/202653: Base of a triangle is 4cm greater than the height The area is 30cm^2
Find the height and length

1 solutions

Answer 152841 by vleith(2825) on 2009-07-10 16:04:07 (Show Source):

You can put this solution on YOUR website!
Let h be the height
Then the base,b, is given by h%2B4

So h is either -10 or 6. Since h must be positive, then height=6
base = height+4 = 10
Dimensions are h=6, b=10
Check your answer, does 30+=+%286%2A10%29%2F2

Coordinate-system/202663: graph the line containing the given pair of points and find the slope. (9,0) and (7,-7)
1 solutions

Answer 152839 by vleith(2825) on 2009-07-10 15:59:47 (Show Source):

You can put this solution on YOUR website!

Solved by pluggable solver: FIND EQUATION of straight line given 2 points

hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (9, 0) and (x2, y2) = (7, -7).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%28-7-0%29%2F%287-9%29+=+3.5

a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%28-7-0%29%2F%287-9%29+=+3.5

.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D

, or

. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D

, or

.

y=(3.5)x + (-31.5)

Your graph:

Numbers_Word_Problems/202659: One number is twice another. The sum of the two numbers is 39. Find the larger number
1 solutions

Answer 152837 by vleith(2825) on 2009-07-10 15:57:46 (Show Source):

You can put this solution on YOUR website!
Let x be the smaller number.
Let y be the larger one
y+=+2x

Coordinate-system/202662: find the intercepts and then use them to graph the equation. y=-3-3x
1 solutions

Answer 152835 by vleith(2825) on 2009-07-10 15:56:16 (Show Source):

You can put this solution on YOUR website!
Set x =0 and solve for y
y=-3-3x

y intercept is (0, -3)
Set y=0 and solve for x
y=-3-3x

x intercept is (-1,0)
Now plot those two points and draw the line thru them
graph%28400%2C400%2C+-5%2C5%2C-5%2C5%2C+-3-3x%29

Graphs/202497: Name the x-intercepts of the graph of f(x)=x^2+4x+1. Can you show me this please.
1 solutions

Answer 152720 by vleith(2825) on 2009-07-09 06:02:53 (Show Source):

You can put this solution on YOUR website!
x intercepts happen with f(x) = 0
So solve this for x
0+=+x%5E2%2B4x%2B1

Use this URL to help you --> http://www.algebra.com/algebra/homework/quadratic/quadratic.solver

Solved by pluggable solver: SOLVE quadratic equation with variable

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

(in our case 1x%5E2%2B4x%2B1+=+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=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+12+%29%29%2F2%5Ca

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+-0.267949192431123

x%5B2%5D+=+%28-%284%29-sqrt%28+12+%29%29%2F2%5C1+=+-3.73205080756888

Quadratic expression 1x%5E2%2B4x%2B1

can be factored:
1x%5E2%2B4x%2B1+=+1%28x--0.267949192431123%29%2A%28x--3.73205080756888%29

Again, the answer is: -0.267949192431123, -3.73205080756888. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B1+%29

Polygons/202502: find the exact area of a reactangle with a base of 5 yards and a height of 8 feet.
1 solutions

Answer 152719 by vleith(2825) on 2009-07-09 05:57:54 (Show Source):

You can put this solution on YOUR website!
Area of a rectangle is L * W
IN this case, the two dimensions are in different units (one is in yards, the other in feet). You need to convert yards to feet before starting
Base+=+5yard+=+5yard%2A%283feet%2Fyard%29+=+15feet

Base+=+5yard+=+5yard%2A%283feet%2Fyard%29+=+15feet

absolute-value/202356: Which of the following is equivalent to /3x-8/>7? (1) -7<3x-8<7 (2) 3x-8<7 or 3x-8>-7 (3) 3x-8>7 or 3x-8<-7 (4) 3x-8>-7 and 3x-8>7
1 solutions

Answer 152593 by vleith(2825) on 2009-07-08 05:30:11 (Show Source):

