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test/752110: Solve equation:
First problem: 4g^2-32g=0
Second problem: 3m^2=-6m 1 solutions
Answer 457563 by nerdybill(6963) on 2013-05-23 22:23:02 (Show Source):
You can put this solution on YOUR website!First problem:
4g^2-32g=0
factor out common factor of 4g:
(4g)(g-8)=0
setting each term to zero:
g = {0, 8}
.
Second problem:
3m^2=-6m
3m^2+6m = 0
factor out common factor of 3m:
(3m)(m+2) = 0
setting each term to zero:
m = {0, -2}
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test/751858: 3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n , find n.
1 solutions
Answer 457457 by nerdybill(6963) on 2013-05-23 09:40:57 (Show Source):
You can put this solution on YOUR website!3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n , find n.
.
3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n
3log 5 - 3log 3 - ( log 5 - 2 log 6 ) = 2 - log n
log 5^3 - log 3^3 - ( log 5 - 2 log 6 ) = 2 - log n
log 125 - log 27 - ( log 5 - 2 log 6 ) = 2 - log n
log 125 - log 27 - ( log 5 - log 6^2 ) = 2 - log n
log 125 - log 27 - ( log 5 - log 36 ) = 2 - log n
log 125 - log 27 - log 5 + log 36 = 2 - log n
log 125/27 - log 5 + log 36 = 2 - log n
log 125/(27*5) + log 36 = 2 - log n
log (125*36)/(27*5) = 2 - log n
log (125*36)/(27*5) = 2 - log n
log (125*36)/(27*5) - 2 = -log n
-[log (125*36)/(27*5) - 2] = log n
10^(-[log (125*36)/(27*5) - 2]) = n
10^(-[log (4500)/(27*5) - 2]) = n
10^(-[log 900/27 - 2]) = n
10^(-[log 100/3 - 2]) = n
10^(-[1.52287874528 - 2]) = n
10^(0.4771212547196624372950) = n
3 = n
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Inverses/751191: If y varies inversely as x, and y=18 when x=3, find y when x = 8.
y=____(simplify your answer.)
1 solutions
Answer 457039 by nerdybill(6963) on 2013-05-21 13:14:25 (Show Source):
You can put this solution on YOUR website!If y varies inversely as x, and y=18 when x=3, find y when x = 8.
y=____(simplify your answer.)
.
Inverse variation:
y = k/x
using:y=18 when x=3 we can find k:
18 = k/3
54 = k
.
our equation:
y = 54/x
now we can answer:find y when x = 8
y = 54/8
y = 6.75
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logarithm/751129: If log[2](7) = a and log[2](5) = b express in terms of a and b the formulas
i) log[2](35)
ii) log [2](2.8)
n.b. [x] is the log base
(Y) is the number after the base number
Please help! 1 solutions
Answer 457007 by nerdybill(6963) on 2013-05-21 10:49:48 (Show Source):
You can put this solution on YOUR website!If log[2](7) = a and log[2](5) = b express in terms of a and b the formulas
i)
log[2](35)
log[2](7*5)
log[2](7) + log[2](5)
a + b
ii)
log [2](2.8)
log [2](7 * .4)
log [2](7 * 4/10)
log [2](7) + log [2](4/10)
log [2](7) + log [2](4) - log [2](10)
log [2](7) + log [2](2^2) - log [2](5*2)
log [2](7) + log [2](2^2) - (log [2](5)+log [2](2))
log [2](7) + log [2](2^2) - (log [2](5)+log [2](2^1))
log [2](7) + log [2](2^2) - (b+1)
log [2](7) + log [2](2^2) -b-1
a + 2 -b-1
a-b+1
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Exponential-and-logarithmic-functions/751125: the max population that earth can sustain is 40 billion. if the current population is 4.2 billion, in how many years will the max population be reached? Assume that each year the population is 2% more than the previous year. 1 solutions
Answer 456998 by nerdybill(6963) on 2013-05-21 10:11:28 (Show Source):
You can put this solution on YOUR website! the max population that earth can sustain is 40 billion. if the current population is 4.2 billion, in how many years will the max population be reached? Assume that each year the population is 2% more than the previous year.
.
Exponential growth equation:
A = Pe^(rt)
the problem give us:
P is 4.2
A is 40
r is .02
.
40 = 4.2e^(.02t)
40/4.2 = e^(.02t)
ln(40/4.2) = .02t
ln(40/4.2)/.02 = t
112.69 = t
or
113 years = t
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Circles/751118: Find the equation of the circle that is tangent to the x-axis and the circle is at (-7,4). 1 solutions
Answer 456995 by nerdybill(6963) on 2013-05-21 10:03:37 (Show Source):
You can put this solution on YOUR website!Find the equation of the circle that is tangent to the x-axis and the circle is at (-7,4).
.
Plotting the center on graph, we can see that the distance between the center and the x-axis is 4. Therefore, the radius is 4.
.
