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Average/317542: Solve each system by the addition method. Determine whether
the equations are independent, dependent, or inconsistent
3x – 2.5y = 7.125
2.5x – 3y = 7.3125

1 solutions

Answer 227471 by Fombitz(13828) About Me  on 2010-06-25 23:12:45 (Show Source):
You can put this solution on YOUR website!
1.3x-%285%2F2%29y=57%2F8
2.%285%2F2%29x-3y=117%2F16
Multipy both equations by 16 first.
1.48x-40y=114
2.40x-48x=117
Multiply eq. 1 by (5) and eq. 2 by (-6) and add them,
240x-200y-240x%2B288y=570-702
88y=-132
y=-132%2F88
highlight%28y=-3%2F2%29
Then use either equation to solve for x,
48x-40%28-3%2F2%29=114
48x%2B60=114
48x=54
x=54%2F48
highlight%28x=9%2F8%29
This system has one solution. It's indepedent.


Number-Line/317547: Graph -5/2 and -3 on a number line. Compare the numbers in an inequality form.
1 solutions

Answer 227468 by Fombitz(13828) About Me  on 2010-06-25 23:04:22 (Show Source):


Travel_Word_Problems/317587: An airplane travels 2277km against the wind in 3 hours and 2667km with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?
1 solutions

Answer 227466 by Fombitz(13828) About Me  on 2010-06-25 23:02:28 (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
.
.
Let V be the speed of the plane in still air.
Let W be the wind speed.
.
.
%28V%2BW%293=2667
1.V%2BW=889
.
.
.
%28V-W%293=2277
2.V-W=759
.
.
Add eq. 1 and eq. 2,
V%2BW%2BV-W=889%2B759
2V=1648
highlight%28V=824%29 kph
.
.
824%2BW=889
highlight%28W=65%29 kph


Equations/317577: Simplify. (b^3a^5z^6)/(b^4a)
1 solutions

Answer 227462 by Fombitz(13828) About Me  on 2010-06-25 22:56:50 (Show Source):


Quadratic_Equations/317554: How do you find an equation with the solutions -9 and -7? Also, could you show me the solution and possibly another example of this type of quadratic equation.
1 solutions

Answer 227460 by Fombitz(13828) About Me  on 2010-06-25 22:55:16 (Show Source):
You can put this solution on YOUR website!
A quadratic equation with roots a and b can take the form of,
y=%28x-a%29%28x-b%29.
In your example,
y=%28x-%28-9%29%29%28x-%28-7%29%29=%28x%2B9%29%28x%2B7%29
Similarly,
x=1 and x=0 are roots for
y=x%28x-1%29


Linear-equations/317642: Find a formula for the linear function given below.
The function f has f(9)=-39 and f(16)=-81
f(x)=
i have no clue how to find a formula for the function, if you can help me that would be great!
1 solutions

Answer 227458 by Fombitz(13828) About Me  on 2010-06-25 22:53:05 (Show Source):
You can put this solution on YOUR website!
Linear functions have the form, y=mx%2Bb
Calculate the slope, m,using the two points, (9,-39) and (16,-81)
m=%28y2-y1%29%2F%28x2-x1%29=%28-81-%28-39%29%29%2F%2816-9%29=-42%2F7=-6
Then use either point to find b.
y=-6x%2Bb
-39=-6%289%29%2Bb
-39=-54%2Bb
b=15
.
.
.
highlight%28y=-6x%2B15%29


Parallelograms/317567: Plot the points (1,2) (8,3) (9,6) (2,5), and verify that the points form the polygon (parallelogram)
1 solutions

Answer 227457 by Fombitz(13828) About Me  on 2010-06-25 22:49:23 (Show Source):


Polynomials-and-rational-expressions/317627: what are the restrictions on x ²+2x = 0 ?
thanks!
1 solutions

Answer 227456 by Fombitz(13828) About Me  on 2010-06-25 22:45:25 (Show Source):
You can put this solution on YOUR website!
No restrictions on the domain.


