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checkley77 answered: 12560 problems
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Linear-equations/157030: y=8x+12
1 solutions

Answer 115796 by checkley77(12569) About Me  on 2008-09-15 10:13:47 (Show Source):
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y=8x+12
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+15%2C+8x+%2B12%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 15, 8x +12).


Polynomials-and-rational-expressions/157032: 4. I need help solving this using factoring. I appreciate all help. Thank you.


5x^2 = 2x - 7x^2

1 solutions

Answer 115795 by checkley77(12569) About Me  on 2008-09-15 10:12:19 (Show Source):
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5x^2 = 2x - 7x^2
5x^2+7x^2-2x=0
12x^2-2x=0
2x(6x-1)=0
2x=0
x=0/2
x=0 answer.
6x-1=0
6x=1
x=1/6 answer.
Proof:
5(1/6)^2=2*1/6-7(1/6)^2
5/36=2/6-7/36
5/36=(2*6)/36-7/36
5/36=12/36-7/36
5/36=5/36


percentage/157040: An operation has a 10 percent scrap rate. As a result, 72 pieces per hour are produced. What is the potential increase in labor productivity that could be achieved by eliminating the scrap?
1 solutions

Answer 115793 by checkley77(12569) About Me  on 2008-09-15 10:06:02 (Show Source):
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x-.1x=72
.9x=72
x=72/.9
x=80 is production if scrap is eliminated.


percentage/157041: An operation has a 10 percent scrap rate. As a result, 72 pieces per hour are produced. What is the potential increase in labor productivity that could be achieved by eliminating the scrap?
1 solutions

Answer 115792 by checkley77(12569) About Me  on 2008-09-15 10:05:22 (Show Source):
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x-.1x=72
.9x=72
x=72/.9
x=80 is production if scrap is eliminated.


percentage/157042: Please explain. A manager checked production records and found that a worker produced 160 units while working 40 hours. In the previous week, the same worker produced 138 units while working 36 hours. Did the worker's productivity increase, decrease, or remain the same? Explain how?
1 solutions

Answer 115791 by checkley77(12569) About Me  on 2008-09-15 10:02:45 (Show Source):
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160/40=4 units per hour
138/36=3.8333 per hour a lower rate.


Linear-systems/156924: write a linear equation in standard form, given the following information...
A line through -3,2 and parallel to a line with a slope of -4
1 solutions

Answer 115696 by checkley77(12569) About Me  on 2008-09-14 18:24:49 (Show Source):
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2=-4*-3+b
2=12+b
b=2-12
b=-10
Thus the line equation is:
Y=-4X-10
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+-4x+-10%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, -4x -10).


Quadratic_Equations/156920: Graph the quadratic equation, label the ordered pairs for the vertex and the y-intercept
y= x^2 + x-2
1 solutions

Answer 115695 by checkley77(12569) About Me  on 2008-09-14 18:21:19 (Show Source):
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y= x^2 + x-2
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+x%5E2+%2Bx+-2%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, x^2 +x -2).
y intercept=(0,-2)
vertex=(-.5,-2.25)


Surface-area/156906: If sides of a square are lengthened by 8 centimeters, the area becomes 144 cm. Find the length of a side of the original square
1 solutions

Answer 115692 by checkley77(12569) About Me  on 2008-09-14 18:08:25 (Show Source):
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(x+8)^2=144 taking the sqrt of both sides we get:
x+8=sqrt144
x+8=12
x=12-8
x=4 cm for the original sides of the square.
Proof:
(4+8)^2=144
12^2=144
144=144


Unit_Conversion_Word_Problems/156907: The population of San Francisco in 750,000 in an area on 49 square miles. What is the population density in San Francisco? Explain your answers in people per acre.
1 solutions

Answer 115691 by checkley77(12569) About Me  on 2008-09-14 18:02:27 (Show Source):
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750,000/49=15,306.122 people per acre.