Standard form of a circle is:
(x-h)^2 + (y-k)^2 = r^2
where
(h,k) is the center and r is the radius
.
plug in our data:
(x-(-7))^2 + (y-4)^2 = 4^2
(x+7)^2 + (y-4)^2 = 16
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Coordinate-system/750622: Hi there I need to calculate out how far and high a boy named Jose throws in a ball in a football match, Y stands for the height in meters and X for the diatance in meters from where jose is standing.
How do I calculate Y=-0,04x^2+0,6x+2 1 solutions
Answer 456739 by nerdybill(6963) on 2013-05-20 03:22:09 (Show Source):
You can put this solution on YOUR website!Y=-0.04x^2+0.6x+2
.
Maximum is at vertex:
x-value of vertex is "axis of symmetry":
x = -b/(2a)
x = -0.6/(2*(-0.04))
x = -0.6/(-0.08)
x = 0.6/(0.08)
x = 7.5
Max height:
Y=-0.04(7.5)^2+0.6(7.5)+2
Y= 4.25 meters (max height)
.
Max distance, we set Y to zero and solve for x:
0=-0.04x^2+0.6x+2
0=0.04x^2-0.6x-2
0=0.02x^2-0.3x-1
applying the "quadratic formula" yields:
x = {17.81, -2.81}
throw out the negative solution (extraneous) leaving
x = 17.81 meters (max distance)
.
details of "quadratic formula":
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=0.17 is greater than zero. That means that there are two solutions: .


Quadratic expression can be factored:

Again, the answer is: 17.8077640640442, -2.80776406404415.
Here's your graph:
 |
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Rate-of-work-word-problems/749732: from pipe a it takes 4 hours to fill the tank.from pipe b it takes 8 hours empty the tank.if the both pipes are opened how many hours to fill the tank? 1 solutions
Answer 456126 by nerdybill(6963) on 2013-05-17 01:17:26 (Show Source):
You can put this solution on YOUR website!from pipe a it takes 4 hours to fill the tank.from pipe b it takes 8 hours empty the tank.if the both pipes are opened how many hours to fill the tank?
.
Let x = time (hours) to fill tank w/both pipes open
then
x(1/4 - 1/8) = 1
x(2/8 - 1/8) = 1
x(1/8) = 1
x/8 = 1
multiply both sides by 8:
x = 8 hours
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logarithm/748318: log(x-3) + log(x+2) = log(4x)
I need to know what steps to take to get the answer. Thank you! 1 solutions
Answer 455448 by nerdybill(6963) on 2013-05-13 18:25:48 (Show Source):
You can put this solution on YOUR website!log(x-3) + log(x+2) = log(4x)
adding two logs is equivalent to multiplication:
log(x-3)(x+2) = log(4x)
now, we can eliminate the logs from both sides:
(x-3)(x+2) = (4x)
x^2-x-6 = 4x
x^2-5x-6 = 0
(x+1)(x-6) = 0
x = {-1, 6}
we throw out the -1 (extraneous solution) leaving
x = 6
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Graphs/748049: Please help. Ive been stuck on this question for a while and can't seem to figure it out. The question is, "Find an equation of the line that passes through (4, 2); perpendicular to 2x-3y=2" 1 solutions
Answer 455310 by nerdybill(6963) on 2013-05-13 03:40:46 (Show Source):
You can put this solution on YOUR website!Find an equation of the line that passes through (4, 2); perpendicular to 2x-3y=2
.
find slope of:
2x-3y=2
2x=3y+2
2x-2=3y
(2/3)x-2/3=y
slope is 2/3
a line perpendicular must have a slope that is the "negative reciprocal": -3/2
.
plug slope (-3/2) and point (4,2) into the "point-slope form"
y - y1 = m(x - x1)
y - 2 = (-3/2)(x - 4)
y - 2 = (-3/2)x - (-3/2)4
y - 2 = (-3/2)x - (-6)
y - 2 = (-3/2)x + 6
y = (-3/2)x + 8 (answer)
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Mixture_Word_Problems/748065: 5.) A chemist mixes liquid that's 87% gas. Together with another liquid that's 93% gas, to obtain 6 gallons that has a blend of 88% gas. How much of the 93% did the chemist use?
A.) 1
B.) 3
C.) 5
D.) 6 1 solutions
Answer 455309 by nerdybill(6963) on 2013-05-13 03:35:35 (Show Source):
You can put this solution on YOUR website!5.) A chemist mixes liquid that's 87% gas. Together with another liquid that's 93% gas, to obtain 6 gallons that has a blend of 88% gas. How much of the 93% did the chemist use?
A.) 1
B.) 3
C.) 5
D.) 6
.
Let x = amount (gallons) of 93% gas
then
6-x = amount (gallons) of 87% gas
.
.93x + .87(6-x) = .88(6)
.93x + 5.22-.87x = 5.28
.06x + 5.22 = 5.28
.06x = .06
x = 1
.
