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Recent problems solved by 'JBarnum'

JBarnum answered: 2042 problems
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Rational-functions/318853: solve: 3/5 + 2 / x - 1 = 4 / 5x - 5
a) 5 / 3
b) - 5 / 3
c) 1
d) -1
1 solutions
Answer 228234 by JBarnum(2044) About Me  on 2010-06-30 15:18:49 (Show Source):
You can put this solution on YOUR website!
%283%2F5%29%2B%282%2F%28x-1%29%29=%284%2F%285x-5%29%29factor what u can
%283%2F5%29%2B%282%2F%28x-1%29%29=%284%2F%285%28x-1%29%29%29common denominator is 5(x-1)
multiply the 1's to the problem
%283%28x-1%29%2F%285%28x-1%29%29%29%2B%2810%2F5%28x-1%29%29=%284%2F%285%28x-1%29%29%29add numerators
%283%28x-1%29%2B10-4%29%2F%285%28x-1%29%29=0
%283x-3%2B6%29%2F%285%28x-1%29%29=0
%283x%2B3%29%2F%285%28x-1%29%29=0factor
3%28x%2B1%29%2F%285%28x-1%29%29=0 multiply each side by denominator
3%28x%2B1%29=0 divide by 3
%28x%2B1%29=0 subtract 1
%28x%29=-1

Complex_Numbers/318654: One half of the sum of three consecutive multiples of 10 is 90. What are the multiples of 10?
1 solutions
Answer 228098 by JBarnum(2044) About Me  on 2010-06-29 19:24:24 (Show Source):
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%281%2F2%29%28x%2B%28x%2B10%29%2B%28x%2B20%29%29=90
%28x%2B%28x%2B10%29%2B%28x%2B20%29%29=180
%283x%2B30%29=180
3x=150
x=50
50,60,70


50+60+70=180/2=90
multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100....


Average/318655: what is the average grade for scores of 68,70 and a 78

1 solutions
Answer 228096 by JBarnum(2044) About Me  on 2010-06-29 19:05:40 (Show Source):
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%2868%2B70%2B78%29%2F3=A A=average
216/3=72

Sequences-and-series/318658: a number whose product with 6 is the same as its sum with 60?
1 solutions
Answer 228095 by JBarnum(2044) About Me  on 2010-06-29 19:02:58 (Show Source):
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6n=n+60 subtract n
5n=60 divide by 5
highlight%28n=12%29

Radicals/318549: Hello can you please help me solve this problem?
Use the laws of exponents
9/10 2/11
(7 )
1 solutions
Answer 228073 by JBarnum(2044) About Me  on 2010-06-29 16:38:04 (Show Source):
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um i dont even see a problem just 3 numbers

Square-cubic-other-roots/318551: Can yhou please walk me through this?
4 = 5 + sqrt(2 x + 59)
x = ?
Is this solution extraneous? Yes or No
Jerry
jerry@san.rr.com
1 solutions
Answer 228060 by JBarnum(2044) About Me  on 2010-06-29 15:45:07 (Show Source):
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4=5%2Bsqrt%282x%2B59%29 subtract 5
-1=sqrt%282x%2B59%29 square both sides
1=2x%2B59 subtract 59
-58=2xdivide by 2
highlight%28-29=x%29


checking
4=5%2Bsqrt%282x%2B59%29
4=5%2Bsqrt%282%28-29%29%2B59%29
4=5%2Bsqrt%28%28-58%29%2B59%29
4=5%2Bsqrt%281%29
4=5%2B%28-1%29 or 4=5%2B%281%29 this one doesnt work 4=6
4=4
correct


Money_Word_Problems/318590: On Friday, Niles sold $3.25 more than twice what she sold on Thursday. She sold $20.25 Friday. How much did she sell Thursday?

