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Miscellaneous_Word_Problems/322374: A lawn mower cost $490 when new and is expected to last 10 years. What will it be worth in 6.5 years?

1 solutions

Answer 230787 by Fombitz(13828) About Me  on 2010-07-14 10:44:49 (Show Source):
You can put this solution on YOUR website!
In 10 years, it will be worth $0.
Find the slope of the depreciation curve using the points (0,490) and (10,0).
m=%28y2-y1%29%2F%28x2-1%29=%280-490%29%2F%2810-0%29=-49
y=-49x%2Bb
490=-49%280%29%2Bb
b=490
highlight%28y=-49x%2B490%29
Find y when x=6.5
y=-49%286.5%29%2B490
y=-318.5%2B490
y=171.50
The value would be $171.50.


Volume/322375: what is the circumference of a 10 ft cylinder?
1 solutions

Answer 230786 by Fombitz(13828) About Me  on 2010-07-14 10:40:24 (Show Source):
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A 10 ft diameter cylinder would have a circumference of
C=pi%2AD=10pi
A 10 ft radius cylinder would have a circumference of
C=2%2Api%2AR=20pi


Rectangles/322320: the length of a rectangle is 6m longer than its width. what are the possible widths if the area is at least 630 cm^2
1 solutions

Answer 230785 by Fombitz(13828) About Me  on 2010-07-14 10:39:12 (Show Source):
You can put this solution on YOUR website!
For a rectangle,
A=L%2AW
In this case,
L%2AW%3E=630
and
L=6%2BW
%286%2BW%29W%3E=630
W%5E2%2B6W%2B9-630%3E=9
%28W%2B3%29%5E2%3E=639
W%2B3%3E=sqrt%28639%29
W%3E=sqrt%28639%29-3
or approximately,
W%3E=22.278 cm
Then
L%3E=28.278 cm
and the area,
A%3E=630


Graphs/322370: Find the equation of the line parallel to the line y = -9 and passing through the midpoint of the segment joining (-3, 1) and (-2, 9).

1 solutions

Answer 230783 by Fombitz(13828) About Me  on 2010-07-14 10:30:40 (Show Source):
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Find the y coordinate of the midpoint.
ym=%28y1%2By2%29%2F2
ym=%281%2B9%29%2F2=5
Use the slope intercept form with slope=0.
y=mx%2Bb=ym
b=ym=5
highlight%28y=5%29
.
.
.


Pythagorean-theorem/322352: Which of the following sets of 3 segments would make up the three sides of a right triangle?
I. 3 cm – 4 cm – 5 cm
II. 4 cm – 4 cm – 5 cm
III. 13 cm – 12 cm – 5cm
IV. 24 cm – 7 cm – 25 cm
a. I only
b. I and II only
c. I, II, and III only
d. I and IV only
e. I, III, and IV only

1 solutions

Answer 230782 by Fombitz(13828) About Me  on 2010-07-14 10:26:34 (Show Source):
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All right triangles follow the Pythagorean theorem.
A%5E2%2BB%5E2=C%5E2
.
.
I) 3%5E2%2B4%5E2=5%5E2
9%2B16=25
25=25
YES
.
.
II) 16%2B16=25
32=25
NO
.
.
III)5%5E2%2B12%5E2=13%5E2
25%2B144=169
169=169
YES
.
.
IV)7%5E2%2B24%5E2=25%5E2
49%2B576=625
625=625
YES
.
.
.
e) is the correct answer.


Triangles/322362: an isosceles right triangle with an hypotenuse of length 8 inches, find the area
1 solutions

Answer 230781 by Fombitz(13828) About Me  on 2010-07-14 10:20:23 (Show Source):
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s%5E2%2Bs%5E2=8%5E2
s%5E2=4
s=2
Find the height,
h%5E2=s%5E2-%28s%2F2%29%5E2
h%5E2=4-1
h=sqrt%283%29
The area of the triangle is,
A=%281%2F2%29bh
A=%281%2F2%298%28sqrt%283%29%29
A=4sqrt%283%29sq.in.


Linear-equations/322364: what are the intercepts of the equation 7x-2y-14z=56
1 solutions

Answer 230780 by Fombitz(13828) About Me  on 2010-07-14 10:17:43 (Show Source):
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x-intercept, +y=z=0
+7x-2y-14z=56
+7x=56
+x=8
(8,0,0)
.
.
.
y-intercept, x=z=0
++7x-2y-14z=56
+-2y=56
+y=-28
(0,-28,0)
.
.
.
z-intercept, +x=y=0
++7x-2y-14z=56
+-14z=56
+z=-4
(0,0,-4)


Expressions-with-variables/322365: Write the equation of the line that passes through the following point and is parallel to the following line. Write the answer in slope-intercept form.
(-3 3) y+4x= -13
1 solutions

