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Inequalities/359462: find the slope of a line parallel or perpendicular to each given line.
3x+y=0
x=0

1 solutions

Answer 256555 by Fombitz(13828) About Me  on 2010-10-21 08:17:39 (Show Source):
You can put this solution on YOUR website!
Parallel lines have slopes that are identical.
m%5B1%5D=m%5B2%5D
Perpendicular line have slopes that are negative reciprocals.
m%5B1%5D%2Am%5B2%5D=-1
.
.
.
3x%2By=0
y=-3x
m%5B1%5D=-3
Parallel, m%5B2%5D=-3
Perpendicular, m%5B2%5D=1%2F3
.
.
.
x=0
Slope is undefined.
Parallel, slope is undefined.
Perpendicular, m%5B2%5D=0.


Probability-and-statistics/359556: Determine whether each of the distributions given below represents a probability distribution. Justify your answer.

x
1
2
3
4

P(x)
1/12
5/12
1/3
1/12

(A)

x
3
6
8

P(x)
2/10
.5
1/5


(B)
x
20
35
40
50

P(x)
0.4
-0.2
0.5
0.3

(C)

1 solutions

Answer 256554 by Fombitz(13828) About Me  on 2010-10-21 08:14:55 (Show Source):
You can put this solution on YOUR website!
A) No, sum%28P%28x%29%29=11%2F12, must be 1.
B) No, sum%28P%28x%29%29=9%2F10, must be 1.
C) No, P%28x%29%3E=0 for every x.


real-numbers/359557: Can you help me with this problem?
find slope if it exists of the line containing the pair of points (-2,-16,
(-9, -18)
Slope is ???
If I do y2 - y1/x2 - x1
-16 - (-18) / -2 - (-9) = -16 + 18/ -2 +9
= (2, 7)
Would the slope of the line be 2? Or (2,7)?
Thanks for your help

1 solutions

Answer 256553 by Fombitz(13828) About Me  on 2010-10-21 08:11:45 (Show Source):
You can put this solution on YOUR website!
The slope is just a number,
m=%28y2+-+y1%29%2F%28x2+-+x1%29-+%28-16+-+%28-18%29%29+%2F+%28-2+-+%28-9%29%29+
m=%28+-16+%2B+18%29%2F+%28-2+%2B9%29
highlight%28m=2%2F7%29
Since slope is change in y over change in x, then when x moves 7 units, y moves 2 units.


Length-and-distance/359558: From the distance from (-4,-1) to the line defined by y=-2x+1. Express as a radical or a number rounded to the nearest hundredth.
1 solutions

Answer 256552 by Fombitz(13828) About Me  on 2010-10-21 08:08:42 (Show Source):
You can put this solution on YOUR website!
1.y=-2x%2B1
The closest distance is formed by the line perpendicular to y=-2x%2B1 that goes through the point (-4,-1).
To find the perpendicular line, use the slope since perpendicular lines have slopes that are negative reciprocals.
m%5B1%5D%2Am%5B2%5D=-1
-2%2Am%5B2%5D=-1
m%5B2%5D=1%2F2
Now use the point slope form of a line, y-y%5Bp%5D=m%28x-x%5Bp%5D%29
y-%28-1%29=%281%2F2%29%28x-%28-4%29%29
y%2B1=%281%2F2%29%28x%2B4%29
2y%2B2=x%2B4
2.-x%2B2y=2
Now that you have both lines, find the intersection of the two lines.
The distance you're after is the distance from point (-4,-1) to the intersection point.
Substitute eq. 1 into eq. 2 and solve for x.
-x%2B2%28-2x%2B1%29=2
-x-4x%2B2=2
-5x=0
x=0
Then from eq. 1,
y=-2%280%29%2B1
y=1
.
.