Answer: A
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logarithm/747651: Write as a single log and simplify
a) log(base 3)√45 - log(base 3)√5
Can you please help me out? Thanks so much in advance:)
Can you also please show the work:) 1 solutions
Answer 455067 by nerdybill(6963) on 2013-05-11 21:59:43 (Show Source):
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logarithm/747583: Please help me solve this:
Express as a logarithm of a single logarithm:
Ln(x-1) + ln (x^2-3) - 1/2ln (y+1) 1 solutions
Answer 454986 by nerdybill(6963) on 2013-05-11 14:33:31 (Show Source):
You can put this solution on YOUR website!Ln(x-1) + ln (x^2-3) - 1/2ln (y+1)
Ln(x-1) + ln (x^2-3) - ln (y+1)^(1/2)
ln(x-1)(x^2-3) - ln (y+1)^(1/2)
ln(x-1)(x^2-3)/(y+1)^(1/2)
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Circles/747502: Find the center and radius for the circle defined by the equation: x2 + y2 + 5x − y + 2 = 0 1 solutions
Answer 454965 by nerdybill(6963) on 2013-05-11 10:45:44 (Show Source):
You can put this solution on YOUR website!Put in "standard form" of a circle:
(x-h)^2 + (y-k)^2 = r^2
.
x^2 + y^2 + 5x − y + 2 = 0
x^2 + y^2 + 5x − y = -2
x^2 + 5x + y^2 − y = -2
(x^2 + 5x) + (y^2 − y) = -2
(x^2 + 5x+ 25/4) + (y^2 − y + 1/4) = -2 +25/4+1/4
(x^2 + 5/2)^2 + (y^2 − 1/2)^2 = -8/4 +25/4+1/4
(x^2 + 5/2)^2 + (y^2 − 1/2)^2 = (-8+25+1)/4
(x^2 + 5/2)^2 + (y^2 − 1/2)^2 = 18/4
(x^2 + 5/2)^2 + (y^2 − 1/2)^2 = (3sqrt(2)/2)^2
.
center: (-5/2, 1/2)
radius: 3sqrt(2)/2
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Systems-of-equations/747442: Hello, I recentaly got a packet of homework from school. I am out due to medical reasons but have been homeschooled since the middle of the year. I am also in a new state so everything is different. And they just gave me a packet to complete as Exam reviews, and homework for a final marking period grade. I don't want to fail this year so It would really help if I could have a online tutor email me daily or phone calls or something to help me out. I only have about less then 2 weeks to complete this packet. It isn't much only about, 9 pages? Im a A+ student, I just haven't seen anything like this before. Im in Algerbra 1. I am a 9th grader, and The issue currently is solutions to a system? Not sure how to write out the problem as it is a graph, it would help I if I could attached photos. But if you could help please let me know asap! 1 solutions
Answer 454946 by nerdybill(6963) on 2013-05-11 07:52:37 (Show Source):
You can put this solution on YOUR website!I can help you. Email your questions directly to me at nerdybill@gmail.com and I can help you through the semester.
.
The issue currently is solutions to a system?
Using graphs, the "intersection" is the solution (although not very accurate).
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Quadratic_Equations/747342: h = –16t^2 + vt + c
The equation shown above is the vertical motion formula, where h is the ending height, t is the time in seconds, v is the starting velocity in feet per second, and c is the starting height in feet.
If Adam, who is 6 feet tall, threw his baseball 80 feet per second straight up into the air, which of the following answers is the best estimate of how long it took the ball to come back to the ground?
I think this is the equation, h= -16t^2+80t+6 1 solutions
Answer 454846 by nerdybill(6963) on 2013-05-10 15:46:44 (Show Source):
You can put this solution on YOUR website!h= -16t^2+80t+6 (is correct)
.
when the ball is on the ground, h is zero. So, set h to zero and solve for t:
0 = -16t^2+80t+6
0 = 16t^2-80t-6
0 = 8t^2-40t-3
solve using the "quadratic formula" yields:
x = {5.07, -0.07}
throw out the negative value (extraneous) leaving
x = 5.07 seconds
.
Details of quadratic formula follows:
| Solved by pluggable solver: SOLVE quadratic equation with variable |
Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=1696 is greater than zero. That means that there are two solutions: .


Quadratic expression can be factored:

Again, the answer is: 5.07390753524675, -0.0739075352467502.
Here's your graph:
 |
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Average/747092: What is the average arithmetic mean of (4x+3), (-8x+-2) and (7x+8) 1 solutions
Answer 454742 by nerdybill(6963) on 2013-05-10 04:36:02 (Show Source):
You can put this solution on YOUR website!What is the average arithmetic mean of (4x+3), (-8x+-2) and (7x+8)
.
"sum" divided by 3:
[(4x+3)+(-8x+-2)+(7x+8)]/3
[4x+3-8x-2+7x+8]/3
[3-4x-2+7x+8]/3
[1-4x+7x+8]/3
[1+3x+8]/3
[3x+9]/3
x+3
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Polygons/746807: what is the measure of each interior angle of a 40 sided polygon 1 solutions
Answer 454508 by nerdybill(6963) on 2013-05-09 09:16:27 (Show Source):
You can put this solution on YOUR website!what is the measure of each interior angle of a 40 sided polygon
.
Interior Angle = 180° - 360°/n
Interior Angle = 180 - 360/40
Interior Angle = 180 - 9
Interior Angle = 171°
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