Graphs/156911: Mr.O'Leary is 4 times as old as his son. In 16 years he will be only twice as old. What are theri ages. (Hint: If the son is x years old now, how old will he be in another 16 years?)
1 solutions

Answer 115690 by checkley77(12569) About Me  on 2008-09-14 18:00:17 (Show Source):
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4x=x son=x thus mr=4*son=4x
In 16 years they will be:
4x+16=2(x+16)
4x+16=2x+32
4x-2x=32-16
2x=16
x=16/2
x=8 years old for the son.
Dad=4*8=32 years old.
Proof:
4*8+16=2(8+16)
32+16=2*24
48=48


Equations/156913: Mr.O'Leary is 4 times as old as his son. In 16 years he will be only twice as old. What are their ages. (Hint: If the son is x years old now, how old will be in another 16 years?)
1 solutions

Answer 115689 by checkley77(12569) About Me  on 2008-09-14 17:58:12 (Show Source):
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4x=x son=x thus mr=4*son=4x
In 16 years they will be:
4x+16=2(x+16)
4x+16=2x+32
4x-2x=32-16
2x=16
x=16/2
x=8 years old for the son.
Dad=4*8=32 years old.
Proof:
4*8+16=2(8+16)
32+16=2*24
48=48


Equations/156916: whats a-1/2=3/5 ?
1 solutions

Answer 115688 by checkley77(12569) About Me  on 2008-09-14 17:53:02 (Show Source):
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a-1/2=3/5
a=3/5+1/2
a=(2*3+1*5)/10
a=(6+5)/10
a=11/10
a=1 1/10 answer.
or
a=.6+.5=1.1 answer.


Finance/156807: find the accumulated value of an investment of $8,000 at 9% compounded continuously for 4 years.
1 solutions

Answer 115687 by checkley77(12569) About Me  on 2008-09-14 17:48:48 (Show Source):
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8,000(e)^rt
8,000*1.732^.09*4
8000*1.732^.36
8,000*1.433=$11,466.64 Value of the 4 year investment @9% continuous compounding.


Quadratic_Equations/156824: for what values of p is 4x^2+px+49=0 a perfect square?
1 solutions

Answer 115686 by checkley77(12569) About Me  on 2008-09-14 17:10:38 (Show Source):
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4x^2+px+49=0
p=+/-28
(4x^2+/-28x+49)=0
Proof:
2x+7
2x+7
---------------
4x^2+14x+14x+49=4x^2+28x+49
2x-7
2x-7
------------------
4x^2-14x-14x+49=4x^2-28x+49


Quadratic_Equations/156833: prove that y=x-3 is a tangent to the curve y=x^2-5x+6.
1 solutions

Answer 115682 by checkley77(12569) About Me  on 2008-09-14 16:49:58 (Show Source):
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y=x-3 (red line)
y=x^2-5x+6 (green curve)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+x+-3%2C+x%5E2+-5x+%2B6%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions x -3 and x^2 -5x +6).
A picture is worth many calculations.


Travel_Word_Problems/156837: trains a and b sre traveling in the same direction on parallel tracks. train a is traveling at 40 mile per hour and train b is traveling at 60 miles per hour. train a passes a station at 5:25pm. if train b pass the same station at 5:37pm what time will train b catch up to train a
1 solutions

Answer 115681 by checkley77(12569) About Me  on 2008-09-14 16:45:05 (Show Source):
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40t=60(t-.2)
40t=60t-12
40t-60t=-12
-20t=-12
t=-12/-20
t=.6 hours or 36 minutes they will meet.
Proof:
40*.6=60(.6-.2)
24=60*.4
24=24


Problems-with-consecutive-odd-even-integers/156843: The product of two consecutive odd integer is 1 less than 4 times their sum find the two integers
1 solutions

Answer 115679 by checkley77(12569) About Me  on 2008-09-14 16:31:43 (Show Source):
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x(x+2)=4(x+x+2)-1
x^2+2x=4(2x+2)-1
x^2+2x=8x+8-1
x^2+2x-8x-8+1=0
x^2-6x-7=0
(x-7)(x+1)=0
x-7=0
x=7 for the smaller integer.
7=2=9 for the larger integer.
Proof:
7*9=4(7+9)-1
63=4*16-1
63=64-1
63=63