You can put this solution on YOUR website!
3

Graphs/202357: Which of the following is the radius for the circle whose equation is x^2+6x+y^2-8y=-9? thanks for your help.
1 solutions

Answer 152592 by vleith(2825) on 2009-07-08 05:28:39 (Show Source):

You can put this solution on YOUR website!
You need to get this equation into the standard form for a circle %28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2

So you need to complete the squares for both x and y in your equation and see what comes from that
x%5E2%2B6x%2By%5E2-8y=-9

So r^2 = 16 --> r=4. Center is at (h,k) = (-3,4)
Here is a plot --> http://www30.wolframalpha.com/input/?i=x^2%2B6x%2By^2-8y%3D-9

logarithm/202362: If Log N = 4 then Log10N is _________
1 solutions

Answer 152591 by vleith(2825) on 2009-07-08 05:23:27 (Show Source):

You can put this solution on YOUR website!
log10%5En

So if n=4, the you have your answer

Travel_Word_Problems/202364: while waiting for a train, bong takes a bus ride at 60 kph to a certain point and then walks back leisurely at 10 kph. The bus takes 15 minutes less than his walking. how far has he walked and for how long?
this what i did:
d=60(15-t)
d=10t
d=900-60t
60t+10t=900-60t i transposed the 60t
70t=900 and i divide both sides by 70 but i cant get the answer for the 900
Please if you can even include how to get the answer thanks in advance
1 solutions

Answer 152590 by vleith(2825) on 2009-07-08 05:19:51 (Show Source):

You can put this solution on YOUR website!
You're on the right track, but have an error in the logic used to represent the bus ride time
Let t be the time it takes to walk in hours. Then bus ride time is t-15%2F60

(remember your time needs to be in the same units. So we have to convert 15 minutes into hours)
You know that Distance=Rate+%2A+time

And you also know the distance is the same in both directions.
So BusDistance+=+WalkingDistance

BusRate%2ABusTime+=+WalkingRate%2AWalkingTime

<--- this is where your error in bustime messed you up
60t+-+15+=+10t

hours
That's 18 minutes.
If Bong walks at 10kph for 0.3 hours, thats Distance+=+%2810k%2Fh%29%2A0.3h

Polynomials-and-rational-expressions/202300: Could u please help me this question? How is the number 13,000 abbreviated in scientific notation? thank you.
1 solutions

Answer 152524 by vleith(2825) on 2009-07-07 14:44:20 (Show Source):

You can put this solution on YOUR website!
scientific notation coefficient is always 'between 1 and 10'
So 13000

Linear-equations/202304: Y-intercept of a line
Find the -intercept of the line whose equation is
y = 0.2 x + 4.7
Y- intercept:___
1 solutions

Answer 152522 by vleith(2825) on 2009-07-07 14:41:49 (Show Source):

You can put this solution on YOUR website!
that line is already in the form y+=+mx+%2B+b

, the slope/intercept form
b is the intercept. So in your case, the y-intercept is the point (0,4.7)

Linear-equations/202256: This question is from textbook
20 - x/3 = x/2 solve the equation.

1 solutions

Answer 152497 by vleith(2825) on 2009-07-07 08:04:19 (Show Source):

You can put this solution on YOUR website!
20+-+x%2F3+=+x%2F2

Radicals/202252: I am using w=Crˉ²(the exponent is -2). I have a word problem in which an object is 100 pounds at sea level. I need to find the value of C that makes this equation true, seal level is 3,963 miles from the center of the earth.
100= C*3,963ˉ²(the exponent is -2).
C = 100/3,963ˉ² (the exponenet is -2).
At this point I am not sure what direction to take, can someone please help me toward the right direction.
1 solutions

Answer 152494 by vleith(2825) on 2009-07-07 06:58:03 (Show Source):

You can put this solution on YOUR website!
Not a lot of pointing required. You have the 'numbers correct'. Wat you still need to add in are the 'units'.
100pounds+=+C+%2A+%28r%5Bmiles%5D%29%5E%28-2%29