.
.
.
Now use the distance formula to find the distance from (-4,-1) to (0,1).
D%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2
D%5E2=%280-%28-4%29%29%5E2%2B%281-%28-1%29%29%5E2
D%5E2=%284%29%5E2%2B%282%29%5E2
D%5E2=20
highlight%28D=2%2Asqrt%285%29%29 or approximately,
D=4.47


Mixture_Word_Problems/359560: Hi, doing my statistic homework and I need help. The question is you spin a number wheel that has 19 numbers 950 times. The random variable represents the the winning numbers on each spin of the wheel. I don't really get the question and how I'm suppose to do it.

1 solutions

Answer 256551 by Fombitz(13828) About Me  on 2010-10-21 07:57:19 (Show Source):
You can put this solution on YOUR website!
Each number has an equal probability of being chosen.
So when you spin 950 times, on average, you would get each number 50 times.
Since 50%2A19=950
So the random variable would look like,
(x,P%28x%29)
(1,50%2F950)
(2,50%2F950)
(3,50%2F950)
.
.
.
(18,50%2F950)
(19,50%2F950)


Polynomials-and-rational-expressions/359440: When asked to solve the equation (x + 3)(2x - 1) = 5 a student proceeded as follows:
x+3=5 or 2x-1=5
x=2 or x=3
Describe, in your own words, what this student did wrong and what he/she should have
done.

1 solutions

Answer 256549 by Fombitz(13828) About Me  on 2010-10-21 06:25:59 (Show Source):
You can put this solution on YOUR website!
That would only work if their product equals 5 simultaneously.
So when one factor equals 5, the other equals 1.
When x%2B3=5, x=2, but 2%282%29-1=4, so then the product equals 5%2A4=20%7D%7D+and+not+%7B%7B%7B5 as expected.
When 2x-1=5, x=3, but 3%2B3=6, so then the product equals 5%2A6=30 and not 5 as expected.


Sequences-and-series/359548: Consider the series: 68, 81, x, 113, 132, find the value of x?
1 solutions

Answer 256547 by Fombitz(13828) About Me  on 2010-10-21 06:22:22 (Show Source):
You can put this solution on YOUR website!
Look at the first differences,
d1=81-68=13
d2=x-81
d3=113-x
d4=132-11=19
Looks like the second differences vary from each other by 2.
So the missing values should be 15 and 17.
x-81=15
x=96
.
.
113-x=17
x-96
.
.
highlight%28x=96%29


Systems-of-equations/359427: Discuss whether the statement, (x + y)3 is equivalent to x^3 + y^3, is true or not.
Identify a pair of values of x and y for which this statement is true and another pair of values for which it is not true.


1 solutions

Answer 256545 by Fombitz(13828) About Me  on 2010-10-21 06:18:40 (Show Source):
You can put this solution on YOUR website!
%28x%2By%29%5E3=x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3
.
.
.
%28x%2By%29%5E3=x%5E3%2By%5E3 when
3x%5E2y%2B3xy%5E2=0
highlight%28x=-y%29
.
.
.
Example, x=5, y=-5
%28x%2By%29%5E3=0
x%5E3%2By%5E3=125-125=0
%28x%2By%29%5E3=x%5E3%2By%5E3
.
.
.
Counterexample, x=5,y=5
%28x%2By%29%5E3=10%5E3=1000
x%5E3%2By%5E3=125%2B125=250
%28x%2By%29%5E3%3C%3Ex%5E3%2By%5E3


logarithm/359524: Solve for x. Please round answer to four decimal places.
2^(4/log base 3 (x)) = 1/256
I have tried to solve for x by
2^4/logbase3 x = 2^-8
and then I am stuck.
Please help
1 solutions

Answer 256543 by Fombitz(13828) About Me  on 2010-10-21 06:12:59 (Show Source):
You can put this solution on YOUR website!
You're on the right track.
2%5E%284%2Flog%283%2C%28x%29%29%29=+2%5E-8
.
.
4%2Flog%283%2C%28x%29%29=-8
.
.
log%283%2C%28x%29%29=-4%2F8=-1%2F2
.
.
x=3%5E%28-1%2F2%29
.
.
x=1%2Fsqrt%283%29
.
.
highlight%28x=sqrt%283%29%2F3%29