Answer 230779 by Fombitz(13828) About Me  on 2010-07-14 10:15:04 (Show Source):
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The new equation would have the same left hand side (relationship between x and y) and a different right hand side.
Use the point to determine the right hand side.
y%2B4x=3%2B4%28-3%29=3-12=-9
y%2B4x=-9
highlight%28y=-4x-9%29


Rectangles/322321: A rectangle is inscribed inside the semi-circle y=square root of 100-x^2. what are the dimensions of the rectangle with maximum area? include a diagram
1 solutions

Answer 230778 by Fombitz(13828) About Me  on 2010-07-14 10:13:23 (Show Source):
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For a rectangle,
A=L%2AW
In this case, L=2x and W=y
A=2xy
y=sqrt%28100-x%5E2%29
A=2x%2Asqrt%28100-x%5E2%29
Now area is only a function of x.
Differentiate with respect to x to find the maximum.
dA%2Fdx=2x%2A%281%2F2%29%28100-x%5E2%29%5E%28-1%2F2%29%28-2x%29%2Bsqrt%28100-x%5E2%29%282%29
dA%2Fdx=2sqrt%28100-x%5E2%29-2x%5E2%2Fsqrt%28100-x%5E2%29
Set the derivative equal to zero.
2sqrt%28100-x%5E2%29-2x%5E2%2Fsqrt%28100-x%5E2%29=0
2sqrt%28100-x%5E2%29=2x%5E2%2Fsqrt%28100-x%5E2%29
100-x%5E2=x%5E2
2x%5E2=100
x%5E2=50
x=sqrt%2850%29=5sqrt%282%29
y=sqrt%28100-50%29=5sqrt%282%29
A=2%285sqrt%282%29%29%2A5sqrt%282%29
A=100
.
.
.




Problems-with-consecutive-odd-even-integers/322326: i redid this problem a cpl of time and this is what i keep getting can someone help me as what step i am missing = 5^10-[1/(5^8)]
lcd = 5^8
Rewrite each fraction with the lcd as its denominator:
[(5*8*5^10)/5*8] - [1/(5^8)]
= [5^18/lcd] - [1/lcd]
= [5^18 - 1]/5^8

1 solutions

Answer 230775 by Fombitz(13828) About Me  on 2010-07-14 09:55:59 (Show Source):
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Yes, you're correct.
5%5E%2810%29-1%2F5%5E%288%29=%285%5E%2818%29-1%29%2F5%5E%288%29


Polynomials-and-rational-expressions/322359: pat has been assigned the job of picking apples from the family orchard.he could do the job alone in 8 hours. he knows that his sister patti,could do the job in 7 hours.he begs her to help,and she agrees.how long will both of them take to pick the apples? round your answer to the nearest tenth
1 solutions

Answer 230772 by Fombitz(13828) About Me  on 2010-07-14 09:54:10 (Show Source):
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Rate*Time=Output
.
.
.
Let Z be the total output of the orchard.
Let Rp be Pat's rate,
Rp%2A8=Z
Rp=Z%2F8
Let Ri be Patti's rate,
Ri%2A7=Z
Ri=Z%2F7
.
.
.
%28Rp%2BRi%29T=Z
%28Z%2F8%2BZ%2F7%29T=Z <--- Divide both sides by Z
%287%2F56%2B8%2F56%29T=1
%2813%2F56%29T=1
T=56%2F13
T=4.3hours


Angles/322328: two angles are complementary the larger angle is 9 less than twice the smaller angle find the two angles

1 solutions

Answer 230771 by Fombitz(13828) About Me  on 2010-07-14 09:50:06 (Show Source):
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Let A and B be the two angles.
A%2BB=90
B=2A-9
Substitute,
A%2B%282A-9%29=90
3A-9=90
3A=99
A=33degrees
B=2%2833%29-9=66-9
B=57degrees


Square-cubic-other-roots/322357: please explain how this works 4square root of 2401. please help!!!!!
1 solutions

Answer 230770 by Fombitz(13828) About Me  on 2010-07-14 09:46:04 (Show Source):
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In other words, what number to the 4th power equals 2401?
x%5E4=2401
x=root%284%2C2401%29
highlight%28x=7%29


Graphs/322358: What is the equation of the line that passes through (-3, -1) and has a slope of 2/5 ? Put your answer in slope-intercept form.
1 solutions

Answer 230769 by Fombitz(13828) About Me  on 2010-07-14 09:44:54 (Show Source):
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Use the point-slope form of a line,
y-yp=m%28x-xp%29
y-%28-1%29=%282%2F5%29%28x-%28-3%29%29
y%2B1=%282%2F5%29%28x%2B3%29
y%2B1=%282%2F5%29x%2B6%2F5
highlight%28y=%282%2F5%29x%2B1%2F5%29
.
.
.