100pounds+=+C+%2A+%28r%5Bmiles%5D%29%5E%28-2%29

C+=+100pounds%2F%283963%5E2%2Amiles%5E2%29

Now just simplify the number, but remember to leave in the units. C ends up being in terms of pounds/miles^2

Expressions-with-variables/202172: 1/(x+2) + 1/(x-2) = 1/(x^2-4)
1 solutions

Answer 152424 by vleith(2825) on 2009-07-06 14:18:53 (Show Source):

You can put this solution on YOUR website!
1%2F%28x%2B2%29+%2B+1%2F%28x-2%29+=+1%2F%28x%5E2-4%29

%28%28x-2%29+%2B+%28x%2B2%29%29%2F%28%28x%2B2%29%28x-2%29%29+=++1%2F%28x%5E2-4%29

See this URL --> http://www46.wolframalpha.com/input/?i=1%2F(x%2B2)+%2B+1%2F(x-2)+%3D+1%2F(x^2-4)

Quadratic_Equations/202156: Solve by completing the square: x^2+6x-5=0
1 solutions

Answer 152423 by vleith(2825) on 2009-07-06 14:16:11 (Show Source):

You can put this solution on YOUR website!
x%5E2%2B6x-5=0

Here are more words - same thing

Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics

Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert 1x%5E2%2B6x%2B-5=0

to standard form by dividing both sides by 1:
We have: 1x%5E2%2B6x%2B-5=0

. What we want to do now is to change this equation to a complete square %28x%2Bsomenumber%29%5E2+%2B+othernumber

. How can we find out values of somenumber and othernumber that would make it work?
Look at %28x%2Bsomenumber%29%5E2

. Since the coefficient in our equation 1x%5E2%2Bhighlight_red%28+6%29+%2A+x%2B-5=0

that goes in front of x is 6, we know that 6=2*somenumber, or somenumber+=+6%2F2

. So, we know that our equation can be rewritten as %28x%2B6%2F2%29%5E2+%2B+othernumber

is equivalent to our original equation 1x%5E2%2B6x%2Bhighlight_green%28+-5+%29=0

The highlighted red part must be equal to -5 (highlighted green part).

6%5E2%2F4+%2B+othernumber+=+-5

, or

.
So, the equation converts to %28x%2B6%2F2%29%5E2+%2B+-14+=+0

, or

.

Our equation converted to a square %28x%2B6%2F2%29%5E2

, equated to a number (14).

Since the right part 14 is greater than zero, there are two solutions:

system%28+%28x%2B6%2F2%29+=+%2Bsqrt%28+14+%29%2C+%28x%2B6%2F2%29+=+-sqrt%28+14+%29+%29

system%28+%28x%2B6%2F2%29+=+%2Bsqrt%28+14+%29%2C+%28x%2B6%2F2%29+=+-sqrt%28+14+%29+%29

, or

system%28+%28x%2B6%2F2%29+=+3.74165738677394%2C+%28x%2B6%2F2%29+=+-3.74165738677394+%29

system%28+x%2B6%2F2+=+3.74165738677394%2C+x%2B6%2F2+=+-3.74165738677394+%29

system%28+x+=+3.74165738677394-6%2F2%2C+x+=+-3.74165738677394-6%2F2+%29

system%28+x+=+0.741657386773941%2C+x+=+-6.74165738677394+%29

Answer: x=0.741657386773941, -6.74165738677394.

Graphs/202170: is this correct?
2x – 2y = 6 by graphing 3 points.
-2x -2x
-------------
-2y = -2x + 6
-2y -2x + 6
---- ------
-2 = -2
y = x - 3
y= (0)+3
y= (1)+3
y= (2)+3
x , y
-------
3 , 0
1 , 3
2 , 5

1 solutions

Answer 152422 by vleith(2825) on 2009-07-06 14:08:49 (Show Source):

You can put this solution on YOUR website!
Not quite.
You are good up thru y = x - 3 is fine
when x =0, y = -3
when x = 1 y =-2
when x = 2, y=-1
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx-3%29

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx-3%29

See tutors' answers!

Recent problems solved by 'vleith'