Numbers_Word_Problems/156863: At 11:00a.m. Kate left the Clinton toll booth traveling west at 80 km/h. At 12:00p.m. Juan left the toll booth traveling west at 72 km/h. At what time will the two cars be 98 km apart?
This is what I have so far...Kate: 80(x+1)
Juan: 72x
80(x+1)+72x=98
152x=18
x=.118
Not sure what to do after this..thanks.
1 solutions

Answer 115678 by checkley77(12569) About Me  on 2008-09-14 16:27:04 (Show Source):
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80(x+1)+72x=98
------------------------------------------
Equation should be 80(t+1)-72t=98
80t+80-72t=98
8t=98-80
8t=18
t=18/8
t=2.25 hours they'll be 98 miles apart.
Proof:
80(2.25+1)-72*2.25=98
80*3.25-162=98
260-162=98
98=98
-----------------------------------------
152x=18
x=.118


Money_Word_Problems/156867:
3. In 2002, Home Depot’s sales amounted to $58,200,000,000. In 2006, its sales were $90,800,000,000.
a. Write Home Depot’s 2002 sales and 2006 sales in scientific notation.
You can find the percent of growth in Home Depot’s sales from 2002 to 2006, follow these steps:
• Find the increase in sales from 2002 to 2006.
• Find what percent that increase is of the 2002 sales.
b. What was the percent growth in Home Depot’s sales from 2002 to 2006? Do all your work by using scientific notation.

1 solutions

Answer 115676 by checkley77(12569) About Me  on 2008-09-14 16:19:16 (Show Source):
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58,200,000,000=5.82 *10^10
90,800,000,000=9.08*10^10
9.08-5.82=3.26*10*^10 is the growth.
3.26/5.82=.56 or 56% increase from 2002


Expressions-with-variables/156873: 2(3x+y)+5(x+2y)
1 solutions

Answer 115675 by checkley77(12569) About Me  on 2008-09-14 16:12:28 (Show Source):
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2(3x+y)+5(x+2y)
6x+2y+5x+10y=11x+12y answer.


Polynomials-and-rational-expressions/156880: Perform the indicated operations and simplify.
(v-8)/(v-9)- (v+1)/(v+9)+(v-27)/(v^2-81)=??
1 solutions

Answer 115673 by checkley77(12569) About Me  on 2008-09-14 16:10:06 (Show Source):
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(v-8)/(v-9)-(v+1)/(v+9)+(v-27)/(v^2-81)
(v^2-81)=(v+9)(v-9) [the common denominator.]
[(v-8)(v+9)-(v+1)(v-9)+(v-27)]/(v+9)(v-9)
[(v^2+v-72)-(v^2-8v-9)+(v-27)]/(v+9)(v-9)
(v-72+8v+9+v-27)/(v+9)(v-9)
(10v-90)/(v+9)(v-9)
10(v-9)/(v+9)(v-9)
10/(v+9) answer.


Quadratic_Equations/156881: 9) Solve. Round results to the nearest thousandth.
7x2 - 6x - .4255 = 0

1 solutions

Answer 115672 by checkley77(12569) About Me  on 2008-09-14 16:01:47 (Show Source):
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7x2 - 6x - .4255 = 0
Using the quadratic equation:x=%28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29 WE get;
x=(6+-sqrt[-6^2-4*7*-.4255])/2*7
x=(6+-sqrt[36+11.914])/14
x=(6+-sqrt47.914)/14
x=(6+-6.922)/14
x=12.922/14
x=.923 answer.
x=(6-6.922)/14
x=-.922/14
x=-.066 answer.