Quadratic_Equations/317553: Can I have help finding the vortex, line of symmetry, maximum/minimum and if the graph opens up or down for the quadratic equation:
f(x)= 3x^2-6x+6
1 solutions

Answer 227417 by Fombitz(13828) About Me  on 2010-06-25 16:25:03 (Show Source):
You can put this solution on YOUR website!
Convert to vertex form, y=a%28x-h%29%5E2%2Bk by completing ths square.
(h,k) is then the vertex.
f%28x%29=3%28x%5E2-2x%29%2B6
f%28x%29=3%28x%5E2-2x%2B1%29%2B6-3
f%28x%29=3%28x-1%29%5E2%2B3
The vertex is (1,3).
The axis of symmetry contains the vertex and is x=1.
The coefficient of x%5E2 term is positive so the parabola opens upwards and the vertex value is the minimum value.
fmin=3
.
.
.


Quadratic_Equations/317549: Quadratic equation: Solve for a, assume all variables represent non negative numbers:
a^2+1^2=g^2
Could you please show the steps of how to solve this equation.
1 solutions

Answer 227416 by Fombitz(13828) About Me  on 2010-06-25 16:19:38 (Show Source):
You can put this solution on YOUR website!
a%5E2%2B1%5E2=g%5E2+
a%5E2=g%5E2-1+
a=sqrt%28g%5E2-1%29 and a=-sqrt%28g%5E2-1%29
However the assumption is that a is not negative,
highlight%28a=sqrt%28g%5E2-1%29%29


expressions/317564: Simplify: [2^3+4(7-3)]/8.
1 solutions

Answer 227415 by Fombitz(13828) About Me  on 2010-06-25 16:17:28 (Show Source):


Angles/317562: In a triangle ABC, angle B is 4 times angle A and angle C is 15 degrees less than 5 times angle A.
Find the size of the angles.
1 solutions

Answer 227414 by Fombitz(13828) About Me  on 2010-06-25 16:15:31 (Show Source):
You can put this solution on YOUR website!
The sum of the angles in a triangle is 180.
A%2BB%2BC=180
A%2B4A%2B%285A-15%29=180
10A-15=180
10A=195
highlight%28+A=19.5%29
.
.
B=4A
highlight%28B=78%29
.
.
C=5A-15
highlight%28+C=82.5%29


Expressions-with-variables/317545: I have two questions I need help working through:
1) Multiply. Write the answer in a + bi form. (5-i)(3+i)
2) Perform the operation. Write the answer in a + bi form. 3 / 1 + i
Can you please help me work through these?
Jerry
jerry@san.rr.com

1 solutions

Answer 227413 by Fombitz(13828) About Me  on 2010-06-25 16:03:46 (Show Source):
You can put this solution on YOUR website!
Use the FOIL method.
%285-i%29%283%2Bi%29=15%2B5i-3i-i%5E2
%285-i%29%283%2Bi%29=%2815%2B1%29%2B2i
%285-i%29%283%2Bi%29=16%2B2i
.
.
.





Polynomials-and-rational-expressions/317552: Solve: s= -1/2gt^2 + vt for g.
1 solutions

Answer 227412 by Fombitz(13828) About Me  on 2010-06-25 15:52:38 (Show Source):


Systems-of-equations/317544: Rewrite without parenthesis and simplify. (7t-6)^2
1 solutions

Answer 227410 by Fombitz(13828) About Me  on 2010-06-25 15:34:42 (Show Source):
You can put this solution on YOUR website!
Use the FOIL method.
%287t-6%29%5E2=%287t-6%29%287t-6%29
%287t-6%29%5E2=49t%5E2-42t-42t%2B36
%287t-6%29%5E2=49t%5E2-84t%2B36


Average/317538: Solve each system by addition
2x = 2 – y
3x + y = -1

1 solutions

Answer 227409 by Fombitz(13828) About Me  on 2010-06-25 15:33:01 (Show Source):
You can put this solution on YOUR website!
1.2x%2By+=+2
2.3x+%2B+y+=+-1
Multiply eq. 1 by (-1) and add to eq. 2,
-2x-y%2B3x%2By=-2-1
highlight%28x=-3%29
Then use either equation to solve for y.3
2%28-3%29%2By=2
-6%2By=2
highlight%28y=8%29


Angles/317540: 1) find angle complement of itself
2) Angle equal to the supplement
3) Angle double to the supplement
Please assist on above query . Thankful if same is answered in rekhaksn@gmail.com

1 solutions

Answer 227408 by Fombitz(13828) About Me  on 2010-06-25 15:16:08 (Show Source):
You can put this solution on YOUR website!
1)A%2BC=90
A=C
A%2BA=90
2A=90
highlight%28A=C=45%29
.
.
.
2)A%2BS=180
A=S
A%2BA=180
2A=180
highlight%28A=S=90%29
.
.
.
3)A%2BS=180
A=2S
2S%2BS=180
3S=180
highlight%28S=60%29
A=2S
highlight%28A=120%29
.
.
.