Graphs/322360: Find the x and y intercept
1-3y=7-2x
1 solutions

Answer 230767 by Fombitz(13828) About Me  on 2010-07-14 09:42:26 (Show Source):
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To find the x-intercept, set y=0+and solve for x.
1-3y=7-2x
1-3%280%29=7-2x
1=7-2x
-2x=-6
x=3
(3,0)
.
.
.
To find the y-intercept, set x=0 and solve for y.
1-3y=7-2x
1-3y=7-2%280%29
1-3y=7
-3y=6
y=-2
(0,-2)


Inequalities/322251: how do I solve h(x)=5x/(x-8)(x+3)>=0
1 solutions

Answer 230766 by Fombitz(13828) About Me  on 2010-07-14 09:40:23 (Show Source):
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Break up the number line into 4 regions.
Region 1:(-infinity,-3)
Region 2:(-3,0]
Region 3:[0,8)
Region 4:(8,infinity)
The regions cannot contain x=-3 and x=8 since there is a discontinuity at those points.
Hence the use of "(" and ")" instead of "[" and "]" at those points.
Choose a point in each region (not an endpoint) and test the inequality.
If the point satisfies the inequality, the region is part of the solution region.
.
.
.
Region 1: Let x=-5
5x%2F%28%28x-8%29%28x%2B3%29%29%3E=0
-25%2F%28%28-13%29%28-2%29%29%3E=0
-25%2F26%3E=0
False, Region 1 is not in the solution region.
.
.
.
Region 2: Let x=-2
5x%2F%28%28x-8%29%28x%2B3%29%29%3E=0
-10%2F%28%28-10%29%281%29%29%3E=0
1%3E=0
True, Region 2 is part of the solution region.
.
.
.
Region 3: Let x=5
5x%2F%28%28x-8%29%28x%2B3%29%29%3E=0
25%2F%28%28-3%29%288%29%29%3E=0
-25%2F24%3E=0
False, Region 3 is not part of the solution region.
.
.
.
Region 4: Let x=10
5x%2F%28%28x-8%29%28x%2B3%29%29%3E=0
50%2F%28%282%29%2813%29%29%3E=0
50%2F26%3E=0
True, Region 4 is part of the solution region.
.
.
.
Solution Region:(-3,0] U (8,infinity)
.
.
.
Graphical verification with h(x) plotted.
Look for regions where h%28x%29%3E=0
.
.
.



Geometry_Word_Problems/322348: in square ABCD , p is the midpoint of DC and Q is the midpoint of AD. if the area of the quadrilateral QBCP is 15. what is the area of square ABCD ?
1 solutions

Answer 230761 by Fombitz(13828) About Me  on 2010-07-14 09:24:51 (Show Source):
You can put this solution on YOUR website!

.
.
.
Let the side of the square equal s.
The area of QBCP plus the area of triangle ABQ and the area of triangle PDQ equal the area of the square ABCD.
The area of the triangle is,
A=%281%2F2%29bh
ABQ:A1=%281%2F2%29%28s%2F2%29%28s%29=s%5E2%2F4
PDQ:A2=%281%2F2%29%28s%2F2%29%28s%2F2%29=s%5E2%2F8
QBCP:15
ABCD:s%5E2
Put it all together,
s%5E2%2F4%2Bs%5E2%2F8%2B15=s%5E2
2s%5E2%2Bs%5E2%2B120=8s%5E2
5s%5E2=120
s%5E2=24
s=2sqrt%286%29


logarithm/322336: rewrite as single logarithm. 1/3logz + 5logx - 2logy
Thanks
1 solutions

Answer 230759 by Fombitz(13828) About Me  on 2010-07-14 09:11:01 (Show Source):


Systems-of-equations/322249: please help me solve this equation
3+(4-2)*3
1 solutions

Answer 230758 by Fombitz(13828) About Me  on 2010-07-14 09:08:36 (Show Source):
You can put this solution on YOUR website!
It's not an equation, it's an expression.
Equations have equal signs.
3%2B%284-2%29%2A3=3%2B%282%29%2A3
3%2B%284-2%29%2A3=3%2B6
3%2B%284-2%29%2A3=9


Angles/322346: Find 7°39’46” + 5°24’33”.
1 solutions

Answer 230757 by Fombitz(13828) About Me  on 2010-07-14 09:06:43 (Show Source):
You can put this solution on YOUR website!
Start with seconds first.
46"+33"=79"=1' 19"
Then with minutes,
39'+24'+1'(from above)=64'=1°4'
Finally degrees,
7°+5°+1°(from above)=13°
Put it all together,
7°39’46” + 5°24’33”=13°4'19"


Equations/322337: if 5/x = 24/5, what is x?
1 solutions

Answer 230756 by Fombitz(13828) About Me  on 2010-07-14 09:03:26 (Show Source):
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5%2Fx+=+24%2F5
Multiply both side by 5x
25=24x
highlight%28x=25%2F24%29