1 solutions
Answer 228058 by JBarnum(2044) About Me  on 2010-06-29 15:41:05 (Show Source):
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3.25%2B2x=20.25
2x=17
x=8.50
$8.50 sold on thursday

Linear-equations/318599: i am not understanding how to find an equation of a line that has a slope of -8 and passes through (-1,5). Write in slope intercept form
1 solutions
Answer 228056 by JBarnum(2044) About Me  on 2010-06-29 15:35:50 (Show Source):
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slope intercept form is y=mx%2Bb where m=slope and b= intercept
you have the following:
m=-8
x=-1
y=5
substitute the letters for the numbers and solve for "b"
y=mx%2Bb
5=%28-8%29%28-1%29%2Bb multiply -8 and -1
5=%288%29%2Bb subtract 8
-3=b


rewrite equation
y=mx%2Bb
m=-8
-3=b
y=-8x-3


Geometry_Word_Problems/318594: The perimeter of a rectangle is 92 if the widths were doubled and the lengths increased by 12 the new perimeter would be 140. What are the length and width of the rectangle?
1 solutions
Answer 228052 by JBarnum(2044) About Me  on 2010-06-29 15:28:46 (Show Source):
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p=92
p=2(L+W)
92=2%28L%2BW%29 = 46=%28L%2BW%29
140=2%28%28L%2B12%29%2B%282W%29%29 = 70=%28%28L%2B12%29%2B%282W%29%29 = 58=L%2B2W


58=L%2B2Wi will use the subtraction property of elimination method
46=L%2BW
12=0%2BW
12=W


46=L%2BW
46=L%2B12
34=L


Checking
140=2%28%28%2834%29%2B12%29%2B%282%2812%29%29%29
140=2%28%2846%29%2B%2824%29%29
140=2%2870%29
140=140
correct



Polynomials-and-rational-expressions/318138: I've been stuck on this problem for a while. What is the solution to:
(6x^2-24) / (6x^2-12)
1 solutions
Answer 228047 by JBarnum(2044) About Me  on 2010-06-29 15:18:38 (Show Source):
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im guessing ur simplifying it i dont see how u can solve for x so
start by factoring out a 6 in numerator and denominator
6%28x%5E2-4%29%2F6%28x%5E2-2%296's cancel and can factor numerator
%28%28x-2%29%28x%2B2%29%29%2F%28x%5E2-2%29 denominator has fractional factors so i left it in this form

Polynomials-and-rational-expressions/318533: Will someone please help me solved this problem?

v^2-9u^2
1 solutions
Answer 228045 by JBarnum(2044) About Me  on 2010-06-29 15:11:12 (Show Source):
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this is a perfect square. the more of these you do the more u will start recognizing them
the factor for this is simple, when its a minus sign in the middle theres a + and - in the factors
%28v-3u%29%28v%2B3u%29
check by foiling
v%5E2-3uv%2B3uv-9u%5E2
v%5E2-0-9u%5E2
v%5E2-9u%5E2
correct

Divisibility_and_Prime_Numbers/318589: Factor completely. If prime, say so.
a. 40x^3-64x^2y
b. 125r^3-8s^3

1 solutions
Answer 228042 by JBarnum(2044) About Me  on 2010-06-29 14:59:47 (Show Source):
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40x%5E3-64x%5E2yi start with the variables first
x%5E2%2840x-64y%29 then factor a 4 out
4x%5E2%2810x-16%29 then factor out the 2
8x%5E2%285x-8%29


i see the cube but i dont think i can factor it correctly
5%5E3r%5E3-2%5E3s%5E3
be something like
%28%285r%2B2s%29%285r-2s%29%29%285r%2B2s%29 but this doesnt seem to come out right when foiled


Equations/318139: 12x2 + 23x + 10 = 0
A. 5/4, 2/3 B. -5/12, -1/5 C. -5/4, -2/3 D. 5/4, -2/3
1 solutions
Answer 228039 by JBarnum(2044) About Me  on 2010-06-29 14:55:46 (Show Source):
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12x%5E2+%2B+23x+%2B+10+=+0 use quadratic formula
(-0.666666666666667, -1.25)
or (-2%2F3, -5%2F4)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B23x%2B10+=+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: b%5E2-4ac=%2823%29%5E2-4%2A12%2A10=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-23%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2823%29%2Bsqrt%28+49+%29%29%2F2%5C12+=+-0.666666666666667
x%5B2%5D+=+%28-%2823%29-sqrt%28+49+%29%29%2F2%5C12+=+-1.25