Functions/359526: Is this a linear equation, and if so, how can it be written in standard form?
x + 1/y = 7
1 solutions

Answer 256542 by Fombitz(13828) About Me  on 2010-10-21 06:09:43 (Show Source):
You can put this solution on YOUR website!
No, it's a non-linear equation.
x%2B1%2Fy=7
1%2Fy=7-x
y=1%2F%287-x%29
.
.
.
graph%28300%2C300%2C-2%2C12%0D%0A%2C-10%2C10%2C1%2F%287-x%29%29


Trigonometry-basics/359529: If sinetheta > 0 and Tantheta < 0,explain how to find the quadrant in which P (theta) lies
1 solutions

Answer 256541 by Fombitz(13828) About Me  on 2010-10-21 06:07:53 (Show Source):
You can put this solution on YOUR website!
sin%28theta%29%3E0, QI or QII
tan%28theta%29%3C0 means cos%28theta%29%3C0, QII or QIII.
Taken together,
QII


Square-cubic-other-roots/359541: Hi. I have x as a function of z(below). I need z as a function of x!
x=sqrt(z-1)(4z-1)/sqrt(3z-1)
I can't seem to figure it out in hand! So i tried to solve it on a ti89, but it only gives me strange answers involving irregular numbers. I also tried to solve it on mathcad, wiyhout any luck.
If i insert say 0,3 as z, i get 0,529. Shouldn't i then be able to find a equation for z, where i can insert the 0,529 and get 0,3?
Is this possible or what?
1 solutions

Answer 256539 by Fombitz(13828) About Me  on 2010-10-21 06:05:53 (Show Source):
You can put this solution on YOUR website!
x%5E2=%28%28z-1%29%284z-1%29%29%2F%283z-1%29
%283z-1%29x%5E2=4z%5E2-z-4z%2B1
%283z-1%29x%5E2=4z%5E2-5z%2B1
3zx%5E2-x%5E2=4z%5E2-5z%2B1
4z%5E2-%285%2B3x%5E2%29z%2B%281%2Bx%5E2%29=0
Use the quadratic formula,


highlight%28z=%28%285%2B3x%5E2%29+%2B-+sqrt%289x%5E4%2B14x%5E2%2B9%29%29%2F%288%29%29


Equations/359224: The line through (-2,0)with slope 3/4
1 solutions

Answer 256386 by Fombitz(13828) About Me  on 2010-10-20 16:28:17 (Show Source):
You can put this solution on YOUR website!
Use the point slope form of a line , y-y%5Bp%5D=m%28x-x%5Bp%5D%29
y-0=%283%2F4%29%28x-%28-2%29%29
highlight%28y=%283%2F4%29x%2B3%2F2%29
.
.
.



Equations/359227: The line through (-2,4)that is perpendicular to the x-axis
1 solutions

Answer 256385 by Fombitz(13828) About Me  on 2010-10-20 16:26:21 (Show Source):
You can put this solution on YOUR website!
Lines perpendicular to the x-axis have the form, x=a.
x=-2
.
.
.



Linear-equations/359216: write an equation of the line containing the given points
1. A(2,7), B(3,4) 2. P(-1,3), Q(0,4) 3. S(10,2), T(2,-2) 4. D(7,-4), E(-5,2)

1 solutions

Answer 256379 by Fombitz(13828) About Me  on 2010-10-20 16:14:32 (Show Source):
You can put this solution on YOUR website!
Find the slope first.
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
.
.
m=%284-7%29%2F%283-2%29
m=-3%2F1
m=-3
Then use the point-slope form of a line with either point,y-y%5Bp%5D=m%28x-x%5Bp%5D%29
y-4=-3%28x-3%29
y-4=-3x%2B9
highlight%28y=-3x%2B13%29
.
.
.