Equations/322345: Tickets to a concert sere sold to adults for $3 and to students for $2. Is the total receipts were $824, and twice as many adult tickets were sold as student tickets, how many of each were sold?
1 solutions

Answer 230755 by Fombitz(13828) About Me  on 2010-07-14 09:00:51 (Show Source):
You can put this solution on YOUR website!
Let A be the number of adult tickets, S students tickets.
1.3A%2B2S=824
2.A=2S
Substitute eq. 2 into eq. 1,
3%282S%29%2B2S=824
6S%2B2S=824
8S=824
S=103tickets
Then from eq. 2,
A=2%28103%29=206tickets


Radicals/322342: (3a^2)^1/2*(3^2a)^3/2
I know the answer is 3^7/3 9^5/2 but I just don't know how it was acheived.
1 solutions

Answer 230754 by Fombitz(13828) About Me  on 2010-07-14 08:58:25 (Show Source):


Expressions-with-variables/322276: Find the slope of the line determined by the following equation.
x=y
1 solutions

Answer 230753 by Fombitz(13828) About Me  on 2010-07-14 08:54:32 (Show Source):
You can put this solution on YOUR website!
The line is in slope-intercept form, y=mx%2Bb where m is the slope, b the y-intercept.
Comparing,
m=1


Graphs/322294: x + 2y = -4
how can i graph the equation above
1 solutions

Answer 230752 by Fombitz(13828) About Me  on 2010-07-14 08:52:50 (Show Source):
You can put this solution on YOUR website!
Quickest way is to find the x and y intercepts.
To find the x-intercept, set y=0 and solve for x.
+x%2B2y=-4+
x%2B0=-4
x=-4
(-4,0)
Plot it.
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To find the y-intercept, set x=0 and solve for y.
x%2B2y=-4
0%2B2y=-4
y=-2
(0,-2)
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Plot that point too.
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Now draw the line that goes through both points.
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Problems-with-consecutive-odd-even-integers/322327: the problem involves multiplication, not subtraction. An exponent rule involving multiplying like bases should lead to the correct result.
(a^3 b)(ab)^4
(a^(3^b ) )*(ab)^4=a^3 +^4*b^1 +^4
(a^(3^b ) )*(ab)^4=a^7*b^5
i did multiply what did i do wrong
1 solutions

Answer 230751 by Fombitz(13828) About Me  on 2010-07-14 08:47:48 (Show Source):
You can put this solution on YOUR website!
%28a%5E3b%29%28ab%29%5E4+=a%5E%283%2B4%29b%5E%281%2B4%29
%28a%5E3b%29%28ab%29%5E4+=a%5E7b%5E5
You have the correct answer.


Linear-systems/322298: Solve the following system of linear equations by graphing: -6x+y=20
-4x+y=12
1 solutions

Answer 230750 by Fombitz(13828) About Me  on 2010-07-14 08:45:48 (Show Source):
You can put this solution on YOUR website!
+-6x%2By=20+
y=6x%2B20
Plot it.

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-4x%2By=12+
y=4x%2B12
Plot it too.

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Looks like (-4,-4) is a solution.
Verify using both equations.
-6x%2By=20+
-6%28-4%29%2B%28-4%29=20
24-4=20
20=20
True
-4x%2By=12
-4%28-4%29%2B%28-4%29=12
16-4=12
12=12
True
The ordered pair solves both equations, it's a good solution.


Conjunction/322301: Given p is true, q is true, and r is false, find the truth value of the statement ~p (~q r)
1 solutions

Answer 230749 by Fombitz(13828) About Me  on 2010-07-14 08:39:44 (Show Source):
You can put this solution on YOUR website!
There are no operators between p, q, and r.
Please repost with symbols or explain them in words.


test/322309: -|2-3|+|-2-3| solve
1 solutions

Answer 230748 by Fombitz(13828) About Me  on 2010-07-14 08:38:11 (Show Source):


Matrices-and-determiminant/322329: |-2 -3 -3 3|
|-1 -2 -2 4|
| 1 2 1 1|
|-1 4 4 -2|

1 solutions

Answer 230747 by Fombitz(13828) About Me  on 2010-07-14 08:36:41 (Show Source):
You can put this solution on YOUR website!
What's the question?


Square-cubic-other-roots/322330: The cube root of 600 lies between what two consecutive numbers?
1 solutions

Answer 230746 by Fombitz(13828) About Me  on 2010-07-14 08:33:53 (Show Source):
You can put this solution on YOUR website!
+4%5E3=64+
5%5E3=125
6%5E3=216
7%5E3=343
8%5E3=512
9%5E3=729
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The cube root of 600 is between 8 and 9.