Quadratic expression 12x%5E2%2B23x%2B10 can be factored:
12x%5E2%2B23x%2B10+=+12%28x--0.666666666666667%29%2A%28x--1.25%29
Again, the answer is: -0.666666666666667, -1.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B23%2Ax%2B10+%29


Graphs/318234: Graph:
y = 3x - 1
1 solutions
Answer 228038 by JBarnum(2044) About Me  on 2010-06-29 14:51:05 (Show Source):
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y-intercept is -1
y=3x-1
if y=0 then
0=3x-1
1=3x
1/3=x this is x intercept
so plot
either (0,-1)(1%2F3,0)
or (0,-1)(1,2)
the second one shows first point at y-intercept and then uses slope going up 3 and to the right 1
draw your line your graph is made

Graphs/318231: Is (0, 0) a solution of -3x - 5y = -1?
1 solutions
Answer 228035 by JBarnum(2044) About Me  on 2010-06-29 14:44:49 (Show Source):
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no, plug in 0 for x and 0 for y u get 0-0=-1

Square-cubic-other-roots/318325: SQUARE ROOT OF W+16=3
1 solutions
Answer 228034 by JBarnum(2044) About Me  on 2010-06-29 14:41:13 (Show Source):
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sqrt%28W%2B16%29=3square each side
%28W%2B16%29=9 subtract 16
W=-7

test/318174: deleted
1 solutions
Answer 228032 by JBarnum(2044) About Me  on 2010-06-29 14:37:12 (Show Source):
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dont waste our time and space.

Rational-functions/318578: Divide: (4m + 16) / (10) / (3m + 12) / (18)
a) 12 / 5
b) (m + 4)^2 / 15
c) 15 / (m + 4)^2
d) 5 /12
1 solutions
Answer 228027 by JBarnum(2044) About Me  on 2010-06-29 14:30:30 (Show Source):
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%28%284m%2B16%29%2F%2810%29%29%2F%28%283m%2B12%29%2F%2818%29%29 seperate into a fraction divided by a fraction
%28%284m%2B16%29%2F%2810%29%29%2A%28%2818%29%2F%283m%2B12%29%29 use the multiply by reciprical property
%28%284%28m%2B4%29%29%2F%2810%29%29%2A%28%2818%29%2F%283%28m%2B4%29%29%29 factor out the 3 and the 4
%284%2A2%2A3%2A3%28m%2B4%29%29%2F%282%2A5%2A3%28m%2B4%29%29 factor the numbers to see whats incommon
%2812%2A6%28m%2B4%29%29%2F%285%2A6%28m%2B4%29%29 i multiplied them to show you what i will be canceling
%2812%2Across%286%28m%2B4%29%29%29%2F%285%2Across%286%28m%2B4%29%29%29 shows cancelation
highlight%2812%2F5%29 this is all thats left over

Equations/318572: The sum of two numbers is 33. Twice the first number minus the seconed number equals 18. Find both numbers.
1 solutions
Answer 228018 by JBarnum(2044) About Me  on 2010-06-29 14:18:10 (Show Source):
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a%2Bb=33
2a-b=18
im using the addition property in elimination method
3a=51
a=17
17%2Bb=33
b=16

Expressions-with-variables/318575: The width of a rectangle is fixed at 22 cm. What lengths will make the perimeter greater than 86 cm?
The length must be greater than?

1 solutions
Answer 228016 by JBarnum(2044) About Me  on 2010-06-29 14:12:16 (Show Source):
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p=2(L+W)
P=86
W=22
find L
86=2(L+22)
43=L+22
21=L
so for the perimeter to be greater then 86 L must be greater then 21
L%3E21

Miscellaneous_Word_Problems/318563: What is the length and width of a room that is 185 square feet?
1 solutions
Answer 228012 by JBarnum(2044) About Me  on 2010-06-29 14:06:45 (Show Source):
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is the room rectangle or square...ibelieve theres not enough information to solve properly or you are left with many solutions.
for example
L=1 W=185 rectangle
L=2 W=92.5 rectangle
L=3 W=61(2/3) rectangle
L=4 W=46.25 rectangle
L=13.604 W=13.604 square
....
you can see what i mean. without more information there are many answers.