.
.
.
Follow the same procedures for the remaining problems.


absolute-value/359211: Hello! I'm a ninth grader who needs help with graphing functions with absolute value. For instance, the first problem in my Algebra II/Trigonometry homework is:
f(x) = |x|
I already understand what a function is, as well as the absolute value, it's just my teacher didn't explain very thoroughly on how to graph them. I'd be very grateful if you were able to give me a step-by-step explanation on how to graph this problem. Thank you so much in advance for voluntarily helping students like me.
Sincerely,
sunshine2739
1 solutions

Answer 256376 by Fombitz(13828) About Me  on 2010-10-20 16:09:49 (Show Source):
You can put this solution on YOUR website!
abs%28x%29=x when x%3E=0
.
.
.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%29
.
.
.
abs%28x%29=-x when x%3C0
.
.
.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-x%29
.
.
.
Now put those two together,
f%28x%29=abs%28x%29
.
.
.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cabs%28x%29%29
.
.
.
The key is the argument (inside the absolute value brackets).
Make sure you understand how to find up the limits.
So if the function is,
abs%282x%2B4%29=%282x%2B4%29 when 2x%2B4%3E=0
abs%282x%2B4%29=2x%2B4 when 2x%3E=4
abs%282x%2B4%29=2x%2B4 when x%3E=2
.
.
abs%282x%2B4%29=-%282x%2B4%29 when 2x%2B4%3C0
abs%282x%2B4%29=-2x-4 when x%3C2
.
.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cabs%282x-4%29%29


Quadratic_Equations/359206: what are the x and y intercepts of the equation x^2+y^2=49 ?
1 solutions

Answer 256375 by Fombitz(13828) About Me  on 2010-10-20 16:02:17 (Show Source):
You can put this solution on YOUR website!
To find the x-intercept, set y=0 and solve for x.
x%5E2%2By%5E2=49+
x%5E2%2B0=49
x=0+%2B-+7
(-7,0) and (7,0)
.
.
.
To find the y-intercept, set x=0 and solve for y.
x%5E2%2By%5E2=49+
0%2By%5E2=49+
y=0+%2B-+7
(0,7) and (0,-7)
.
.
.


Human-and-algebraic-language/358741: if 4n=3.60 what is the value of n
1 solutions

Answer 256374 by Fombitz(13828) About Me  on 2010-10-20 15:58:52 (Show Source):


Quadratic_Equations/359205: find the domain and range of
14x^2-16
1 solutions

Answer 256373 by Fombitz(13828) About Me  on 2010-10-20 15:57:59 (Show Source):
You can put this solution on YOUR website!
Domain:(-infinity,infinity)
Range:(-16,infinity)
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graph%28300%2C300%2C-5%2C5%2C-20%2C20%2C14x%5E2-16%29


expressions/359204: 4x2 + 3y + 5xy + 10. cut by 3/4

1 solutions

Answer 256371 by Fombitz(13828) About Me  on 2010-10-20 15:56:07 (Show Source):
You can put this solution on YOUR website!
By cut, you mean divide?
Dividing by a fraction is equivalent to multiplying by its reciprocal.
%284x%5E2%2B3y%2B5xy%2B10%29%2F%283%2F4%29=%284x%5E2%2B3y%2B5xy%2B10%29%2A%284%2F3%29



Probability-and-statistics/359201: A sample of 4 different calculators is randomly selected from a group containing 17 that are defective and 36 that have no defects. what is the probability that atleast one of the calculators is defective?
1 solutions

Answer 256370 by Fombitz(13828) About Me  on 2010-10-20 15:53:42 (Show Source):
You can put this solution on YOUR website!
P(good)=36%2F%2817%2B36%29=36%2F53
P(bad)=17%2F%2817%2B36%29=17%2F53
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P(at least one bad)+P(none bad)=1
P(at least one bad)=1-P(non bad)
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P(none bad)=%2836%2F53%29%2836%2F53%29%2836%2F53%29%2836%2F53%29=0.21287
P(at least one bad)=1-0.21287
P(at least one bad)=highlight%280.78713%29


logarithm/358815: 53^(log(x)) = 8
solve for exact answer.
1 solutions

Answer 256369 by Fombitz(13828) About Me  on 2010-10-20 15:50:22 (Show Source):