Quadratic_Equations/156882: Solve for the specified variable.
S =a/1-r for r

1 solutions

Answer 115670 by checkley77(12569) About Me  on 2008-09-14 15:53:44 (Show Source):
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S =(a/1)-r
r=-S+a/1 answer.
OR:
S=a/(1-r)
S(1-r)=a
S-Sr=a
-Sr=a-S
r=(a-S)/-S answer.


Linear-equations/156883: 2y+3=0
1 solutions

Answer 115668 by checkley77(12569) About Me  on 2008-09-14 15:49:16 (Show Source):
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2y+3=0
2y=-3
y=-3/2 answer.


Volume/156887: 19.The exterior dimensions of an empty cooler in the shape of a rectangular prism are 18 inches by 18 inches by 24 inches. For insulation, the top, the bottom and each of the four walls are two inches thick. What is the volume of the empty space inside the cooler?

1 solutions

Answer 115665 by checkley77(12569) About Me  on 2008-09-14 15:46:57 (Show Source):
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(18-4)(18-4)(24-4)=14*14*20=3,920 in^3 is the inner empty space.


Polynomials-and-rational-expressions/156471: 9/x^2-9x+14 - 7/x-2
1 solutions

Answer 115564 by checkley77(12569) About Me  on 2008-09-13 18:03:27 (Show Source):
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9/(x^2-9x+14)-7/(x-2)
If this what you mean????? Then:
9/(x-2)(x-7)-7/(x-2)
[9-7(x-7)]/(x-2)(x-7)
[9-7x+49)/(x-2)(x-7)
(-7x+58)/(x-2)(x-7) Answer.


Radicals/156727: sqrt to the 3rd power, 250x^5y^3 divided by sqrt to the 3rd power, 2x^3
1 solutions

Answer 115562 by checkley77(12569) About Me  on 2008-09-13 17:55:00 (Show Source):
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sqrt to the 3rd power, 250x^5y^3 divided by sqrt to the 3rd power, 2x^3
Do you mean: sqrt(250x^5y^3)^3/sqrt(2x^3)^3?
sqrt(250*250*250x^14*xy^9)/sqrt(2*2*2y^9) factoring the 250 & the 8.
cancel out the sqrt(y^9), extract the 250, x^7 & the 2.
250x^7sqrt(250*x)/2sqrt2 divide by 2.
125sqrt(250x)/sqrt2 factor the 250=25810
125sqrt(25*10x)/sqrt2 extract the 5.
625sqrt(10x)/sqrt2


Polynomials-and-rational-expressions/156720: Please check my answers
Please check my work
add,subtract,multiply or divide the polynomials
3x(-4x^2+5x+14) = -12x^3+15x^2+42x
(7x-5)^2 = 49x^2+25
(3x+4y)(3x-4y) = 9x^2-16y^2
(4x^2-17x-2)divided by (2x+3) =2x+23x-2/2x+3
(2/3x^3-1/2x+1/4)-(2/5x^2-1/3x+1/9) =2/3x^3-1/6x+5/26-2/5x^2
(4x^3+19x^2-7x-14) divided by(3x+4)= 4/3x^2+41/9x
(-7x^2+5xy-2y^2)+(3x^2-5xy-4y^2) = -4x^2-6y^2
(6r^3-8rs+4s^2)-(-5r^3+3rs+s^2) = 11r^2-11rs+2r^2
(8x^2+11xy-17y^2)+(2x^2+4xy-18y^2) = 10x^2+15xy-35y^2
(-4x^2y-2z^2y)-(8x^2y-4z^2y)+(-6x^2y+14xy^2) = -18x^2y=2z^2y+14xy^2
Thank you so much