Rectangles/318557: If the length of a rectangle were decreased by twenty-seven feet the rectangle would be a square. The perimeter of the rectangle is two hundred ninety-four feet. What are the dimensions of the rectangle?
1 solutions
Answer 228005 by JBarnum(2044) About Me  on 2010-06-29 13:43:20 (Show Source):
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L-27=W because if the length is decreased by 27 on both sides then all sides would be equal making a square
P=2%28L%2BW%29
P=294
294=2%28L%2B%28L-27%29%29 add like terms
294=2%282L-27%29 distribute the 2
294=4L-54%29 add 54
348=4L divide by 4
62=L
L-27=W
62-27=W
35=W

Equations/318308: Using the multiplication principle solve;
-6x>1/13

1 solutions
Answer 227811 by JBarnum(2044) About Me  on 2010-06-28 14:37:58 (Show Source):
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-6x%3E1%2F13 multiply by 13
-78x%3E1 divide by -78
x%3C-1%2F78

Angles/318319: Find the complementary angle to 83 digrees
1 solutions
Answer 227810 by JBarnum(2044) About Me  on 2010-06-28 14:34:42 (Show Source):
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complementary angles are 2 angles that add to 90 degrees
90-83=7
7 degrees

Rational-functions/318311: Which of the following is equivalent to the rational number [3x / 4x]?
a) 6x / 8x
b) 12x / 24x
c) 48x / 56x
d) 3x / 5x
1 solutions
Answer 227809 by JBarnum(2044) About Me  on 2010-06-28 14:33:03 (Show Source):
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all u need to do is find out what number was multiplied to both 3 and 4 that equals one of the answers. looking at a) 3*2=6 and 4*2=8
so 3x%2F4x=6x%2F8x

Polynomials-and-rational-expressions/317506: The length of a metal bar is 7x-5. If one part of the metal bar has the length of x-2. Find the length of the other part
1 solutions
Answer 227360 by JBarnum(2044) About Me  on 2010-06-25 13:01:04 (Show Source):

Equations/317497: Solve each system by addition.
x + y = 7
x – y = 9

1 solutions
Answer 227359 by JBarnum(2044) About Me  on 2010-06-25 12:55:36 (Show Source):
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add them together
2x+0=16 divide by 2
x=8
can also subtract them
2y=-2
y=-1

Average/317489: The average of 5/6 and 7/12 minus the average of 2/3 and 3/4 is equal to
A)1/24 B)0 C)-1/12 D)1 E)1/24
1 solutions
Answer 227351 by JBarnum(2044) About Me  on 2010-06-25 12:23:22 (Show Source):

Probability-and-statistics/317479: Find the variance of the binomial distribution with the given values.

n = 50
p = 0.9

1 solutions
Answer 227350 by JBarnum(2044) About Me  on 2010-06-25 12:13:50 (Show Source):
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where is the binomial distribution? there are no equations. n=50 and p=.9 means nothing without some kind of equation. might aswell say z=459 and Q=.2345

Money_Word_Problems/317343: You are buying a new car. You have $10,000 from Savings and $12,000 from a car loan. What integer would represent your total budget for buying a new car?
I realize the answer to that is 22,000 but the next question I'm stuck:
Using your answer from 1: You will use 15% of your budget to pay for tax and title fees. Write an algebraic expression (meaning you DO NOT SOLVE) showing how much of your budget you will be spending on the cost of the car.

1 solutions
Answer 227349 by JBarnum(2044) About Me  on 2010-06-25 12:07:09 (Show Source):
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.15%2822000%29=T
T=tax and fees
so
22000-T=Cthis is your equation where C=money spent on car

Numbers_Word_Problems/317466: y is 2.5 when x is 5, and y varies directly with x.
Find y when x is 10.
5
7.5
12.5
20

1 solutions
Answer 227348 by JBarnum(2044) About Me  on 2010-06-25 12:02:47 (Show Source):
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2.5=(1/2)5
y=(1/2)10
y=5