Average/317539: Solve each system by the addition method. Determine whether
the equations are independent, dependent, or inconsistent
X – y = 3
-6x + 6y = 17

1 solutions

Answer 227406 by Fombitz(13828) About Me  on 2010-06-25 15:12:58 (Show Source):
You can put this solution on YOUR website!
1.x+-y+=+3
2.-6x+%2B+6y+=+17
Multiply eq. 1 by 6 and add to eq. 2,
6x-6y-6x%2B6y=18%2B17
0=35
These lines are parallel.
There is no solution.
Independent, inconsistent.


Average/317533: Solve each system by addition.
x – 2y = -1
-x + 5y = 4

1 solutions

Answer 227405 by Fombitz(13828) About Me  on 2010-06-25 15:08:58 (Show Source):
You can put this solution on YOUR website!
1.x+-2y+=+-1
2.-x+%2B+5y+=+4
Add the equations,
x-2y-x%2B5y=-1%2B4
3y=3
highlight%28y=1%29
Then use either equation,
-x%2B5=4
-x=-1
highlight%28x=1%29


Average/317534: What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2?
1 solutions

Answer 227404 by Fombitz(13828) About Me  on 2010-06-25 15:07:12 (Show Source):
You can put this solution on YOUR website!
A=%288%2B+7%2B+7%2B+5%2B+3%2B+2%2B2%29%2F7=34%2F7
or approximately,
A=4.86


Equations/317531: Simplify your answer. (5u+6x+5)(u+4x+7)
1 solutions

Answer 227403 by Fombitz(13828) About Me  on 2010-06-25 15:05:41 (Show Source):


Travel_Word_Problems/317526: Car A is currently 80 km south of a perpendicular intersection with an east-west road. Car B is on the east-west road, 260 km west of the same intersection. Car A is travelling north at 80 km/h; Car B is travelling east at 100 km/h. Assuming that the cars will continue in a straight line with constant velocities, after 2 hours how fast is the distance between the two cars changing?
1 solutions

Answer 227402 by Fombitz(13828) About Me  on 2010-06-25 15:00:05 (Show Source):
You can put this solution on YOUR website!
Let's call A, the distance from the intersection to car A.
Let's call B, the distance from the intersection to car B.
The distance between the cars is D.
A and B form a right triangle with D as the hypotenuse.
D%5E2=A%5E2%2BB%5E2
If you differentiate with respect to time,
2D%2A%28dD%2Fdt%29=2A%2A%28dA%2Fdt%29%2B2B%2A%28dB%2Fdt%29
After 2 hours,
A=-80%2B80%2A2=80
B=-260%2B100%2A2=-60
dA%2Fdt=80
dB%2Fdt=100
D%5E2=A%5E2%2BB%5E2=80%5E2%2B60%5E2=100%5E2
D=100
.
.
.
2D%2AdD%2Fdt=2A%2AdA%2Fdt%2B2%2AB%2AdB%2Fdt
2%28100%29dD%2Fdt=2%2A80%2A80%2B2%28-60%29%2880%29
200%2AdD%2Fdt=2%2880%29%2880-60%29=3200
dD%2Fdt=3200%2F200
dD%2Fdt=16
.
.
.
The only issue remaining is the sign of the rate of change.
Distance A is growing while Distance B is diminishing (A is growing slower than B).
Distance D is therefore diminishing.
highlight%28dD%2Fdt=-16%29 km/h


Average/317530: A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentration, C(t), in milligrams per liter after t hours is modeled by C(t)=(7t)/(2t^2+3). Estimate the drug's concentration after 4 hours. Round to the nearest hundreth. The choices are 2.69 m/l, 2.55 m/l, 0.94 m/l and 0.80 m/l. I cannot get any of these answers when I try to solve the problem.
Ken
1 solutions

Answer 227393 by Fombitz(13828) About Me  on 2010-06-25 14:37:08 (Show Source):


Equations/317525: (w^3)^-7
1 solutions

Answer 227392 by Fombitz(13828) About Me  on 2010-06-25 14:35:08 (Show Source):