Equations/358812: equation of m=(1/4), b = (-3/4)
1 solutions

Answer 256367 by Fombitz(13828) About Me  on 2010-10-20 15:45:28 (Show Source):


Equations/358757: How do you find a exponential equation when given a table?
1 solutions

Answer 256366 by Fombitz(13828) About Me  on 2010-10-20 15:43:47 (Show Source):
You can put this solution on YOUR website!
You mean fitting data with an exponential function.
EXCEL can do that using the chart wizard.
You can also do it by hand.
Do you have an example??


Matrices-and-determiminant/358780: Find the dimensions of the matrix.
[-1 2 5 0
-5 0 9 7
9 12 8 -1
8 -5 0 6]
1 solutions

Answer 256365 by Fombitz(13828) About Me  on 2010-10-20 15:42:19 (Show Source):
You can put this solution on YOUR website!
4 rows x 4 columns
4x4.


Linear-equations/359196: Use the linear combination to solve the system.
X + 3y = 2
-X + 2y = 3
1 solutions

Answer 256363 by Fombitz(13828) About Me  on 2010-10-20 15:40:33 (Show Source):
You can put this solution on YOUR website!
Add the two equations,
x%2B3y-x%2B2y=2%2B3
5y=5
highlight%28y=1%29
Now use either equation to solve for x.
x%2B3%281%29=2
highlight%28x=-1%29


Polynomials-and-rational-expressions/359197: my question is how do you solve for the variable in this problem.
3.7b+7=8.1b-19.4 please show work so I can figure it out thanks
1 solutions

Answer 256362 by Fombitz(13828) About Me  on 2010-10-20 15:39:27 (Show Source):
You can put this solution on YOUR website!
3.7b%2B7=8.1b-19.4
Multiply by 10 to get rid of decimals.
37b%2B70=81b-194
Now solve for b.


Graphs/358811: use the slope-intercept form to graph the equation y=3/5x-3
1 solutions

Answer 256361 by Fombitz(13828) About Me  on 2010-10-20 15:38:17 (Show Source):
You can put this solution on YOUR website!
Start with the y-intercept (0,-3).
Slope is m=3%2F5 and represents change in y over change in x.
5 units change in x will give a 3 units change in y.
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X:0%2B5=5
Y:-3%2B3=0
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(5,0) is another point on the line.
Plot the two points and connect them with a line.
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Quadratic-relations-and-conic-sections/358742: Please help me solve this problem!
I have to write the equation in vertex form, find the max/min values and state the domain and range.
+y+=+2x%5E2+-+12x+%2B+27+
1 solutions

Answer 256360 by Fombitz(13828) About Me  on 2010-10-20 15:34:25 (Show Source):
You can put this solution on YOUR website!
+y+=+2x%5E2+-+12x+%2B+27+
Complete the square to get to vertex form, y=a%28x-h%29%5E2%2Bk.
y=2%28x%5E2-6x%29%2B27
y=2%28x%5E2-6x%2B9%29%2B27-2%289%29
y=2%28x-3%29%5E2%2B27-18
highlight%28y=2%28x-3%29%5E2%2B9%29
Since a%3E0, the parabola opens upwards and the vertex value is a minimum.
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y%5Bmin%5D=9
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Domain: (-infinity,infinity)
Range : (9,infinity)
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Geometry_Word_Problems/358738: How do you find area of a square room, if the perimeter of the room is 76 feet?
1 solutions

Answer 256359 by Fombitz(13828) About Me  on 2010-10-20 15:29:56 (Show Source):
You can put this solution on YOUR website!
For a square room, the perimeter is,
4s=76
s=19
For a square room, the area is,
A=s%5E2=19%5E2=361sq.ft.


test/358838: X/a+bx=c/a
1 solutions

Answer 256358 by Fombitz(13828) About Me  on 2010-10-20 15:28:19 (Show Source):