1 solutions

Answer 115559 by checkley77(12569) About Me  on 2008-09-13 17:40:13 (Show Source):
You can put this solution on YOUR website!
(2/3 x^3 - 1/2 x + 1/4)-(2/5 x^2 - 1/3 x + 1/9) please do that one again.
OK. I'll try.
2x^3/3-x/2+1/4-2x^2/5+x/3-1/9
2x^3/3-2x^2/5-x/2+x/3-1/9+1/4
2x^3/3-2x^2/5-(3x-2x)/2*3-(-4+9)/9*4
2x^3/3-2x^2/5-x/6-5/36
IF YOU NEED TO COMBINE THE FRACTIONS THEN THE COMMON DENOMINATOR IS 36*5=180:
(60*2x^3-36*2x^2-30*x-5*5)/180
120x^3-72x^2-30x-25)/180
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{used to show the correct values}
3x(-4x^2+5x+14) = -12x^3+15x^2+42x OK.
(7x-5)^2 = 49x^2+25 WRONG
(49x^2{-70x}+25) CORRECT.
(3x+4y)(3x-4y) = 9x^2-16y^2 OK.
(4x^2-17x-2)divided by (2x+3) =2x+23x-2/2x+3 WRONG.
(2x-{11.5) & 32.5/(2x+3)}CORRECT.
(2/3x^3-1/2x+1/4)-(2/5x^2-1/3x+1/9) =2/3x^3-1/6x+5/26-2/5x^2 WRONG.
2x^3/3-2x^2/5-x/2-x/3+1/4+1/9=2x^3/3-2x^2/5-(3x+2x)/6+(9+4)/36
2x^3/3-2x^2/5-{5x/6+13/36} CORRECT.
(4x^3+19x^2-7x-14) divided by(3x+4)= 4/3x^2+41/9x WRONG.
4x^2/3+41x/9-{227/27 & (19 17/27)/(3x+4)} CORRECT.
(-7x^2+5xy-2y^2)+(3x^2-5xy-4y^2) = -4x^2-6y^2 OK.
(6r^3-8rs+4s^2)-(-5r^3+3rs+s^2) = 11r^2-11rs+2r^2 WRONG.
11r^3-11rs+2{s^}2 CORRECT.
(8x^2+11xy-17y^2)+(2x^2+4xy-18y^2) = 10x^2+15xy-35y^2 OK.
(-4x^2y-2z^2y)-(8x^2y-4z^2y)+(-6x^2y+14xy^2) = -18x^2y=2z^2y+14xy^2 WRONG.
-18x^2y{+}2z^2y+14xy^2 CORRECT.


Polynomials-and-rational-expressions/156334: 2X^2-18
1 solutions

Answer 115556 by checkley77(12569) About Me  on 2008-09-13 17:00:50 (Show Source):
You can put this solution on YOUR website!
2X^2-18
2(x^2-9)=2(x+3)(x-3) answer.


Polynomials-and-rational-expressions/156400: This question is from textbook elementary and intermediate algebra
Express the following rational expressions in lowest terms:
4z
_____
8z-12


y^5-3y^3+8y^2
______________
5y



z^3+4z^2
_________
z^2+8z+16

1 solutions

Answer 115555 by checkley77(12569) About Me  on 2008-09-13 16:58:12 (Show Source):
You can put this solution on YOUR website!
4z
_____ =4z/4(2z-3)=z/(2z-3) answer.
8z-12


y^5-3y^3+8y^2
______________ = y(y^4-3y^2+8y)/5y=(y^4-3y^2+8y)/5 answer.
5y



z^3+4z^2
_________ = z^2(z+4)/(z+4)(z+4)=z^2/(z+4) answer.
z^2+8z+16


Expressions-with-variables/156506: 1-2/3y=9/5-y/5+3/5
1 solutions

Answer 115553 by checkley77(12569) About Me  on 2008-09-13 16:52:59 (Show Source):
You can put this solution on YOUR website!
1-2/3y=9/5-y/5+3/5
1-2y/3=9/5-y/5+3/5
-2y/3+y/5=9/5+3/5-1
(5*-2y+3y)/15=12/5-5/5
(-10y+3y)/15=7/5
-7y/15=7/5 cross multiply
5*-7y=15*7
-35y=105
y=105/-35
y=-3 answer.
Proof:
1-2*-3/3=9/5-(-3/5)+3/5
1+6/3=9/5+3/5+3/5
1+2=15/5
3=3