Expressions-with-variables/317492: Solve each system by substitution. Determine whether the
equations are independent, dependent, or inconsistent.
Y = -3x + 19
Y = 2x – 1

1 solutions

Answer 227391 by Fombitz(13828) About Me  on 2010-06-25 14:34:37 (Show Source):
You can put this solution on YOUR website!
1.y+=+-3x+%2B+19
2.y+=+2x+%96+1
Substitute eq. 2 into eq. 1,
2x-1=-3x%2B19
5x=20
highlight%28x=4%29
Now use either equation to solve for y.
y=2x-1=2%284%29-1=8-1
highlight%28y=7%29
One solution, the equations are independent.


Miscellaneous_Word_Problems/317487: A ball loses half of its energy every time it hits a surface. After each bounce, it rises to half the height from which it fell. After how many bounces will it rise to a height of less than 1 metre, if the ball initially falls from a height of l00 metres?
A)5 B)6 C)7 D)8 E)9
1 solutions

Answer 227390 by Fombitz(13828) About Me  on 2010-06-25 14:29:48 (Show Source):
You can put this solution on YOUR website!
h=100%281%2F2%29%5E%28n%29
h%3C1
100%281%2F2%29%5En%3C1
%281%2F2%29%5En%3C0.01
n%3Elog%280.5%2C0.01%29
n%3Elog%280.01%29%2Flog%280.5%29
n%3E%28-2%2F-0.301%29
highlight%28n%3E6.64%29
.
.
.
C) is the correct answer.


expressions/317522: Simplify. Write the answer without parentheses. (b^2/-2a)^3
1 solutions

Answer 227389 by Fombitz(13828) About Me  on 2010-06-25 14:26:41 (Show Source):


Equations/317527: Simplify. Use only positive exponents in your answer.
4z^7u^9 x 3y^-1z^-5 x 4u^-9y
1 solutions

Answer 227387 by Fombitz(13828) About Me  on 2010-06-25 14:24:32 (Show Source):
You can put this solution on YOUR website!
I think you're using "x" to signify multiplication?



%284z%5E7u%5E9%29%283y%5E%28-1%29z%5E%28-5%29%29%284u%5E%28-9%29y%29=48%2Az%5E%282%29%29


Miscellaneous_Word_Problems/317481: Hooke's Law states that the distance a spring strethes varies directly as the weight on the spring. A weight of 67 pounds stretches a spring 6 inches. How far will a weight of 81 pounds stretch the spring? Round to the nearest tenth of an inch. Please show me how to work this!
thank you in advance
cz
1 solutions

Answer 227384 by Fombitz(13828) About Me  on 2010-06-25 14:03:08 (Show Source):
You can put this solution on YOUR website!
+d=kW+
Use your data to determine k.
6=k%2867%29
k=6%2F67
So then the equation is,
d=%286%2F67%29W, when W is in lbs, d in inches.
When W+=+81 lbs, then
d=%286%2F67%29%2A81=486%2F67+or approximately
d=7.25 inches.


Expressions-with-variables/317493: Solve each system by substitution. Determine whether the
equations are independent, dependent, or inconsistent.
Y = -4x – 7
Y = 3x

1 solutions

Answer 227383 by Fombitz(13828) About Me  on 2010-06-25 13:58:27 (Show Source):
You can put this solution on YOUR website!
1.y+=+-4x-7
2.y+=+3x
Substitute eq. 2 into eq. 1,
3x=-4x-7
7x=-7
highlight%28x=-1%29
Then from eq. 2,
y=3%28-1%29
highlight%28y=-3%29
.
.
.
There is one solution, the equations are independent.


Inverses/317501: Find the inverse of the followin matrix, if the inverse exists.
A = [2 1 0]
[0 2 1]
[1 0 -1]
1 solutions

Answer 227380 by Fombitz(13828) About Me  on 2010-06-25 13:56:02 (Show Source):
You can put this solution on YOUR website!
[A]=%28matrix%283%2C3%2C2%2C1%2C0%2C0%2C2%2C1%2C1%2C0%2C-1%29%29
.
.
.
det[A]=-3
.
.
.
[A]inv=-%281%2F3%29%2A%28matrix%283%2C3%2C-2%2C1%2C1%2C1%2C-2%2C-2%2C-2%2C1%2C4%29%29